Von Neumann entropy in a Rashba-Dresselhaus nanodot; dynamical electronic spin-orbit entanglement
Safaiee, Rosa; Golshan, Mohammad Mehdi
2017-06-01
The main purpose of the present article is to report the characteristics of von Neumann entropy, thereby, the electronic hybrid entanglement, in the heterojunction of two semiconductors, with due attention to the Rashba and Dresselhaus spin-orbit interactions. To this end, we cast the von Neumann entropy in terms of spin polarization and compute its time evolution; with a vast span of applications. It is assumed that gate potentials are applied to the heterojunction, providing a two dimensional parabolic confining potential (forming an isotropic nanodot at the junction), as well as means of controlling the spin-orbit couplings. The spin degeneracy is also removed, even at electronic zero momentum, by the presence of an external magnetic field which, in turn, leads to the appearance of Landau states. We then proceed by computing the time evolution of the corresponding von Neumann entropy from a separable (spin-polarized) initial state. The von Neumann entropy, as we show, indicates that electronic hybrid entanglement does occur between spin and two-dimensional Landau levels. Our results also show that von Neumann entropy, as well as the degree of spin-orbit entanglement, periodically collapses and revives. The characteristics of such behavior; period, amplitude, etc., are shown to be determined from the controllable external agents. Moreover, it is demonstrated that the phenomenon of collapse-revivals' in the behavior of von Neumann entropy, equivalently, electronic hybrid entanglement, is accompanied by plateaus (of great importance in quantum computation schemes) whose durations are, again, controlled by the external elements. Along these lines, we also make a comparison between effects of the two spin-orbit couplings on the entanglement (von Neumann entropy) characteristics. The finer details of the electronic hybrid entanglement, which may be easily verified through spin polarization measurements, are also accreted and discussed. The novel results of the present
Quantum entanglement and Kaniadakis entropy
Ourabah, Kamel; Hiba Hamici-Bendimerad, Amel; Tribeche, Mouloud
2015-04-01
A first use of Kaniadakis entropy in the context of quantum information is presented. First we show that (as all smooth and concave trace-form entropies) it exhibits some properties allowing it to be a possible candidate for a generalized quantum information theory. We then use it to determine the degree of entanglement. The influence of the parameter κ, that underpins Kaniadakis entropy, on the mutual information measure is then highlighted. It is shown that Kaniadakis entropy reduces the mutual information, which is always smaller than its usual von Neumann counterpart. Our results may contribute to the ongoing investigation involving generalized entropies in the context of quantum information.
Causality & holographic entanglement entropy
Energy Technology Data Exchange (ETDEWEB)
Headrick, Matthew [Martin Fisher School of Physics, Brandeis University, MS 057, 415 South Street, Waltham, MA 02454 (United States); Hubeny, Veronika E. [Centre for Particle Theory & Department of Mathematical Sciences,Science Laboratories, South Road, Durham DH1 3LE (United Kingdom); Lawrence, Albion [Martin Fisher School of Physics, Brandeis University, MS 057, 415 South Street, Waltham, MA 02454 (United States); Rangamani, Mukund [Centre for Particle Theory & Department of Mathematical Sciences,Science Laboratories, South Road, Durham DH1 3LE (United Kingdom)
2014-12-29
We identify conditions for the entanglement entropy as a function of spatial region to be compatible with causality in an arbitrary relativistic quantum field theory. We then prove that the covariant holographic entanglement entropy prescription (which relates entanglement entropy of a given spatial region on the boundary to the area of a certain extremal surface in the bulk) obeys these conditions, as long as the bulk obeys the null energy condition. While necessary for the validity of the prescription, this consistency requirement is quite nontrivial from the bulk standpoint, and therefore provides important additional evidence for the prescription. In the process, we introduce a codimension-zero bulk region, named the entanglement wedge, naturally associated with the given boundary spatial region. We propose that the entanglement wedge is the most natural bulk region corresponding to the boundary reduced density matrix.
Calibrated entanglement entropy
Bakhmatov, I.; Deger, N. S.; Gutowski, J.; Colgáin, E. Ó.; Yavartanoo, H.
2017-07-01
The Ryu-Takayanagi prescription reduces the problem of calculating entanglement entropy in CFTs to the determination of minimal surfaces in a dual anti-de Sitter geometry. For 3D gravity theories and BTZ black holes, we identify the minimal surfaces as special Lagrangian cycles calibrated by the real part of the holomorphic one-form of a spacelike hypersurface. We show that (generalised) calibrations provide a unified way to determine holographic entanglement entropy from minimal surfaces, which is applicable to warped AdS3 geometries. We briefly discuss generalisations to higher dimensions.
Holographic entanglement entropy
Rangamani, Mukund
2017-01-01
This book provides a comprehensive overview of developments in the field of holographic entanglement entropy. Within the context of the AdS/CFT correspondence, it is shown how quantum entanglement is computed by the area of certain extremal surfaces. The general lessons one can learn from this connection are drawn out for quantum field theories, many-body physics, and quantum gravity. An overview of the necessary background material is provided together with a flavor of the exciting open questions that are currently being discussed. The book is divided into four main parts. In the first part, the concept of entanglement, and methods for computing it, in quantum field theories is reviewed. In the second part, an overview of the AdS/CFT correspondence is given and the holographic entanglement entropy prescription is explained. In the third part, the time-dependence of entanglement entropy in out-of-equilibrium systems, and applications to many body physics are explored using holographic methods. The last part f...
Anyonic entanglement and topological entanglement entropy
Bonderson, Parsa; Knapp, Christina; Patel, Kaushal
2017-10-01
We study the properties of entanglement in two-dimensional topologically ordered phases of matter. Such phases support anyons, quasiparticles with exotic exchange statistics. The emergent nonlocal state spaces of anyonic systems admit a particular form of entanglement that does not exist in conventional quantum mechanical systems. We study this entanglement by adapting standard notions of entropy to anyonic systems. We use the algebraic theory of anyon models (modular tensor categories) to illustrate the nonlocal entanglement structure of anyonic systems. Using this formalism, we present a general method of deriving the universal topological contributions to the entanglement entropy for general system configurations of a topological phase, including surfaces of arbitrary genus, punctures, and quasiparticle content. We analyze a number of examples in detail. Our results recover and extend prior results for anyonic entanglement and the topological entanglement entropy.
Entanglement entropy and duality
Energy Technology Data Exchange (ETDEWEB)
Radičević, Ðorđe [Stanford Institute for Theoretical Physics and Department of Physics, Stanford University, Stanford, CA 94305-4060 (United States)
2016-11-22
Using the algebraic approach to entanglement entropy, we study several dual pairs of lattice theories and show how the entropy is completely preserved across each duality. Our main result is that a maximal algebra of observables in a region typically dualizes to a non-maximal algebra in a dual region. In particular, we show how the usual notion of tracing out external degrees of freedom dualizes to a tracing out coupled to an additional summation over superselection sectors. We briefly comment on possible extensions of our results to more intricate dualities, including holographic ones.
A New Generalization of von Neumann Relative Entropy
Li, Jing; Cao, Huaixin
2017-11-01
In quantum information, von Neumann relative entropy has a great applications and operational interpretations in diverse fields, and von Neumann entropy is an important tool for describing the uncertainty of a quantum state. In this paper, we generalize the classical von Neumann relative entropy S( ρ|| σ) and von Neumann entropy S( ρ) to f-von Neumann relative entropy \\widetilde {S}f(ρ ||σ ) and f-von Neumann entropy \\widetilde {S}f(ρ ) induced by a logarithm-like function f, respectively, and explore their properties. We prove that \\widetilde {S}f(ρ ||σ ) is nonnegative and then prove that \\widetilde {S}f(ρ ) has nonnegativity, boundedness, concavity, subadditivity and so on. Later, we show the stability and continuity of the \\widetilde {S}f(ρ ) with respect to the trace distance. In the case that f( x) = -log x, the resulted entropies reduce the classical von Neumann relative entropy and von Neumann entropy, respectively. This means that our results extend the usual results to a more general setting and then have some potential applications in quantum information.
Entanglement Entropy of Black Holes
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Sergey N. Solodukhin
2011-10-01
Full Text Available The entanglement entropy is a fundamental quantity, which characterizes the correlations between sub-systems in a larger quantum-mechanical system. For two sub-systems separated by a surface the entanglement entropy is proportional to the area of the surface and depends on the UV cutoff, which regulates the short-distance correlations. The geometrical nature of entanglement-entropy calculation is particularly intriguing when applied to black holes when the entangling surface is the black-hole horizon. I review a variety of aspects of this calculation: the useful mathematical tools such as the geometry of spaces with conical singularities and the heat kernel method, the UV divergences in the entropy and their renormalization, the logarithmic terms in the entanglement entropy in four and six dimensions and their relation to the conformal anomalies. The focus in the review is on the systematic use of the conical singularity method. The relations to other known approaches such as ’t Hooft’s brick-wall model and the Euclidean path integral in the optical metric are discussed in detail. The puzzling behavior of the entanglement entropy due to fields, which non-minimally couple to gravity, is emphasized. The holographic description of the entanglement entropy of the black-hole horizon is illustrated on the two- and four-dimensional examples. Finally, I examine the possibility to interpret the Bekenstein-Hawking entropy entirely as the entanglement entropy.
Left-right entanglement entropy of Dp-branes
Energy Technology Data Exchange (ETDEWEB)
Zayas, Leopoldo A. Pando [The Abdus Salam International Centre for Theoretical Physics,Strada Costiera 11, 34014 Trieste (Italy); Michigan Center for Theoretical Physics, Randall Laboratory of Physics,The University of Michigan,450 Church Street, Ann Arbor, MI 48109-1120 (United States); Quiroz, Norma [Departamento de Ciencias Exactas, Tecnología y Metodología,Centro Universitario del Sur, Universidad de Guadalajara,Enrique Arreola Silva 883, C.P. 49000, Cd. Guzmán, Jalisco (Mexico)
2016-11-04
We compute the left-right entanglement entropy for Dp-branes in string theory. We employ the CFT approach to string theory Dp-branes, in particular, its presentation as coherent states of the closed string sector. The entanglement entropy is computed as the von Neumann entropy for a density matrix resulting from integration over the left-moving degrees of freedom. We discuss various crucial ambiguities related to sums over spin structures and argue that different choices capture different physics; however, we advance a themodynamic argument that seems to favor a particular choice of replica. We also consider Dp branes on compact dimensions and verify that the effects of T-duality act covariantly on the Dp brane entanglement entropy. We find that generically the left-right entanglement entropy provides a suitable generalization of boundary entropy and of the D-brane tension.
Linearity of holographic entanglement entropy
National Research Council Canada - National Science Library
Almheiri, Ahmed; Dong, Xi; Swingle, Brian
2017-01-01
We consider the question of whether the leading contribution to the entanglement entropy in holographic CFTs is truly given by the expectation value of a linear operator as is suggested by the Ryu-Takayanagi formula...
Holographic avatars of entanglement entropy
Energy Technology Data Exchange (ETDEWEB)
Barbon, J.L.F. [Instituto de Fisica Teorica IFT UAM/CSIC, Ciudad Universitaria de Cantoblanco 28049, Madrid (Spain)
2009-07-15
This is a rendering of the blackboard lectures at the 2008 Cargese summer school, discussing some elementary facts regarding the application of AdS/CFT techniques to the computation of entanglement entropy in strongly coupled systems. We emphasize the situations where extensivity of the entanglement entropy can be used as a crucial criterion to characterize either nontrivial dynamical phenomena at large length scales, or nonlocality in the short-distance realm.
Entanglement entropy and anomaly inflow
Hughes, Taylor L.; Leigh, Robert G.; Parrikar, Onkar; Ramamurthy, Srinidhi T.
2016-03-01
We study entanglement entropy for parity-violating (time-reversal breaking) quantum field theories on R1 ,2 in the presence of a domain wall between two distinct parity-odd phases. The domain wall hosts a 1 +1 -dimensional conformal field theory (CFT) with nontrivial chiral central charge. Such a CFT possesses gravitational anomalies. It has been shown recently that, as a consequence, its intrinsic entanglement entropy is sensitive to Lorentz boosts around the entangling surface. Here, we show using various methods that the entanglement entropy of the three-dimensional bulk theory is also sensitive to such boosts owing to parity-violating effects, and that the bulk response to a Lorentz boost precisely cancels the contribution coming from the domain wall CFT. We argue that this can naturally be interpreted as entanglement inflow (i.e., inflow of entanglement entropy analogous to the familiar Callan-Harvey effect) between the bulk and the domain-wall, mediated by the low-lying states in the entanglement spectrum. These results can be generally applied to 2 +1 -d topological phases of matter that have edge theories with gravitational anomalies, and provide a precise connection between the gravitational anomaly of the physical edge theory and the low-lying spectrum of the entanglement Hamiltonian.
Entanglement entropy: a perturbative calculation
Energy Technology Data Exchange (ETDEWEB)
Rosenhaus, Vladimir; Smolkin, Michael [Center for Theoretical Physics and Department of Physics,University of California, Berkeley, CA 94720 (United States)
2014-12-31
We provide a framework for a perturbative evaluation of the reduced density matrix. The method is based on a path integral in the analytically continued spacetime. It suggests an alternative to the holographic and ‘standard’ replica trick calculations of entanglement entropy. We implement this method within solvable field theory examples to evaluate leading order corrections induced by small perturbations in the geometry of the background and entangling surface. Our findings are in accord with Solodukhin’s formula for the universal term of entanglement entropy for four dimensional CFTs.
Entanglement entropy in flat holography
Jiang, Hongliang; Song, Wei; Wen, Qiang
2017-07-01
BMS symmetry, which is the asymptotic symmetry at null infinity of flat spacetime, is an important input for flat holography. In this paper, we give a holographic calculation of entanglement entropy and Rényi entropy in three dimensional Einstein gravity and Topologically Massive Gravity. The geometric picture for the entanglement entropy is the length of a spacelike geodesic which is connected to the interval at null infinity by two null geodesics. The spacelike geodesic is the fixed points of replica symmetry, and the null geodesics are along the modular flow. Our strategy is to first reformulate the Rindler method for calculating entanglement entropy in a general setup, and apply it for BMS invariant field theories, and finally extend the calculation to the bulk.
Accuracy of topological entanglement entropy on finite cylinders.
Jiang, Hong-Chen; Singh, Rajiv R P; Balents, Leon
2013-09-06
Topological phases are unique states of matter which support nonlocal excitations which behave as particles with fractional statistics. A universal characterization of gapped topological phases is provided by the topological entanglement entropy (TEE). We study the finite size corrections to the TEE by focusing on systems with a Z2 topological ordered state using density-matrix renormalization group and perturbative series expansions. We find that extrapolations of the TEE based on the Renyi entropies with a Renyi index of n≥2 suffer from much larger finite size corrections than do extrapolations based on the von Neumann entropy. In particular, when the circumference of the cylinder is about ten times the correlation length, the TEE obtained using von Neumann entropy has an error of order 10(-3), while for Renyi entropies it can even exceed 40%. We discuss the relevance of these findings to previous and future searches for topological ordered phases, including quantum spin liquids.
The smooth entropy formalism for von Neumann algebras
Energy Technology Data Exchange (ETDEWEB)
Berta, Mario, E-mail: berta@caltech.edu [Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125 (United States); Furrer, Fabian, E-mail: furrer@eve.phys.s.u-tokyo.ac.jp [Department of Physics, Graduate School of Science, University of Tokyo, Tokyo, Japan and Institute for Theoretical Physics, Leibniz University Hanover, Hanover (Germany); Scholz, Volkher B., E-mail: scholz@phys.ethz.ch [Institute for Theoretical Physics, ETH Zurich, Zurich (Switzerland)
2016-01-15
We discuss information-theoretic concepts on infinite-dimensional quantum systems. In particular, we lift the smooth entropy formalism as introduced by Renner and collaborators for finite-dimensional systems to von Neumann algebras. For the smooth conditional min- and max-entropy, we recover similar characterizing properties and information-theoretic operational interpretations as in the finite-dimensional case. We generalize the entropic uncertainty relation with quantum side information of Tomamichel and Renner and discuss applications to quantum cryptography. In particular, we prove the possibility to perform privacy amplification and classical data compression with quantum side information modeled by a von Neumann algebra.
Entanglement entropy for nonzero genus topologies
Kumar, S. Santhosh; Ghosh, Suman; Shankaranarayanan, S.
2014-03-01
Over the last three decades, entanglement entropy has been obtained for quantum fields propagating in Genus-0 topologies (spheres). For scalar fields propagating in these topologies, it has been shown that the entanglement entropy scales as area. In the last few years, nontrivial topologies are increasingly relevant for different areas. For instance, in describing quantum phases, it has been realized that long-range entangled states are described by topological order. If quantum entanglement can plausibly provide explanation for these, it is then imperative to obtain entanglement entropy in these topologies. In this work, using two different methods, we explicitly show that the entanglement entropy scales as area of the Genus-1 geometry.
Ground state entanglement and geometric entropy in the Kitaev model
Energy Technology Data Exchange (ETDEWEB)
Hamma, Alioscia [Institute for Scientific Interchange (ISI), Villa Gualino, Viale Settimio Severo 65, I-10133 Turin (Italy); Dipartimento di Scienze Fisiche, Universita Federico II, Via Cintia ed. G, I-80126 Napoli (Italy); Ionicioiu, Radu [Institute for Scientific Interchange (ISI), Villa Gualino, Viale Settimio Severo 65, I-10133 Turin (Italy); Zanardi, Paolo [Institute for Scientific Interchange (ISI), Villa Gualino, Viale Settimio Severo 65, I-10133 Turin (Italy)]. E-mail: zanardi@isiosf.isi.it
2005-03-28
We study the entanglement properties of the ground state in Kitaev's model. This is a two-dimensional spin system with a torus topology and non-trivial four-body interactions between its spins. For a generic partition (A,B) of the lattice we calculate analytically the von Neumann entropy of the reduced density matrix {rho}{sub A} in the ground state. We prove that the geometric entropy associated with a region A is linear in the length of its boundary. Moreover, we argue that entanglement can probe the topology of the system and reveal topological order. Finally, no partition has zero entanglement and we find the partition that maximizes the entanglement in the given ground state.
Entanglement Entropy of Black Shells
Arenas, J Robel; 10.1393/ncb/i2010-10922-3
2011-01-01
We present a coherent account of how the entanglement interpretation, thermofield dynamical description and the brick wall formulations (with the ground state correctly identified) fit into a connected and self-consistent explanation of what Bekenstein-Hawking entropy is, and where it is located.
Modular invariance and entanglement entropy
Energy Technology Data Exchange (ETDEWEB)
Lokhande, Sagar Fakirchand; Mukhi, Sunil [Indian Institute of Science Education and Research,Homi Bhabha Rd, Pashan, Pune 411 008 (India)
2015-06-17
We study the Rényi and entanglement entropies for free 2d CFT’s at finite temperature and finite size, with emphasis on their properties under modular transformations of the torus. We address the issue of summing over fermion spin structures in the replica trick, and show that the relation between entanglement and thermal entropy determines two different ways to perform this sum in the limits of small and large interval. Both answers are modular covariant, rather than invariant. Our results are compared with those for a free boson at unit radius in the two limits and complete agreement is found, supporting the view that entanglement respects Bose-Fermi duality. We extend our computations to multiple free Dirac fermions having correlated spin structures, dual to free bosons on the Spin(2d) weight lattice.
Entanglement Entropy in Warped Conformal Field Theories
Castro, A.; Hofman, D.M.; Iqbal, N.
We present a detailed discussion of entanglement entropy in (1+1)-dimensional Warped Conformal Field Theories (WCFTs). We implement the Rindler method to evaluate entanglement and Renyi entropies for a single interval and along the way we interpret our results in terms of twist field correlation
Entanglement entropy in lattice gauge theories
Buividovich, . P. V.
We report on the recent progress in theoretical and numerical studies of entanglement entropy in lattice gauge theories. It is shown that the concept of quantum entanglement between gauge fields in two complementary regions of space can only be introduced if the Hilbert space of physical states is extended in a certain way. In the extended Hilbert space, the entanglement entropy can be partially interpreted as the classical Shannon entropy of the flux of the gauge fields through the boundary between the two regions. Such an extension leads to a reduction procedure which can be easily implemented in lattice simulations by constructing lattices with special topology. This enables us to measure the entanglement entropy in lattice Monte-Carlo simulations. On the simplest example of Z2 lattice gauge theory in (2 + 1) dimensions we demonstrate the relation between entanglement entropy and the classical entropy of the field flux. For SU (2) lattice gauge theory in four dimensions, we find a signature of non-analytic dependence of the entanglement entropy on the size of the region. We also comment on the holographic interpretation of the entanglement entropy.
Entanglement entropies of the quarter filled Hubbard model
Calabrese, Pasquale; Essler, Fabian H. L.; Läuchli, Andreas M.
2014-09-01
We study Rényi and von Neumann entanglement entropies in the ground state of the one dimensional quarter-filled Hubbard model with periodic boundary conditions. We show that they exhibit an unexpected dependence on system size: for L = 4mod 8 the results are in agreement with expectations based on conformal field theory, while for L = 0mod 8 additional contributions arise. We show that these can be understood in terms of a ‘shell-filling’ effect and we develop a conformal field theory approach to calculate the additional contributions to the entropies. These analytic results are found to be in excellent agreement with density matrix renormalization group computations for weak Hubbard interactions. We argue that for larger interactions the presence of a marginal irrelevant operator in the spin sector strongly affects the entropies at the finite sizes accessible numerically and we present an effective way to take them into account.
PURE STATE ENTANGLEMENT ENTROPY IN NONCOMMUTATIVE 2D DE SITTER SPACE TIME
Directory of Open Access Journals (Sweden)
M.F Ghiti
2014-12-01
Full Text Available Using the general modified field equation, a general noncommutative Klein-Gordon equation up to the second order of the noncommutativity parameter is derived in the context of noncommutative 2D De Sitter space-time. Using Bogoliubov coefficients and a special technics called conformal time; the boson-antiboson pair creation density is determined. The Von Neumann boson-antiboson pair creation quantum entanglement entropy is presented to compute the entanglement between the modes created presented.
Entanglement entropy converges to classical entropy around periodic orbits
Energy Technology Data Exchange (ETDEWEB)
Asplund, Curtis T., E-mail: ca2621@columbia.edu [Department of Physics, Columbia University, 538 West 120th Street, New York, NY 10027 (United States); Berenstein, David, E-mail: dberens@physics.ucsb.edu [Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)
2016-03-15
We consider oscillators evolving subject to a periodic driving force that dynamically entangles them, and argue that this gives the linearized evolution around periodic orbits in a general chaotic Hamiltonian dynamical system. We show that the entanglement entropy, after tracing over half of the oscillators, generically asymptotes to linear growth at a rate given by the sum of the positive Lyapunov exponents of the system. These exponents give a classical entropy growth rate, in the sense of Kolmogorov, Sinai and Pesin. We also calculate the dependence of this entropy on linear mixtures of the oscillator Hilbert-space factors, to investigate the dependence of the entanglement entropy on the choice of coarse graining. We find that for almost all choices the asymptotic growth rate is the same.
Directory of Open Access Journals (Sweden)
Chien-Hao Lin
2015-09-01
Full Text Available In the present work, we report an investigation on quantum entanglement in the doubly excited 2s2 1Se resonance state of the positronium negative ion by using highly correlated Hylleraas type wave functions, determined by calculation of the density of resonance states with the stabilization method. Once the resonance wave function is obtained, the spatial (electron-electron orbital entanglement entropies (von Neumann and linear can be quantified using the Schmidt decomposition method. Furthermore, Shannon entropy in position space, a measure for localization (or delocalization for such a doubly excited state, is also calculated.
Generalized entanglement entropy and the Ryu-Takayanagi proposal
Obregón, Octavio
2014-03-01
Non-equilibrium systems with a long-term stationary state that possess as a spatio-temporally fluctuating quality β can be described by a superposition of several statistics, ``superstatistics''. Recently we have proposed entropy(ies) that depend only on the probability distribution pl and which expansion has as a first term the Shannon-entropy. We find the corresponding generalization of the von-Neumann entropy and calculate it for the model considered by Ryu and Takayangi. This results in S =eE (1 -e-EeE)/~ E -E2 2eE + . . . (1) , where E =c/3 .logL/πa sinπl/L , is the usual (2D CFT) entanglement entropy. In this set up the proposed ``area law'' SA =Area/of γA 4GN(d + 2) would need to be modified in order to have agreement with the entropy Eq.(1). It is beyond the scope of this abstract to suggest an expression for SA -modified and its implications for a modified theory of gravity. CONACYT Project 135023.
Holographic entanglement entropy on generic time slices
Kusuki, Yuya; Takayanagi, Tadashi; Umemoto, Koji
2017-06-01
We study the holographic entanglement entropy and mutual information for Lorentz boosted subsystems. In holographic CFTs at zero and finite temperature, we find that the mutual information gets divergent in a universal way when the end points of two subsystems are light-like separated. In Lifshitz and hyperscaling violating geometries dual to non-relativistic theories, we show that the holographic entanglement entropy is not well-defined for Lorentz boosted subsystems in general. This strongly suggests that in non-relativistic theories, we cannot make a real space factorization of the Hilbert space on a generic time slice except the constant time slice, as opposed to relativistic field theories.
Linear response of entanglement entropy from holography
Lokhande, Sagar F.; Oling, Gerben W. J.; Pedraza, Juan F.
2017-10-01
For time-independent excited states in conformal field theories, the entanglement entropy of small subsystems satisfies a `first law'-like relation, in which the change in entanglement is proportional to the energy within the entangling region. Such a law holds for time-dependent scenarios as long as the state is perturbatively close to the vacuum, but is not expected otherwise. In this paper we use holography to investigate the spread of entanglement entropy for unitary evolutions of special physical interest, the so-called global quenches. We model these using AdS-Vaidya geometries. We find that the first law of entanglement is replaced by a linear response relation, in which the energy density takes the role of the source and is integrated against a time-dependent kernel with compact support. For adiabatic quenches the standard first law is recovered, while for rapid quenches the linear response includes an extra term that encodes the process of thermalization. This extra term has properties that resemble a time-dependent `relative entropy'. We propose that this quantity serves as a useful order parameter to characterize far-from-equilibrium excited states. We illustrate our findings with concrete examples, including generic power-law and periodically driven quenches.
Entanglement entropy of critical spin liquids.
Zhang, Yi; Grover, Tarun; Vishwanath, Ashvin
2011-08-05
Quantum spin liquids are phases of matter whose internal structure is not captured by a local order parameter. Particularly intriguing are critical spin liquids, where strongly interacting excitations control low energy properties. Here we calculate their bipartite entanglement entropy that characterizes their quantum structure. In particular we calculate the Renyi entropy S(2) on model wave functions obtained by Gutzwiller projection of a Fermi sea. Although the wave functions are not sign positive, S(2) can be calculated on relatively large systems (>324 spins) using the variational Monte Carlo technique. On the triangular lattice we find that entanglement entropy of the projected Fermi sea state violates the boundary law, with S(2) enhanced by a logarithmic factor. This is an unusual result for a bosonic wave function reflecting the presence of emergent fermions. These techniques can be extended to study a wide class of other phases.
Entanglement entropy in three dimensional gravity
Energy Technology Data Exchange (ETDEWEB)
Maxfield, Henry [Centre for Particle Theory & Department of Mathematical Sciences, Durham University,South Road, Durham DH1 3LE (United Kingdom)
2015-04-07
The Ryu-Takayanagi (RT) and covariant Hubeny-Rangamani-Takayanagi (HRT) proposals relate entanglement entropy in CFTs with holographic duals to the areas of minimal or extremal surfaces in the bulk geometry. We show how, in three dimensional pure gravity, the relevant regulated geodesic lengths can be obtained by writing a spacetime as a quotient of AdS{sub 3}, with the problem reduced to a simple purely algebraic calculation. We explain how this works in both Lorentzian and Euclidean formalisms, before illustrating its use to obtain novel results in a number of examples, including rotating BTZ, the ℝℙ{sup 2} geon, and several wormhole geometries. This includes spatial and temporal dependence of single-interval entanglement entropy, despite these symmetries being broken only behind an event horizon. We also discuss considerations allowing HRT to be derived from analytic continuation of Euclidean computations in certain contexts, and a related class of complexified extremal surfaces.
Holographic entanglement entropy of N =2* renormalization group flow
Pang, Da-Wei
2015-10-01
The N =2* theory is obtained by deforming N =4 supersymmetric Yang-Mills theory with two relevant operators of dimensions 2 and 3. We study the holographic entanglement entropy of the N =2* theory along the whole renormalization group flow. We find that in the UV the holographic entanglement entropy for an arbitrary entangling region receives a universal logarithmic correction, which is related to the relevant operator of dimension 3. This universal behavior can be interpreted on the field theory side by perturbatively evaluating the entanglement entropy of a conformal field theory (CFT) under relevant deformations. In the IR regime, we obtain the large R behavior of the renormalized entanglement entropy for both a strip and a sphere entangling region, where R denotes the size of the entangling region. A term proportional to 1 /R is found for both cases, which can be attributed to the emergent CFT5 in the IR.
Entanglement entropy from the truncated conformal space
Energy Technology Data Exchange (ETDEWEB)
Palmai, T., E-mail: palmai@phy.bme.hu
2016-08-10
A new numerical approach to entanglement entropies of the Rényi type is proposed for one-dimensional quantum field theories. The method extends the truncated conformal spectrum approach and we will demonstrate that it is especially suited to study the crossover from massless to massive behavior when the subsystem size is comparable to the correlation length. We apply it to different deformations of massless free fermions, corresponding to the scaling limit of the Ising model in transverse and longitudinal fields. For massive free fermions the exactly known crossover function is reproduced already in very small system sizes. The new method treats ground states and excited states on the same footing, and the applicability for excited states is illustrated by reproducing Rényi entropies of low-lying states in the transverse field Ising model.
Entanglement entropy from the truncated conformal space
Directory of Open Access Journals (Sweden)
T. Palmai
2016-08-01
Full Text Available A new numerical approach to entanglement entropies of the Rényi type is proposed for one-dimensional quantum field theories. The method extends the truncated conformal spectrum approach and we will demonstrate that it is especially suited to study the crossover from massless to massive behavior when the subsystem size is comparable to the correlation length. We apply it to different deformations of massless free fermions, corresponding to the scaling limit of the Ising model in transverse and longitudinal fields. For massive free fermions the exactly known crossover function is reproduced already in very small system sizes. The new method treats ground states and excited states on the same footing, and the applicability for excited states is illustrated by reproducing Rényi entropies of low-lying states in the transverse field Ising model.
A note on entanglement entropy for topological interfaces in RCFTs
Energy Technology Data Exchange (ETDEWEB)
Gutperle, Michael; Miller, John D. [Department of Physics and Astronomy, University of California Los Angeles,475 Portola Plaza, Los Angeles, CA 90095 (United States)
2016-04-28
In this paper we calculate the entanglement entropy for topological interfaces in rational conformal field theories for the case where the interface lies at the boundary of the entangling interval and for the case where it is located in the center of the entangling interval. We compare the results to each other and also to the recently calculated left/right entropy of a related BCFT. We also comment of the entanglement entropies for topological interfaces for a free compactified boson and Liouville theory.
Entanglement entropy in a holographic p-wave superconductor model
Directory of Open Access Journals (Sweden)
Li-Fang Li
2015-05-01
Full Text Available In a recent paper, arXiv:1309.4877, a holographic p-wave model has been proposed in an Einstein–Maxwell-complex vector field theory with a negative cosmological constant. The model exhibits rich phase structure depending on the mass and the charge of the vector field. We investigate the behavior of the entanglement entropy of dual field theory in this model. When the above two model parameters change, we observe the second order, first order and zeroth order phase transitions from the behavior of the entanglement entropy at some intermediate temperatures. These imply that the entanglement entropy can indicate not only the occurrence of the phase transition, but also the order of the phase transition. The entanglement entropy is indeed a good probe to phase transition. Furthermore, the “retrograde condensation” which is a sub-dominated phase is also reflected on the entanglement entropy.
Finite entanglement entropy and spectral dimension in quantum gravity
Arzano, Michele; Calcagni, Gianluca
2017-12-01
What are the conditions on a field theoretic model leading to a finite entanglement entropy density? We prove two very general results: (1) Ultraviolet finiteness of a theory does not guarantee finiteness of the entropy density; (2) If the spectral dimension of the spatial boundary across which the entropy is calculated is non-negative at all scales, then the entanglement entropy cannot be finite. These conclusions, which we verify in several examples, negatively affect all quantum-gravity models, since their spectral dimension is always positive. Possible ways out are considered, including abandoning the definition of the entanglement entropy in terms of the boundary return probability or admitting an analytic continuation (not a regularization) of the usual definition. In the second case, one can get a finite entanglement entropy density in multi-fractional theories and causal dynamical triangulations.
Entanglement Entropy of AdS Black Holes
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Maurizio Melis
2010-11-01
Full Text Available We review recent progress in understanding the entanglement entropy of gravitational configurations for anti-de Sitter gravity in two and three spacetime dimensions using the AdS/CFT correspondence. We derive simple expressions for the entanglement entropy of two- and three-dimensional black holes. In both cases, the leading term of the entanglement entropy in the large black hole mass expansion reproduces exactly the Bekenstein-Hawking entropy, whereas the subleading term behaves logarithmically. In particular, for the BTZ black hole the leading term of the entanglement entropy can be obtained from the large temperature expansion of the partition function of a broad class of 2D CFTs on the torus.
Entanglement entropy and duality in AdS4
Directory of Open Access Journals (Sweden)
Ioannis Bakas
2015-07-01
Full Text Available Small variations of the entanglement entropy δS and the expectation value of the modular Hamiltonian δE are computed holographically for circular entangling curves in the boundary of AdS4, using gravitational perturbations with general boundary conditions in spherical coordinates. Agreement with the first law of thermodynamics, δS=δE, requires that the line element of the entangling curve remains constant. In this context, we also find a manifestation of electric–magnetic duality for the entanglement entropy and the corresponding modular Hamiltonian, following from the holographic energy–momentum/Cotton tensor duality.
Holographic entanglement entropy for gravitational anomaly in four dimensions
Ali, Tibra; Haque, S. Shajidul; Murugan, Jeff
2017-03-01
We compute the holographic entanglement entropy for the anomaly polynomial Tr R 2 in 3+1 dimensions. Using the perturbative method developed for computing entanglement entropy for quantum field theories, we also compute the parity odd contribution to the entanglement entropy of the dual field theory that comes from a background gravitational Chern-Simons term. We find that, in leading order in the perturbation of the background geometry, the two contributions match except for a logarithmic divergent term on the field theory side. We interpret this extra contribution as encoding our ignorance of the source which creates the perturbation of the geometry.
Entanglement entropy for 2D gauge theories with matters
Aoki, Sinya; Iizuka, Norihiro; Tamaoka, Kotaro; Yokoya, Tsuyoshi
2017-08-01
We investigate the entanglement entropy in 1 +1 -dimensional S U (N ) gauge theories with various matter fields using the lattice regularization. Here we use extended Hilbert space definition for entanglement entropy, which contains three contributions; (1) classical Shannon entropy associated with superselection sector distribution, where sectors are labeled by irreducible representations of boundary penetrating fluxes, (2) logarithm of the dimensions of their representations, which is associated with "color entanglement," and (3) EPR Bell pairs, which give "genuine" entanglement. We explicitly show that entanglement entropies (1) and (2) above indeed appear for various multiple "meson" states in gauge theories with matter fields. Furthermore, we employ transfer matrix formalism for gauge theory with fundamental matter field and analyze its ground state using hopping parameter expansion (HPE), where the hopping parameter K is roughly the inverse square of the mass for the matter. We evaluate the entanglement entropy for the ground state and show that all (1), (2), (3) above appear in the HPE, though the Bell pair part (3) appears in higher order than (1) and (2) do. With these results, we discuss how the ground state entanglement entropy in the continuum limit can be understood from the lattice ground state obtained in the HPE.
Time dependence of entanglement entropy on the fuzzy sphere
Sabella-Garnier, Philippe
2017-08-01
We numerically study the behaviour of entanglement entropy for a free scalar field on the noncommutative ("fuzzy") sphere after a mass quench. It is known that the entanglement entropy before a quench violates the usual area law due to the non-local nature of the theory. By comparing our results to the ordinary sphere, we find results that, despite this non-locality, are compatible with entanglement being spread by ballistic propagation of entangled quasi-particles at a speed no greater than the speed of light. However, we also find that, when the pre-quench mass is much larger than the inverse of the short-distance cutoff of the fuzzy sphere (a regime with no commutative analogue), the entanglement entropy spreads faster than allowed by a local model.
EPR = ER, scattering amplitude and entanglement entropy change
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Seki, Shigenori, E-mail: sigenori@hanyang.ac.kr [Research Institute for Natural Science, Hanyang University, Seoul 133-791 (Korea, Republic of); Sin, Sang-Jin, E-mail: sjsin@hanyang.ac.kr [Department of Physics, Hanyang University, Seoul 133-791 (Korea, Republic of)
2014-07-30
We study the causal structure of the minimal surface of the four-gluon scattering, and find a world-sheet wormhole parametrized by Mandelstam variables, thereby demonstrate the EPR = ER relation for gluon scattering. We also propose that scattering amplitude is the change of the entanglement entropy by generalizing the holographic entanglement entropy of Ryu–Takayanagi to the case where two regions are divided in space–time.
Continuous frequency entanglement: effective finite hilbert space and entropy control
Law; Walmsley; Eberly
2000-06-05
We examine the quantum structure of continuum entanglement and in the context of short-pulse down-conversion we answer the open question of how many of the uncountably many frequency modes contribute effectively to the entanglement. We derive a set of two-photon mode functions that provide an exact, discrete, and effectively finite basis for characterizing pairwise entanglement. Our analysis provides a basis for entropy control in two-photon pulses generated from down-conversion.
Jacobsen, J L; Saleur, H
2008-02-29
We determine exactly the probability distribution of the number N_(c) of valence bonds connecting a subsystem of length L>1 to the rest of the system in the ground state of the XXX antiferromagnetic spin chain. This provides, in particular, the asymptotic behavior of the valence-bond entanglement entropy S_(VB)=N_(c)ln2=4ln2/pi(2)lnL disproving a recent conjecture that this should be related with the von Neumann entropy, and thus equal to 1/3lnL. Our results generalize to the Q-state Potts model.
Measuring entanglement entropy in a quantum many-body system.
Islam, Rajibul; Ma, Ruichao; Preiss, Philipp M; Tai, M Eric; Lukin, Alexander; Rispoli, Matthew; Greiner, Markus
2015-12-03
Entanglement is one of the most intriguing features of quantum mechanics. It describes non-local correlations between quantum objects, and is at the heart of quantum information sciences. Entanglement is now being studied in diverse fields ranging from condensed matter to quantum gravity. However, measuring entanglement remains a challenge. This is especially so in systems of interacting delocalized particles, for which a direct experimental measurement of spatial entanglement has been elusive. Here, we measure entanglement in such a system of itinerant particles using quantum interference of many-body twins. Making use of our single-site-resolved control of ultracold bosonic atoms in optical lattices, we prepare two identical copies of a many-body state and interfere them. This enables us to directly measure quantum purity, Rényi entanglement entropy, and mutual information. These experiments pave the way for using entanglement to characterize quantum phases and dynamics of strongly correlated many-body systems.
Interplay between entanglement and entropy in two-qubit systems
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Mazzola, L; Maniscalco, S; Piilo, J; Suominen, K-A, E-mail: laumaz@utu.f [Department of Physics and Astronomy, University of Turku, FI-20014 Turun yliopisto (Finland)
2010-04-28
We study the exact entanglement and entropy dynamics of two qubits interacting with a common zero-temperature non-Markovian reservoir. It is a commonly held view that entanglement loss due to environmental decoherence is accompanied by loss of purity of the state of the system. We demonstrate that such an intuitive picture does not always apply: the deterioration of entanglement and purity does not necessarily come together; i.e. revivals of entanglement can be accompanied by deterioration of purity. To complete our investigation on entanglement-mixedness interplay we consider the case of initial mixed states and study how the entanglement dynamics and its revivals are related to both the initial purity and the initial entanglement.
Entanglement Entropy in Two-Dimensional String Theory.
Hartnoll, Sean A; Mazenc, Edward A
2015-09-18
To understand an emergent spacetime is to understand the emergence of locality. Entanglement entropy is a powerful diagnostic of locality, because locality leads to a large amount of short distance entanglement. Two-dimensional string theory is among the very simplest instances of an emergent spatial dimension. We compute the entanglement entropy in the large-N matrix quantum mechanics dual to two-dimensional string theory in the semiclassical limit of weak string coupling. We isolate a logarithmically large, but finite, contribution that corresponds to the short distance entanglement of the tachyon field in the emergent spacetime. From the spacetime point of view, the entanglement is regulated by a nonperturbative "graininess" of space.
Holographic entanglement entropy for the most general higher derivative gravity
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Miao, Rong-Xin [Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, 14476 Golm (Germany); Guo, Wu-zhong [Kavli Institute for Theoretical Physics, Key Laboratory of Frontiers in Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190 (China); Yukawa Institute for Theoretical Physics (YITP), Kyoto University, Kyoto 606-8502 (Japan)
2015-08-07
The holographic entanglement entropy for the most general higher derivative gravity is investigated. We find a new type of Wald entropy, which appears on entangling surface without the rotational symmetry and reduces to usual Wald entropy on Killing horizon. Furthermore, we obtain a formal formula of HEE for the most general higher derivative gravity and work it out exactly for some squashed cones. As an important application, we derive HEE for gravitational action with one derivative of the curvature when the extrinsic curvature vanishes. We also study some toy models with non-zero extrinsic curvature. We prove that our formula yields the correct universal term of entanglement entropy for 4d CFTs. Furthermore, we solve the puzzle raised by Hung, Myers and Smolkin that the logarithmic term of entanglement entropy derived from Weyl anomaly of CFTs does not match the holographic result even if the extrinsic curvature vanishes. We find that such mismatch comes from the ‘anomaly of entropy’ of the derivative of curvature. After considering such contributions carefully, we resolve the puzzle successfully. In general, we need to fix the splitting problem for the conical metrics in order to derive the holographic entanglement entropy. We find that, at least for Einstein gravity, the splitting problem can be fixed by using equations of motion. How to derive the splittings for higher derivative gravity is a non-trivial and open question. For simplicity, we ignore the splitting problem in this paper and find that it does not affect our main results.
Comments on universal properties of entanglement entropy and bulk reconstruction
Energy Technology Data Exchange (ETDEWEB)
Haehl, Felix M. [Centre for Particle Theory & Department of Mathematical Sciences, Science Laboratories,South Road, Durham DH1 3LE (United Kingdom)
2015-10-26
Entanglement entropy of holographic CFTs is expected to play a crucial role in the reconstruction of semiclassical bulk gravity. We consider the entanglement entropy of spherical regions of vacuum, which is known to contain universal contributions. After perturbing the CFT with a relevant scalar operator, also the first order change of this quantity gives a universal term which only depends on a discrete set of basic CFT parameters. We show that in gravity this statement corresponds to the uniqueness of the ghost-free graviton propagator on an AdS background geometry. While the gravitational dynamics in this context contains little information about the structure of the bulk theory, there is a discrete set of dimensionless parameters of the theory which determines the entanglement entropy. We argue that for every (not necessarily holographic) CFT, any reasonable gravity model can be used to compute this particular entanglement entropy. We elucidate how this statement is consistent with AdS/CFT and also give various generalizations. On the one hand this illustrates the remarkable usefulness of geometric concepts for understanding entanglement in general CFTs. On the other hand, it provides hints as to what entanglement data can be expected to provide enough information to distinguish, e.g., bulk theories with different higher curvature couplings.
Kawamori, Eiichirou
2017-09-01
A transition from Langmuir wave turbulence (LWT) to coherent Langmuir wave supercontinuum (LWSC) is identified in one-dimensional particle-in-cell simulations as the emergence of a broad frequency band showing significant temporal coherence of a wave field accompanied by a decrease in the von Neumann entropy of classical wave fields. The concept of the von Neumann entropy is utilized for evaluation of the phase-randomizing degree of the classical wave fields, together with introduction of the density matrix of the wave fields. The transition from LWT to LWSC takes place when the energy per one plasmon (one wave quantum) exceeds a certain threshold. The coherent nature, which Langmuir wave systems acquire through the transition, is created by four wave mixings of the plasmons. The emergence of temporal coherence and the decrease in the phase randomization are considered as the development of long-range order and spontaneous symmetry breaking, respectively, indicating that the LWT-LWSC transition is a second order phase transition phenomenon.
Entanglement Entropy of Eigenstates of Quantum Chaotic Hamiltonians.
Vidmar, Lev; Rigol, Marcos
2017-12-01
In quantum statistical mechanics, it is of fundamental interest to understand how close the bipartite entanglement entropy of eigenstates of quantum chaotic Hamiltonians is to maximal. For random pure states in the Hilbert space, the average entanglement entropy is known to be nearly maximal, with a deviation that is, at most, a constant. Here we prove that, in a system that is away from half filling and divided in two equal halves, an upper bound for the average entanglement entropy of random pure states with a fixed particle number and normally distributed real coefficients exhibits a deviation from the maximal value that grows with the square root of the volume of the system. Exact numerical results for highly excited eigenstates of a particle number conserving quantum chaotic model indicate that the bound is saturated with increasing system size.
Universal Entanglement Entropy in 2D Conformal Quantum Critical Points
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Hsu, Benjamin; Mulligan, Michael; Fradkin, Eduardo; Kim, Eun-Ah
2008-12-05
We study the scaling behavior of the entanglement entropy of two dimensional conformal quantum critical systems, i.e. systems with scale invariant wave functions. They include two-dimensional generalized quantum dimer models on bipartite lattices and quantum loop models, as well as the quantum Lifshitz model and related gauge theories. We show that, under quite general conditions, the entanglement entropy of a large and simply connected sub-system of an infinite system with a smooth boundary has a universal finite contribution, as well as scale-invariant terms for special geometries. The universal finite contribution to the entanglement entropy is computable in terms of the properties of the conformal structure of the wave function of these quantum critical systems. The calculation of the universal term reduces to a problem in boundary conformal field theory.
Entanglement entropy and correlations in loop quantum gravity
Feller, Alexandre; Livine, Etera R.
2018-02-01
Black hole entropy is one of the few windows into the quantum aspects of gravitation, and its study over the years has highlighted the holographic nature of gravity. At the non-perturbative level in quantum gravity, promising explanations are being explored in terms of the entanglement entropy between regions of space. In the context of loop quantum gravity, this translates into an analysis of the correlations between the regions of the spin network states defining the quantum state of the geometry of space. In this paper, we explore a class of states, motivated by results in condensed matter physics, satisfying an area law for entanglement entropy and having non-trivial correlations. We highlight that entanglement comes from holonomy operators acting on loops crossing the boundary of the region.
Phase transition of holographic entanglement entropy in massive gravity
Directory of Open Access Journals (Sweden)
Xiao-Xiong Zeng
2016-05-01
Full Text Available The phase structure of holographic entanglement entropy is studied in massive gravity for the quantum systems with finite and infinite volumes, which in the bulk is dual to calculating the minimal surface area for a black hole and black brane respectively. In the entanglement entropy–temperature plane, we find for both the black hole and black brane there is a Van der Waals-like phase transition as the case in thermal entropy–temperature plane. That is, there is a first order phase transition for the small charge and a second order phase transition at the critical charge. For the first order phase transition, the equal area law is checked and for the second order phase transition, the critical exponent of the heat capacity is obtained. All the results show that the phase structure of holographic entanglement entropy is the same as that of thermal entropy regardless of the volume of the spacetime on the boundary.
Entanglement entropy of U (1) quantum spin liquids
Pretko, Michael; Senthil, T.
2016-09-01
We here investigate the entanglement structure of the ground state of a (3 +1 )-dimensional U (1 ) quantum spin liquid, which is described by the deconfined phase of a compact U (1 ) gauge theory. A gapless photon is the only low-energy excitation, with matter existing as deconfined but gapped excitations of the system. It is found that, for a given bipartition of the system, the elements of the entanglement spectrum can be grouped according to the electric flux between the two regions, leading to a useful interpretation of the entanglement spectrum in terms of electric charges living on the boundary. The entanglement spectrum is also given additional structure due to the presence of the gapless photon. Making use of the Bisognano-Wichmann theorem and a local thermal approximation, these two contributions to the entanglement (particle and photon) are recast in terms of boundary and bulk contributions, respectively. Both pieces of the entanglement structure give rise to universal subleading terms (relative to the area law) in the entanglement entropy, which are logarithmic in the system size (logL ), as opposed to the subleading constant term in gapped topologically ordered systems. The photon subleading logarithm arises from the low-energy conformal field theory and is essentially local in character. The particle subleading logarithm arises due to the constraint of closed electric loops in the wave function and is shown to be the natural generalization of topological entanglement entropy to the U (1 ) spin liquid. This contribution to the entanglement entropy can be isolated by means of the Grover-Turner-Vishwanath construction (which generalizes the Kitaev-Preskill scheme to three dimensions).
Entanglement entropy for singular surfaces in hyperscaling violating theories
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Alishahiha, Mohsen [School of Physics, Institute for Research in Fundamental Sciences (IPM),P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of); Astaneh, Amin Faraji [School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM),P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of); Fonda, Piermarco [SISSA and INFN,via Bonomea 265, 34136, Trieste (Italy); Omidi, Farzad [School of Astronomy, Institute for Research in Fundamental Sciences (IPM),P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of)
2015-09-24
We study the holographic entanglement entropy for singular surfaces in theories described holographically by hyperscaling violating backgrounds. We consider singular surfaces consisting of cones or creases in diverse dimensions. The structure of UV divergences of entanglement entropy exhibits new logarithmic terms whose coefficients, being cut-off independent, could be used to define new central charges in the nearly smooth limit. We also show that there is a relation between these central charges and the one appearing in the two-point function of the energy-momentum tensor. Finally we examine how this relation is affected by considering higher-curvature terms in the gravitational action.
Entanglement entropy in Galilean conformal field theories and flat holography.
Bagchi, Arjun; Basu, Rudranil; Grumiller, Daniel; Riegler, Max
2015-03-20
We present the analytical calculation of entanglement entropy for a class of two-dimensional field theories governed by the symmetries of the Galilean conformal algebra, thus providing a rare example of such an exact computation. These field theories are the putative holographic duals to theories of gravity in three-dimensional asymptotically flat spacetimes. We provide a check of our field theory answers by an analysis of geodesics. We also exploit the Chern-Simons formulation of three-dimensional gravity and adapt recent proposals of calculating entanglement entropy by Wilson lines in this context to find an independent confirmation of our results from holography.
Entanglement entropy in excited states of the quantum Lifshitz model
Parker, Daniel E.; Vasseur, Romain; Moore, Joel E.
2017-06-01
We investigate the entanglement properties of an infinite class of excited states in the quantum Lifshitz model (QLM). The presence of a conformal quantum critical point in the QLM makes it unusually tractable for a model above one spatial dimension, enabling the ground state entanglement entropy for an arbitrary domain to be expressed in terms of geometrical and topological quantities. Here we extend this result to excited states and find that the entanglement can be naturally written in terms of quantities which we dub ‘entanglement propagator amplitudes’ (EPAs). EPAs are geometrical probabilities that we explicitly calculate and interpret. A comparison of lattice and continuum results demonstrates that EPAs are universal. This work shows that the QLM is an example of a 2 + 1d field theory where the universal behavior of excited-state entanglement may be computed analytically.
Nodal-line entanglement entropy: Generalized Widom formula from entanglement Hamiltonians
Pretko, Michael
2017-06-01
A system of fermions forming a Fermi surface exhibits a large degree of quantum entanglement, even in the absence of interactions. In particular, the usual case of a codimension one Fermi surface leads to a logarithmic violation of the area law for entanglement entropy as dictated by the Widom formula. We here generalize this formula to the case of arbitrary codimension, which is of particular interest for nodal lines in three dimensions. We first re-derive the standard Widom formula by calculating an entanglement Hamiltonian for Fermi-surface systems, obtained by repurposing a trick commonly applied to relativistic theories. The entanglement Hamiltonian will take a local form in terms of a low-energy patch theory for the Fermi surface, although it is nonlocal with respect to the microscopic fermions. This entanglement Hamiltonian can then be used to derive the entanglement entropy, yielding a result in agreement with the Widom formula. The method is then generalized to arbitrary codimension. For nodal lines, the area law is obeyed, and the magnitude of the coefficient for a particular partition is nonuniversal. However, the coefficient has a universal dependence on the shape and orientation of the nodal line relative to the partitioning surface. By comparing the relative magnitude of the area law for different partitioning cuts, entanglement entropy can be used as a tool for diagnosing the presence and shape of a nodal line in a ground-state wave function.
Holographic entanglement entropy for hollow cones and banana shaped regions
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Dorn, Harald [Institut für Physik und IRIS Adlershof, Humboldt-Universität zu Berlin,Zum Großen Windkanal 6, D-12489 Berlin (Germany)
2016-06-09
We consider banana shaped regions as examples of compact regions, whose boundary has two conical singularities. Their regularised holographic entropy is calculated with all divergent as well as finite terms. The coefficient of the squared logarithmic divergence, also in such a case with internally curved boundary, agrees with that calculated in the literature for infinite circular cones with their internally flat boundary. For the otherwise conformally invariant coefficient of the ordinary logarithmic divergence an anomaly under exceptional conformal transformations is observed. The construction of minimal submanifolds, needed for the entanglement entropy of cones, requires fine-tuning of Cauchy data. Perturbations of such fine-tuning leads to solutions relevant for hollow cones. The divergent parts for the entanglement entropy of hollow cones are calculated. Increasing the difference between the opening angles of their outer and inner boundary, one finds a transition between connected solutions for small differences to disconnected solutions for larger ones.
Entanglement Entropy of Eigenstates of Quadratic Fermionic Hamiltonians.
Vidmar, Lev; Hackl, Lucas; Bianchi, Eugenio; Rigol, Marcos
2017-07-14
In a seminal paper [D. N. Page, Phys. Rev. Lett. 71, 1291 (1993)PRLTAO0031-900710.1103/PhysRevLett.71.1291], Page proved that the average entanglement entropy of subsystems of random pure states is S_{ave}≃lnD_{A}-(1/2)D_{A}^{2}/D for 1≪D_{A}≤sqrt[D], where D_{A} and D are the Hilbert space dimensions of the subsystem and the system, respectively. Hence, typical pure states are (nearly) maximally entangled. We develop tools to compute the average entanglement entropy ⟨S⟩ of all eigenstates of quadratic fermionic Hamiltonians. In particular, we derive exact bounds for the most general translationally invariant models lnD_{A}-(lnD_{A})^{2}/lnD≤⟨S⟩≤lnD_{A}-[1/(2ln2)](lnD_{A})^{2}/lnD. Consequently, we prove that (i) if the subsystem size is a finite fraction of the system size, then ⟨S⟩
Quantum entropy of non-Hermitian entangled systems
Zhang, Shi-Yang; Fang, Mao-Fa; Xu, Lan
2017-10-01
Non-Hermitian Hamiltonians are an effective tool for describing the dynamics of open quantum systems. Previous research shows that the restrictions of conventional quantum mechanics may be violated in the non-Hermitian cases. We studied the entropy of a system of entangled qubits governed by a local non-Hermitian Hamiltonian operator. We find that local non-Hermitian operation influences the entropies of the two subsystems equally and simultaneously. This indicates that non-Hermitian operators possess the property of non-locality, which makes information exchange possible between subsystems. These information exchanges reduce the uncertainty of outcomes associated with two incompatible quantum measurements.
Entanglement Entropy of Quantum Hall Systems with Short Range Disorder
Friedman, Barry; Levine, Greg
2015-03-01
The critical value of the mobility for which the filling 5/2 quantum Hall effect is destroyed by short range disorder is determined from an earlier calculation of the entanglement entropy. The value agrees well with experiment; this agreement is particularly significant in that there are no adjustable parameters. Entanglement entropy vs. disorder strength for filling 1/2, filling 9/2 and filling 7/3 is calculated. For filling 1/2 there is no evidence for a transition for the disorder strengths considered; for filling 9/2 there appears to be a stripe-liquid transition. For filling 7/3 there again appears to be a transition at similar value of the disorder strength as the 5/2 transition but there are stronger finite size effects.
Entanglement entropy of two disjoint blocks in critical Ising models
Alba, Vincenzo; Tagliacozzo, Luca; Calabrese, Pasquale
2009-01-01
We study the scaling of the Renyi and entanglement entropy of two disjoint blocks of critical Ising models, as function of their sizes and separations. We present analytic results based on conformal field theory that are quantitatively checked in numerical simulations of both the quantum spin chain and the classical two dimensional Ising model. Theoretical results match the ones obtained from numerical simulations only after taking properly into account the corrections induced by the finite l...
Entanglement entropy of gapped phase and topological order in three dimensions
Grover, T.; Turner, A.M.; Vishwanath, A.
2011-01-01
We discuss entanglement entropy of gapped ground states in different dimensions, obtained on partitioning space into two regions. For trivial phases without topological order, we argue that the entanglement entropy may be obtained by integrating an ‘entropy density’ over the partition boundary that
Optimal transport and von Neumann entropy in a Heisenberg XXZ chain out of equilibrium.
Salerno, Mario; Popkov, Vladislav
2013-02-01
In this paper we investigate the spin currents and the von Neumann entropy (vNE) of a Heisenberg XXZ chain in contact with twisted XY-boundary magnetic reservoirs by means of the Lindblad master equation. Exact solutions for the stationary reduced density matrix are explicitly constructed for chains of small sizes by using a quantum symmetry operation of the system. These solutions are then used to investigate the optimal transport in the chain in terms of the vNE. As a result we show that the maximal spin current always occurs in the proximity of minima of the vNE and for particular choices of parameters (coupling with reservoirs and anisotropy) it can exactly coincide with them. As the coupling is increased, current reversals may occur and in the limit of strong coupling we show that minima of the vNE tend to zero, meaning that the maximal transport is achieved in this case with states that are very close to pure states.
Relative information entropy in cosmology: The problem of information entanglement
Energy Technology Data Exchange (ETDEWEB)
Czinner, Viktor G., E-mail: czinner.viktor@wigner.mta.hu [Centro de Matemática, Universidade do Minho, Campus de Gualtar, 4710-057 Braga (Portugal); HAS Wigner Research Centre for Physics, H-1525 Budapest, P.O. Box 49 (Hungary); Mena, Filipe C., E-mail: fmena@math.uminho.pt [Centro de Matemática, Universidade do Minho, Campus de Gualtar, 4710-057 Braga (Portugal)
2016-07-10
The necessary information to distinguish a local inhomogeneous mass density field from its spatial average on a compact domain of the universe can be measured by relative information entropy. The Kullback–Leibler (KL) formula arises very naturally in this context, however, it provides a very complicated way to compute the mutual information between spatially separated but causally connected regions of the universe in a realistic, inhomogeneous model. To circumvent this issue, by considering a parametric extension of the KL measure, we develop a simple model to describe the mutual information which is entangled via the gravitational field equations. We show that the Tsallis relative entropy can be a good approximation in the case of small inhomogeneities, and for measuring the independent relative information inside the domain, we propose the Rényi relative entropy formula.
Holographic entanglement entropy close to quantum phase transitions
Energy Technology Data Exchange (ETDEWEB)
Ling, Yi [Institute of High Energy Physics, Chinese Academy of Sciences,Beijing 100049 (China); State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics,Chinese Academy of Sciences, Beijing 100190 (China); Liu, Peng; Niu, Chao [Institute of High Energy Physics, Chinese Academy of Sciences,Beijing 100049 (China); Wu, Jian-Pin [Institute of Gravitation and Cosmology, Department of Physics,School of Mathematics and Physics, Bohai University, Jinzhou 121013 (China); State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics,Chinese Academy of Sciences, Beijing 100190 (China); Xian, Zhuo-Yu [Institute of High Energy Physics, Chinese Academy of Sciences,Beijing 100049 (China)
2016-04-19
We investigate the holographic entanglement entropy (HEE) of a strip geometry in four dimensional Q-lattice backgrounds, which exhibit metal-insulator transitions in the dual field theory. Remarkably, we find that the HEE always displays a peak in the vicinity of the quantum critical points. Our model provides the first direct evidence that the HEE can be used to characterize the quantum phase transition (QPT). We also conjecture that the maximization behavior of HEE at quantum critical points would be universal in general holographic models.
Entanglement entropy and complexity for one-dimensional holographic superconductors
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Mahdi Kord Zangeneh
2017-08-01
Full Text Available Holographic superconductor is an important arena for holography, as it allows concrete calculations to further understand the dictionary between bulk physics and boundary physics. An important quantity of recent interest is the holographic complexity. Conflicting claims had been made in the literature concerning the behavior of holographic complexity during phase transition. We clarify this issue by performing a numerical study on one-dimensional holographic superconductor. Our investigation shows that holographic complexity does not behave in the same way as holographic entanglement entropy. Nevertheless, the universal terms of both quantities are finite and reflect the phase transition at the same critical temperature.
q-entropies and the entanglement dynamics of two-qubits interacting with an environment
Hamadou-Ibrahim, A.; Plastino, A. R.; Plastino, A.
2009-01-01
We investigate entropic aspects of the quantum entanglement dynamics of two-qubits systems interacting with an environment. In particular we consider the detection, based on the violation of classical entropic inequalities involving q-entropies, of the phenomenon of entanglement disappearance and subsequent entanglement revival during the alluded two-qubits' evolution.
Holographic entanglement entropy in superconductor phase transition with dark matter sector
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Yan Peng
2015-11-01
Full Text Available In this paper, we investigate the holographic phase transition with dark matter sector in the AdS black hole background away from the probe limit. We discuss the properties of phases mostly from the holographic topological entanglement entropy of the system. We find the entanglement entropy is a good probe to the critical temperature and the order of the phase transition in the general model. The behaviors of entanglement entropy at large strip size suggest that the area law still holds when including dark matter sector. We also conclude that the holographic topological entanglement entropy is useful in detecting the stability of the phase transitions. Furthermore, we derive the complete diagram of the effects of coupled parameters on the critical temperature through the entanglement entropy and analytical methods.
Entanglement of heavy quark impurities and generalized gravitational entropy
Kumar, S. Prem; Silvani, Dorian
2018-01-01
We calculate the contribution from non-conformal heavy quark sources to the entanglement entropy (EE) of a spherical region in N=4 SUSY Yang-Mills theory. We apply the generalized gravitational entropy method to non-conformal probe D-brane embeddings in AdS5×S5, dual to pointlike impurities exhibiting flows between quarks in large-rank tensor representations and the fundamental representation. For the D5-brane embedding which describes the screening of fundamental quarks in the UV to the antisymmetric tensor representation in the IR, the EE excess decreases non-monotonically towards its IR asymptotic value, tracking the qualitative behaviour of the one-point function of static fields sourced by the impurity. We also examine two classes of D3-brane embeddings, one which connects a symmetric representation source in the UV to fundamental quarks in the IR, and a second category which yields the symmetric representation source on the Coulomb branch. The EE excess for the former increases from the UV to the IR, whilst decreasing and becoming negative for the latter. In all cases, the probe free energy on hyperbolic space with β = 2 π increases monotonically towards the IR, supporting its interpretation as a relative entropy. We identify universal corrections, depending logarithmically on the VEV, for the symmetric representation on the Coulomb branch.
Entanglement entropy of the large $N$ Wilson-Fisher conformal field theory
Whitsitt, Seth; Sachdev, Subir
2016-01-01
We compute the entanglement entropy of the Wilson-Fisher conformal field theory (CFT) in 2+1 dimensions with O($N$) symmetry in the limit of large $N$ for general entanglement geometries. We show that the leading large $N$ result can be obtained from the entanglement entropy of $N$ Gaussian scalar fields with their mass determined by the geometry. For a few geometries, the universal part of the entanglement entropy of the Wilson-Fisher CFT equals that of a CFT of $N$ massless scalar fields. However, in most cases, these CFTs have a distinct universal entanglement entropy even at $N=\\infty$. Notably, for a semi-infinite cylindrical region it scales as $N^0$, in stark contrast to the $N$-linear result of the Gaussian fixed point.
Entanglement entropy of the Q≥4 quantum Potts chain.
Lajkó, Péter; Iglói, Ferenc
2017-01-01
The entanglement entropy S is an indicator of quantum correlations in the ground state of a many-body quantum system. At a second-order quantum phase-transition point in one dimension S generally has a logarithmic singularity. Here we consider quantum spin chains with a first-order quantum phase transition, the prototype being the Q-state quantum Potts chain for Q>4 and calculate S across the transition point. According to numerical, density matrix renormalization group results at the first-order quantum phase transition point S shows a jump, which is expected to vanish for Q→4^{+}. This jump is calculated in leading order as ΔS=lnQ[1-4/Q-2/(QlnQ)+O(1/Q^{2})].
Higher spin entanglement entropy at finite temperature with chemical potential
Energy Technology Data Exchange (ETDEWEB)
Chen, Bin [Department of Physics and State Key Laboratory of Nuclear Physics and Technology,Peking University,Beijing 100871 (China); Collaborative Innovation Center of Quantum Matter,5 Yiheyuan Rd, Beijing 100871 (China); Center for High Energy Physics, Peking University,5 Yiheyuan Rd, Beijing 100871 (China); Beijing Center for Mathematics and Information Interdisciplinary Sciences, Beijing 100048 (China); Wu, Jie-qiang [Department of Physics and State Key Laboratory of Nuclear Physics and Technology,Peking University,Beijing 100871 (China)
2016-07-11
It is generally believed that the semiclassical AdS{sub 3} higher spin gravity could be described by a two dimensional conformal field theory with W-algebra symmetry in the large central charge limit. In this paper, we study the single interval entanglement entropy on the torus in the CFT with a W{sub 3} deformation. More generally we develop the monodromy analysis to compute the two-point function of the light operators under a thermal density matrix with a W{sub 3} chemical potential to the leading order. Holographically we compute the probe action of the Wilson line in the background of the spin-3 black hole with a chemical potential. We find exact agreement.
Holographic entanglement entropy close to crossover/phase transition in strongly coupled systems
Energy Technology Data Exchange (ETDEWEB)
Zhang, Shao-Jun, E-mail: sjzhang84@hotmail.com
2017-03-15
We investigate the behavior of entanglement entropy in the holographic QCD model proposed by Gubser et al. By choosing suitable parameters of the scalar self-interaction potential, this model can exhibit various types of phase structures: crossover, first order and second order phase transitions. We use entanglement entropy to probe the crossover/phase transition, and find that it drops quickly/suddenly when the temperature approaches the critical point which can be seen as a signal of confinement. Moreover, the critical behavior of the entanglement entropy suggests that we may use it to characterize the corresponding phase structures.
Fermion Fields in BTZ Black Hole Space-Time and Entanglement Entropy
Directory of Open Access Journals (Sweden)
Dharm Veer Singh
2015-01-01
Full Text Available We study the entanglement entropy of fermion fields in BTZ black hole space-time and calculate prefactor of the leading and subleading terms and logarithmic divergence term of the entropy using the discretized model. The leading term is the standard Bekenstein-Hawking area law and subleading term corresponds to first quantum corrections in black hole entropy. We also investigate the corrections to entanglement entropy for massive fermion fields in BTZ space-time. The mass term does not affect the area law.
Directory of Open Access Journals (Sweden)
Bernard K. Bonzi
2012-01-01
Full Text Available In this article we study the nonlinear homogeneous Neumann boundary-value problem $$displaylines{ b(u-hbox{div} a(x,abla u=fquad hbox{in } Omegacr a(x,abla u.eta=0 quadhbox{on }partial Omega, }$$ where $Omega$ is a smooth bounded open domain in $mathbb{R}^{N}$, $N geq 3$ and $eta$ the outer unit normal vector on $partialOmega$. We prove the existence and uniqueness of a weak solution for $f in L^{infty}(Omega$ and the existence and uniqueness of an entropy solution for $L^{1}$-data $f$. The functional setting involves Lebesgue and Sobolev spaces with variable exponents.
Directory of Open Access Journals (Sweden)
Weiping Yao
2016-08-01
Full Text Available We study the holographic entanglement entropy in metal/superconductor phase transition with exponential nonlinear electrodynamics (ENE in four and five dimensional spacetimes. We find that the holographic entanglement entropy is powerful tool in studying the properties of the holographic phase transition. For the operator 〈O+〉, we show that the entanglement entropy in 4-dimensional spacetime decreases in metal phase but changes non-monotonously in superconducting phase with the increase of the ENE parameter. Interestingly, the change of the entanglement entropy in 5-dimensional spacetime for the two phases is monotonous as the ENE factor alters. For the operator 〈O−〉, we note that the behavior of entanglement entropy in four and five dimensional spacetimes changes monotonously for the two phases as we tune the strength of the ENE. Furthermore, for both operators, the entanglement entropy in four or five dimensional black hole increases with the increase of the width of the region.
Directory of Open Access Journals (Sweden)
Weiping Yao
2014-12-01
Full Text Available We investigate the holographic entanglement entropy in the metal/superconductor phase transition for the Born–Infeld electrodynamics with full backreaction and note that the entropy is a good probe to study the properties of the phase transition. For the operator 〈O−〉, we find that the entanglement entropy decreases (or increases with the increase of the Born–Infeld parameter b in the metal (or superconducting phase. For the operator 〈O+〉, we observe that, with the increase of the Born–Infeld parameter, the entanglement entropy in the metal phase decreases monotonously but the entropy in the superconducting phase first increases and forms a peak at some threshold bT, then decreases continuously. Moreover, the value of bT becomes smaller as the width of the subsystem A decreases.
Dynamical properties of moving atom–atom entanglement and ...
Indian Academy of Sciences (India)
the atom ensembles [18]. In addition to those, the entanglement of two moving atoms interacting with a single-mode field via a three-photon process is also investigated [19]. The von Neumann entropy measurement is used to measure the amount of entanglement between two moving atoms and a strongly squeezed field ...
Entanglement entropy through conformal interfaces in the 2D Ising model
Brehm, Enrico M
2015-01-01
We consider the entanglement entropy for the 2D Ising model at the conformal fixed point in the presence of interfaces. More precisely, we investigate the situation where the two subsystems are separated by a defect line that preserves conformal invariance. Using the replica trick, we compute the entanglement entropy between the two subsystems. We observe that the entropy, just like in the case without defects, shows a logarithmic scaling behavior with respect to the size of the system. Here, the prefactor of the logarithm depends on the strength of the defect encoded in the transmission coefficient. We also commend on the supersymmetric case.
Ratio of critical quantities related to Hawking temperature–entanglement entropy criticality
Directory of Open Access Journals (Sweden)
Jie-Xiong Mo
2017-10-01
Full Text Available We revisit the Hawking temperature–entanglement entropy criticality of the d-dimensional charged AdS black hole with our attention concentrated on the ratio TcδSEcQc. Comparing the results of this paper with those of the ratio TcScQc, one can find both the similarities and differences. These two ratios are independent of the characteristic length scale l and dependent on the dimension d. These similarities further enhance the relation between the entanglement entropy and the Bekenstein–Hawking entropy. However, the ratio TcδSEcQc also relies on the size of the spherical entangling region. Moreover, these two ratios take different values even under the same choices of parameters. The differences between these two ratios can be attributed to the peculiar property of the entanglement entropy since the research in this paper is far from the regime where the behavior of the entanglement entropy is dominated by the thermal entropy.
An equal area law for holographic entanglement entropy of the AdS-RN black hole
Energy Technology Data Exchange (ETDEWEB)
Nguyen, Phuc H. [Department of Physics, University of Texas at Austin,2515 Speedway, Austin, TX 78712-1192 (United States)
2015-12-21
The Anti-de Sitter-Reissner-Nordström (AdS-RN) black hole in the canonical ensemble undergoes a phase transition similar to the liquid-gas phase transition, i.e. the isocharges on the entropy-temperature plane develop an unstable branch when the charge is smaller than a critical value. It was later discovered that the isocharges on the entanglement entropy-temperature plane also exhibit the same van der Waals-like structure, for spherical entangling regions. In this paper, we present numerical results which sharpen this similarity between entanglement entropy and black hole entropy, by showing that both of these entropies obey Maxwell’s equal area law to an accuracy of around 1%. Moreover, we checked this for a wide range of size of the spherical entangling region, and the equal area law holds independently of the size. We also checked the equal area law for AdS-RN in 4 and 5 dimensions, so the conclusion is not specific to a particular dimension. Finally, we repeated the same procedure for a similar, van der Waals-like transition of the dyonic black hole in AdS in a mixed ensemble (fixed electric potential and fixed magnetic charge), and showed that the equal area law is not valid in this case. Thus the equal area law for entanglement entropy seems to be specific to the AdS-RN background.
Holographic entanglement entropy from 2d CFT: heavy states and local quenches
Energy Technology Data Exchange (ETDEWEB)
Asplund, Curtis T. [Department of Physics, Columbia University,538 West 120th Street, New York, New York, 10027 (United States); Bernamonti, Alice; Galli, Federico [Instituut voor Theoretische Fysica, KU Leuven,Celestijnenlaan 200D, Leuven, B-3001 (Belgium); Hartman, Thomas [Department of Physics, Cornell University,Ithaca, New York, 14853 (United States)
2015-02-26
We consider the entanglement entropy in 2d conformal field theory in a class of excited states produced by the insertion of a heavy local operator. These include both high-energy eigenstates of the Hamiltonian and time-dependent local quenches. We compute the universal contribution from the stress tensor to the single interval Renyi entropies and entanglement entropy, and conjecture that this dominates the answer in theories with a large central charge and a sparse spectrum of low-dimension operators. The resulting entanglement entropies agree precisely with holographic calculations in three-dimensional gravity. High-energy eigenstates are dual to microstates of the BTZ black hole, so the corresponding holographic calculation is a geodesic length in the black hole geometry; agreement between these two answers demonstrates that these individual microstates of holographic CFTs effectively thermalize at the level of the single-interval entanglement entropy. For local quenches, the dual geometry is a highly boosted black hole or conical defect. On the CFT side, the rise in entanglement entropy after a quench is directly related to the monodromy of a Virasoro conformal block.
Bimodal entanglement entropy distribution in the many-body localization transition
Yu, Xiongjie; Luitz, David J.; Clark, Bryan K.
2016-11-01
We introduce the cut-averaged entanglement entropy in disordered periodic spin chains and prove it to be a concave function of subsystem size for individual eigenstates. This allows us to identify the entanglement scaling as a function of subsystem size for individual states in inhomogeneous systems. Using this quantity, we probe the critical region between the many-body localized (MBL) and ergodic phases in finite systems. In the middle of the spectrum, we show evidence for bimodality of the entanglement distribution in the MBL critical region, finding both volume law and area law eigenstates over disorder realizations as well as within single disorder realizations. The disorder-averaged entanglement entropy in this region then scales as a volume law with a coefficient below its thermal value. We discover in the critical region, as we approach the thermodynamic limit, that the cut-averaged entanglement entropy density falls on a one-parameter family of curves. Finally, we also show that without averaging over cuts the slope of the entanglement entropy vs subsystem size can be negative at intermediate and strong disorder, caused by rare localized regions in the system.
Measuring entanglement entropy of a generic many-body system with a quantum switch.
Abanin, Dmitry A; Demler, Eugene
2012-07-13
Entanglement entropy has become an important theoretical concept in condensed matter physics because it provides a unique tool for characterizing quantum mechanical many-body phases and new kinds of quantum order. However, the experimental measurement of entanglement entropy in a many-body system is widely believed to be unfeasible, owing to the nonlocal character of this quantity. Here, we propose a general method to measure the entanglement entropy. The method is based on a quantum switch (a two-level system) coupled to a composite system consisting of several copies of the original many-body system. The state of the switch controls how different parts of the composite system connect to each other. We show that, by studying the dynamics of the quantum switch only, the Rényi entanglement entropy of the many-body system can be extracted. We propose a possible design of the quantum switch, which can be realized in cold atomic systems. Our work provides a route towards testing the scaling of entanglement in critical systems as well as a method for a direct experimental detection of topological order.
On entanglement entropy in non-Abelian lattice gauge theory and 3D quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Delcamp, Clement [Perimeter Institute for Theoretical Physics,31 Caroline Street North, Waterloo, Ontario N2L 2Y5 (Canada); Department of Physics & Astronomy and Guelph-Waterloo Physics Institute, University of Waterloo,200 University Avenue West, Waterloo, Ontario N2L 3G1 (Canada); Dittrich, Bianca; Riello, Aldo [Perimeter Institute for Theoretical Physics,31 Caroline Street North, Waterloo, Ontario N2L 2Y5 (Canada)
2016-11-18
Entanglement entropy is a valuable tool for characterizing the correlation structure of quantum field theories. When applied to gauge theories, subtleties arise which prevent the factorization of the Hilbert space underlying the notion of entanglement entropy. Borrowing techniques from extended topological field theories, we introduce a new definition of entanglement entropy for both Abelian and non-Abelian gauge theories. Being based on the notion of excitations, it provides a completely relational way of defining regions. Therefore, it naturally applies to background independent theories, e.g. gravity, by circumventing the difficulty of specifying the position of the entangling surface. We relate our construction to earlier proposals and argue that it brings these closer to each other. In particular, it yields the non-Abelian analogue of the ‘magnetic centre choice’, as obtained through an extended-Hilbert-space method, but applied to the recently introduced fusion basis for 3D lattice gauge theories. We point out that the different definitions of entanglement entropy can be related to a choice of (squeezed) vacuum state.
Holographic entanglement entropy in two-order insulator/superconductor transitions
Energy Technology Data Exchange (ETDEWEB)
Peng, Yan, E-mail: yanpengphy@163.com; Liu, Guohua
2017-04-10
We study holographic superconductor model with two orders in the five dimensional AdS soliton background away from the probe limit. We disclose properties of phase transitions mostly from the holographic topological entanglement entropy approach. Our results show that the entanglement entropy is useful in investigating transitions in this general model and in particular, there is a new type of first order phase transition in the insulator/superconductor system. We also give some qualitative understanding and obtain the analytical condition for this first order phase transition to occur. As a summary, we draw the complete phase diagram representing effects of the scalar charge on phase transitions.
Holographic entanglement entropy in two-order insulator/superconductor transitions
Directory of Open Access Journals (Sweden)
Yan Peng
2017-04-01
Full Text Available We study holographic superconductor model with two orders in the five dimensional AdS soliton background away from the probe limit. We disclose properties of phase transitions mostly from the holographic topological entanglement entropy approach. Our results show that the entanglement entropy is useful in investigating transitions in this general model and in particular, there is a new type of first order phase transition in the insulator/superconductor system. We also give some qualitative understanding and obtain the analytical condition for this first order phase transition to occur. As a summary, we draw the complete phase diagram representing effects of the scalar charge on phase transitions.
The Effect of Spin Squeezing on the Entanglement Entropy of Kicked Tops
Directory of Open Access Journals (Sweden)
Ernest Teng Siang Ong
2016-04-01
Full Text Available In this paper, we investigate the effects of spin squeezing on two-coupled quantum kicked tops, which have been previously shown to exhibit a quantum signature of chaos in terms of entanglement dynamics. Our results show that initial spin squeezing can lead to an enhancement in both the entanglement rate and the asymptotic entanglement for kicked tops when the initial state resides in the regular islands within a mixed classical phase space. On the other hand, we found a reduction in these two quantities if we were to choose the initial state deep inside the chaotic sea. More importantly, we have uncovered that an application of periodic spin squeezing can yield the maximum attainable entanglement entropy, albeit this is achieved at a reduced entanglement rate.
Energy Technology Data Exchange (ETDEWEB)
Bianchi, Eugenio [Institute for Gravitation and the Cosmos & Physics Department,Penn State, University Park, PA 16802 (United States); Lorenzo, Tommaso De [Università di Pisa, Dipartimento di Fisica “Enrico Fermi”, Largo Bruno Pontecorvo 3, 56127 Pisa (Italy); Smerlak, Matteo [Perimeter Institute for Theoretical Physics,31 Caroline St. N., Waterloo ON N2L 2Y5 (Canada)
2015-06-25
We study the dynamics of vacuum entanglement in the process of gravitational collapse and subsequent black hole evaporation. In the first part of the paper, we introduce a covariant regularization of entanglement entropy tailored to curved spacetimes; this regularization allows us to propose precise definitions for the concepts of black hole “exterior entropy” and “radiation entropy.” For a Vaidya model of collapse we find results consistent with the standard thermodynamic properties of Hawking radiation. In the second part of the paper, we compute the vacuum entanglement entropy of various spherically-symmetric spacetimes of interest, including the nonsingular black hole model of Bardeen, Hayward, Frolov and Rovelli-Vidotto and the “black hole fireworks” model of Haggard-Rovelli. We discuss specifically the role of event and trapping horizons in connection with the behavior of the radiation entropy at future null infinity. We observe in particular that (i) in the presence of an event horizon the radiation entropy diverges at the end of the evaporation process, (ii) in models of nonsingular evaporation (with a trapped region but no event horizon) the generalized second law holds only at early times and is violated in the “purifying” phase, (iii) at late times the radiation entropy can become negative (i.e. the radiation can be less correlated than the vacuum) before going back to zero leading to an up-down-up behavior for the Page curve of a unitarily evaporating black hole.
Sun, Yuan; Zhao, Liu
2016-01-01
The holographic entanglement entropy is studied numerically in (4+1)-dimensional spherically symmetric Gauss-Bonnet AdS black hole spacetime with compact boundary. On the bulk side the black hole spacetime undergoes a van der Waals-like phase transition in the extended phase space, which is reviewed with emphasis on the behavior on the temperature-entropy plane. On the boundary, we calculated the regularized HEE of a disk region of different sizes. We find strong numerical evidence for the failure of equal area law for isobaric curves on the temperature-HEE plane and for the correctness of first law of entanglement entropy, and briefly give an explanation for why the latter may serve as a reason for the former, i.e. the failure of equal area law on the temperature-HEE plane.
Entanglement entropy in (3+1)-d free U(1) gauge theory
Energy Technology Data Exchange (ETDEWEB)
Soni, Ronak M.; Trivedi, Sandip P. [Department of Theoretical Physics, Tata Institute of Fundamental Research,Colaba, Mumbai, 400005 (India)
2017-02-21
We consider the entanglement entropy for a free U(1) theory in 3+1 dimensions in the extended Hilbert space definition. By taking the continuum limit carefully we obtain a replica trick path integral which calculates this entanglement entropy. The path integral is gauge invariant, with a gauge fixing delta function accompanied by a Faddeev -Popov determinant. For a spherical region it follows that the result for the logarithmic term in the entanglement, which is universal, is given by the a anomaly coefficient. We also consider the extractable part of the entanglement, which corresponds to the number of Bell pairs which can be obtained from entanglement distillation or dilution. For a spherical region we show that the coefficient of the logarithmic term for the extractable part is different from the extended Hilbert space result. We argue that the two results will differ in general, and this difference is accounted for by a massless scalar living on the boundary of the region of interest.
Confining gauge theories and holographic entanglement entropy with a magnetic field
Energy Technology Data Exchange (ETDEWEB)
Dudal, David [KU Leuven Campus Kortrijk - KULAK, Department of Physics,Etienne Sabbelaan 51 bus 7800, Kortrijk, 8500 (Belgium); Ghent University, Department of Physics and Astronomy,Krijgslaan 281-S9, Gent, 9000 (Belgium); Mahapatra, Subhash [KU Leuven Campus Kortrijk - KULAK, Department of Physics,Etienne Sabbelaan 51 bus 7800, Kortrijk, 8500 (Belgium)
2017-04-06
We consider the soft wall model for a heuristic holographical modelling of a confining gauge theory and discuss how the introduction of a (constant) magnetic field influences the (de)confinement phase structure. We use the entanglement entropy as a diagnostic tool in terms of the length of an entangling strip geometry. Due to the anisotropy introduced by the magnetic field, we find that the results depend on the orientation of the strip relative to the field. This allows to identify a richer, anisotropic, interplay between confinement and a magnetic field than possibly can be extracted from a more standard order parameter as, for example, the Polyakov loop expectation value.
Entanglement entropy and topological order in resonating valence-bond quantum spin liquids
Wildeboer, Julia; Seidel, Alexander; Melko, Roger G.
2017-03-01
On the triangular and kagome lattices, short-ranged resonating valence-bond wave functions can be sampled without the sign problem using a recently developed Pfaffian Monte Carlo scheme. In this Rapid Communication, we study the Renyi entanglement entropy in these wave functions using a replica-trick method. Using various spatial bipartitions, including the Levin-Wen construction, our finite-size scaled Renyi entropy gives a topological contribution consistent with γ =ln(2 ) , as expected for a gapped Z2 quantum spin liquid. We prove that the mutual statistics is consistent with the toric code anyon model and rule out any other quasiparticle statistics such as the double semion model.
Entanglement entropy of fractional quantum Hall systems with short range disorder
Friedman, B. A.; Levine, G. C.
2015-02-01
The critical value of the mobility for which the ν = 5/2 quantum Hall effect is destroyed by short range disorder is determined from an earlier calculation of the entanglement entropy. The value μ = 2.0 ×106cm2/Vs agrees well with experiment. This agreement is particularly significant in that there are no adjustable parameters. Entanglement entropy versus disorder strength for ν = 1/2, ν = 9/2 and ν = 7/3 is calculated. For ν = 1/2 there is no evidence for a transition for the disorder strengths considered; for ν = 9/2 there appears to be a stripe-liquid transition. For ν = 7/3 there again appears to be a transition at similar value of the disorder strength as the ν = 5/2 transition but there are stronger finite size effects.
Holographic entanglement entropy and the extended phase structure of STU black holes
Energy Technology Data Exchange (ETDEWEB)
Caceres, Elena [Facultad de Ciencias, Universidad de Colima,Bernal Diaz del Castillo 340, Colima (Mexico); Theory Group, Department of Physics, University of Texas,Austin, TX 78712 (United States); Nguyen, Phuc H.; Pedraza, Juan F. [Theory Group, Department of Physics, University of Texas,Austin, TX 78712 (United States); Texas Cosmology Center, University of Texas,Austin, TX 78712 (United States)
2015-09-28
We study the extended thermodynamics, obtained by considering the cosmological constant as a thermodynamic variable, of STU black holes in 4-dimensions in the fixed charge ensemble. The associated phase structure is conjectured to be dual to an RG-flow on the space of field theories. We find that for some charge configurations the phase structure resembles that of a Van der Waals gas: the system exhibits a family of first order phase transitions ending in a second order phase transition at a critical temperature. We calculate the holographic entanglement entropy for several charge configurations and show that for the cases where the gravity background exhibits Van der Waals behavior, the entanglement entropy presents a transition at the same critical temperature. To further characterize the phase transition we calculate appropriate critical exponents and show that they coincide. Thus, the entanglement entropy successfully captures the information of the extended phase structure. Finally, we discuss the physical interpretation of the extended space in terms of the boundary QFT and construct various holographic heat engines dual to STU black holes.
Wen, Xueda; Matsuura, Shunji; Ryu, Shinsei
Topological entanglement entropy of (2+1) dimensional Chern-Simons gauge theories on a general manifold is usually calculated with Witten's method of surgeries and replica trick, in which the spacetime manifold under consideration is very complicated. In this work, we develop an edge theory approach, which greatly simplifies the calculation of topological entanglement entropy of a Chern-Simons theory. Our approach applies to a general manifold with arbitrary genus. The effect of braiding and fusion of Wilson lines can be straightforwardly calculated within our framework. In addition, our method can be generalized to the study of other entanglement measures such as mutual information and entanglement negativity of a topological quantum field theory on a general manifold.
Collapse revival behaviour of the entanglement between V-type ...
Indian Academy of Sciences (India)
In this paper the time evolution of von Neumann entropy, as a measure of entanglement between V-type three-level atoms and the union of a two-mode field, is studied. The atom–field interaction is assumed to occur in a Kerr-type medium with an intensity-dependent coupling. Introducing a Casmir operator whose ...
Collapse revival behaviour of the entanglement between V-type ...
Indian Academy of Sciences (India)
2013-05-02
May 2, 2013 ... Abstract. In this paper the time evolution of von Neumann entropy, as a measure of entanglement between V-type three-level atoms and the union of a two-mode field, is studied. The atom–field interaction is assumed to occur in a Kerr-type medium with an intensity-dependent coupling. Intro- ducing a ...
Spin–momenta entanglement in moving frames: Properties of von ...
Indian Academy of Sciences (India)
disentangled) as seen by moving observers, is used to investigate the properties of von Neumann entropy, as a measure of spin–momentum entanglement. To do so, we partition the total Hilbert space into momentum and spin subspaces so that the ...
The application of asymmetric entangled states in quantum games
Energy Technology Data Exchange (ETDEWEB)
Li Ye [Department of Modern Physics, University of Science and Technology of China, Hefei 230026 (China); Qin Gan [Department of Modern Physics, University of Science and Technology of China, Hefei 230026 (China); Zhou Xianyi [Department of Modern Physics, University of Science and Technology of China, Hefei 230026 (China); Du Jiangfeng [Department of Modern Physics, University of Science and Technology of China, Hefei 230026 (China) and Hefei National Laboratory for Physical Sciences at Microscale, Hefei 230026 (China) and Fachbereich Physik, Universitaet Dortmund, 44221 Dortmund (Germany)]. E-mail: djf@ustc.edu.cn
2006-07-17
We propose a more general entangling operator in the quantization of Cournot model. It is discovered that the total profit at the Nash equilibrium always achieves maximum once the von Neumann entropy tends to infinity. Moreover, the asymmetry introduced here would cause some 'encouraging' and 'suppressing' effect on players' profit.
Entanglement entropy in quantum many-particle systems and their simulation via ansatz states
Energy Technology Data Exchange (ETDEWEB)
Barthel, Thomas
2009-12-10
A main topic of this thesis is the development of efficient numerical methods for the simulation of strongly correlated quantum lattice models. For one-dimensional systems, the density-matrix renormalization-group (DMRG) is such a very successful method. The physical states of interest are approximated within a certain class of ansatz states. These ansatz states are designed in a way that the number of degrees of freedom are prevented from growing exponentially. They are the so-called matrix product states. The first part of the thesis, therefore, provides analytical and numerical analysis of the scaling of quantum nonlocality with the system size or time in different, physically relevant scenarios. For example, the scaling of Renyi entropies and their dependence on boundary conditions is derived within the 1+1-dimensional conformal field theory. Conjectures and analytical indications concerning the properties of entanglement entropy in critical fermionic and bosonic systems are confirmed numerically with high precision. For integrable models in the thermodynamic limit, general preconditions are derived under which subsystems converge to steady states. These steady states are non-thermal and retain information about the initial state. It is shown that the entanglement entropy in such steady states is extensive. For short times, the entanglement entropy grows typically linearly with time, causing an exponential increase in computation costs for the DMRG method. The second part of the thesis focuses on the development and improvement of the abovementioned numerical techniques. The time-dependent DMRG is complemented with an extrapolation technique for the evaluated observables. In this way, the problem of the entropy increase can be circumvented, allowing for a precise determination of spectral functions. The method is demonstrated using the example of the Heisenberg antiferromagnet and results are compared to Bethe-Ansatz data for T=0 and quantum Monte Carlo data
Holographic entanglement entropy of local quenches in AdS4/CFT3: a finite-element approach
Jahn, Alexander; Takayanagi, Tadashi
2018-01-01
Understanding quantum entanglement in interacting higher-dimensional conformal field theories is a challenging task, as direct analytical calculations are often impossible to perform. With holographic entanglement entropy, calculations of entanglement entropy turn into a problem of finding extremal surfaces in a curved spacetime, which we tackle with a numerical finite-element approach. In this paper, we compute the entanglement entropy between two half-spaces resulting from a local quench, triggered by a local operator insertion in a CFT3. We find that the growth of entanglement entropy at early time agrees with the prediction from the first law, as long as the conformal dimension Δ of the local operator is small. Within the limited time region that we can probe numerically, we observe deviations from the first law and a transition to sub-linear growth at later time. In particular, the time dependence at large Δ shows qualitative differences to the simple logarithmic time dependence familiar from the CFT2 case. We hope that our work will motivate further studies, both numerical and analytical, on entanglement entropy in higher dimensions.
Holographic entanglement entropy of mass-deformed Aharony-Bergman-Jafferis-Maldacena theory
Kim, Kyung Kiu; Kwon, O.-Kab; Park, Chanyong; Shin, Hyeonjoon
2014-12-01
We investigate the effect of supersymmetry preserving mass deformation near the UV fixed point represented by the N =6 Aharony-Bergman-Jafferis-Maldacena theory. In the context of the gauge/gravity duality, we analytically calculate the leading small mass effect on the renormalized entanglement entropy (REE) for the most general Lin-Lunin-Maldacena (LLM) geometries in the cases of the strip and disk-shaped entangling surfaces. Our result shows that the properties of the REE in (2 +1 ) dimensions are consistent with those of the c function in (1 +1 ) dimensions. We also discuss the validity of our computations in terms of the curvature behavior of the LLM geometry in the large N limit and the relation between the correlation length and the mass parameter for a special LLM solution.
Deep inelastic scattering as a probe of entanglement
Kharzeev, Dmitri E.; Levin, Eugene M.
2017-06-01
Using nonlinear evolution equations of QCD, we compute the von Neumann entropy of the system of partons resolved by deep inelastic scattering at a given Bjorken x and momentum transfer q2=-Q2. We interpret the result as the entropy of entanglement between the spatial region probed by deep inelastic scattering and the rest of the proton. At small x the relation between the entanglement entropy S (x ) and the parton distribution x G (x ) becomes very simple: S (x )=ln [x G (x )]. In this small x , large rapidity Y regime, all partonic microstates have equal probabilities—the proton is composed by an exponentially large number exp (Δ Y ) of microstates that occur with equal and exponentially small probabilities exp (-Δ Y ), where Δ is defined by x G (x )˜1 /xΔ. For this equipartitioned state, the entanglement entropy is maximal—so at small x , deep inelastic scattering probes a maximally entangled state. We propose the entanglement entropy as an observable that can be studied in deep inelastic scattering. This will require event-by-event measurements of hadronic final states, and would allow to study the transformation of entanglement entropy into the Boltzmann one. We estimate that the proton is represented by the maximally entangled state at x ≤10-3; this kinematic region will be amenable to studies at the Electron Ion Collider.
Entanglement of an Impurity in a Few-Body One-Dimensional Ideal Bose System
DEFF Research Database (Denmark)
García-March, M. A.; Salami Dehkharghani, Amin; Zinner, N. T.
2016-01-01
We study the correlation between an impurity and a small ensemble of bosonic particles in one dimension. Our study analyzes the one-body density matrix and calculates the corresponding von Neumann entanglement entropy as a function of interaction strength between the impurity and the bosons when...
Holographic entanglement entropy in 2D holographic superconductor via AdS3/CFT2
Directory of Open Access Journals (Sweden)
Davood Momeni
2015-07-01
Full Text Available The aim of the present letter is to find the holographic entanglement entropy (HEE in 2D holographic superconductors (HSC. Indeed, it is possible to compute the exact form of this entropy due to an advantage of approximate solutions inside normal and superconducting phases with backreactions. By making the UV and IR limits applied to the integrals, an approximate expression for HEE is obtained. In case the software cannot calculate minimal surface integrals analytically, it offers the possibility to proceed with a numerical evaluation of the corresponding terms. We'll understand how the area formula incorporates the structure of the domain wall approximation. We see that HEE changes linearly with belt angle. It's due to the extensivity of this type of entropy and the emergent of an entropic force. We find that the wider belt angle corresponds to a larger holographic surface. Another remarkable observation is that no “confinement/deconfinement” phase transition point exists in our 2D dual field theory. Furthermore, we observe that the slope of the HEE with respect to the temperature dSdT decreases, thanks to the emergence extra degree of freedom(s in low temperature system. A first order phase transition is detected near the critical point.
Quench action and Rényi entropies in integrable systems
Alba, Vincenzo; Calabrese, Pasquale
2017-09-01
Entropy is a fundamental concept in equilibrium statistical mechanics, yet its origin in the nonequilibrium dynamics of isolated quantum systems is not fully understood. A strong consensus is emerging around the idea that the stationary thermodynamic entropy is the von Neumann entanglement entropy of a large subsystem embedded in an infinite system. Also motivated by cold-atom experiments, here we consider the generalization to Rényi entropies. We develop a new technique to calculate the diagonal Rényi entropy in the quench action formalism. In the spirit of the replica treatment for the entanglement entropy, the diagonal Rényi entropies are generalized free energies evaluated over a thermodynamic macrostate which depends on the Rényi index and, in particular, is not the same state describing von Neumann entropy. The technical reason for this perhaps surprising result is that the evaluation of the moments of the diagonal density matrix shifts the saddle point of the quench action. An interesting consequence is that different Rényi entropies encode information about different regions of the spectrum of the postquench Hamiltonian. Our approach provides a very simple proof of the long-standing issue that, for integrable systems, the diagonal entropy is half of the thermodynamic one and it allows us to generalize this result to the case of arbitrary Rényi entropy.
Evolution of entropy in different types of non-Markovian three-level ...
Indian Academy of Sciences (India)
We solve the Nakajima–Zwanzig (NZ) non-Markovian master equation to study the dynamics of different types of three-level atomic systems interacting with bosonic Lorentzian reservoirs at zero temperature. Von Neumann entropy (S) is used to show the evolution of the degree of entanglement of the subsystems.
Entropy in quantum information theory - Communication and cryptography
DEFF Research Database (Denmark)
Majenz, Christian
Entropies have been immensely useful in information theory. In this Thesis, several results in quantum information theory are collected, most of which use entropy as the main mathematical tool. The rst one concerns the von Neumann entropy. While a direct generalization of the Shannon entropy...... in quantum Shannon theory. While immensely more entanglement-consuming, the variant of port based teleportation is interesting for applications like instantaneous non-local computation and attacks on quantum position-based cryptography. Port based teleportation cannot be implemented perfectly...
Berrada, K.; Al-Rajhi, M. A.
2017-10-01
In this paper, we present a detailed study on the evolution of some measures of nonclassicality and entanglement in the framework of the interaction between a superconducting qubit and deformed bosonic fields under decoherence effect. We compare the dynamical behavior of the different quantum quantifiers by exploiting a large set of nonlinear bosonic fields that are characterized by the deformation parameter. Additionally, we demonstrate how the connection between the appearance of the nonlinearity in the deformed field and the quantum information quantifiers. The time correlation between entropy squeezing, purity, and entanglement is examined in terms of the physical parameters involved in the whole system. Lastly, we explore the exact ranges of the physical parameters in order to combat the decoherence effect and maintain high amount of entanglement during the time evolution.
Lukin, Alexander; Tai, M. Eric; Rispoli, Matthew; Schittko, Robert; Menke, Tim; Kaufman, Adam; Greiner, Markus
2017-04-01
Many-body localized states appear at odds with thermalization as they preserve the memory of their initial state. This behavior has drawn significant theoretical and experimental attention in recent years. Real space localization has been observed on various platforms and under a number of experimental conditions, both with and without interactions. However, the characteristic logarithmic growth of entanglement entropy, which distinguishes the many-body localized state from the non-interacting Anderson localized state, has only been studied in numerics and has yet to be investigated experimentally. We are working towards the phenomenon of localization in one dimensional, interacting Bose-Hubbard system using a quantum gas microscope. With site-resolved addressing and readout, our microscope provides full control over the studied system, in particular it allows us to add disorder into our system using a Fourier plane hologram. This gives us access to both local observables, such as the occupation of individual lattice sites, as well as the entanglement entropy. I will present our progress towards measuring the dependence of the entanglement entropy grows on the disorder strength and interactions in our system. National Science Foundation, Gordon and Betty Moore Foundation's EPiQS Initiative, Air Force Office of Scientific Research MURI program, NSF Graduate Research Fellowship Program (MNR).
Holographic entanglement entropies for Schwarzschild and Reisner-Nordstr\\"om spacetimes
Sun, Yuan
2016-01-01
The holographic entanglement entropies (HEE) associated with four dimensional Schwarzschild and Reisner-Nordstr\\"om spacetimes are investigated. Unlike the cases of asymptotically AdS spacetimes for which the boundaries are always taken at (timelike) conformal infinities, we take the boundaries at either large but finite radial coordinate (far boundary) or very close to the black hole event horizons (near horizon boundary). The reason for such choices is that such boundaries are similar to the conformal infinity of AdS spacetime in that they are all timelike, so that there may be some hope to define dual systems with ordinary time evolution on such boundaries. Our results indicate that, in the case of far boundaries, the leading order contribution to the HEEs come from the background Minkowski spacetime, however, the next to leading order contribution which arises from the presence of the black holes is always proportional to the black hole mass, which constitutes a version of the first law of the HEE for asy...
López-Rosa, S.; Esquivel, R. O.; Plastino, A. R.; Dehesa, J. S.
2015-09-01
In this work we have performed state-of-the-art configuration-interaction (CI) calculations to determine the linear and von Neumann entanglement entropies for the helium-like systems with varying nuclear charge Z in the range 1≤slant Z≤slant 10. The focus of the work resides on determining accurate entanglement values for 2-electron systems with the lowest computational cost through compact CI-wave functions. Our entanglement results for the helium atom fully agree with the results obtained with higher quality wave functions of the Kinoshita type (Dehesa [5]). We find that the correlation energy is linearly related to the entanglement measures associated with the linear and von Neumann entropies of the single-particle reduced density matrizes, which sheds new light on the physical implications of entanglement in helium-like systems. Moreover, we report CI-wave-function-based benchmark results for the entanglement values for all members of the helium isoelectronic series with an accuracy similar to that of Kinoshita-type wave functions. Finally, we give parametric expressions of the linear and von Neumann entanglement measures for two-electron systems as Z varies from 1 to 10.
Entanglement Dynamics in a Model Tripartite Quantum System
Laha, Pradip; Sudarsan, B.; Lakshmibala, S.; Balakrishnan, V.
2016-09-01
A Λ-type atom interacting with two radiation fields exhibits electromagnetically induced transparency and other nonclassical effects that appear in the entanglement dynamics of the atomic subsystem and in appropriate field observables. Both EIT and field-atom entanglement are important for quantum information processing. We investigate the roles played by specific initial field states, detuning parameters, field nonlinearities and intensity-dependent field-atom couplings on EIT and the entanglement between subsystems. Departure from coherence of the initial field states produces significant effects. We investigate these aspects in a model that exhibits the salient features of entangled tripartite systems. For initial photon-added coherent states, collapses and revivals of the atomic subsystem von Neumann entropy appear as the intensity parameter varies over a narrow range of values. These features could be useful in enabling entanglement.
Bidzhiev, Kemal; Misguich, Grégoire
2017-11-01
We investigate the out-of-equilibrium properties of a simple quantum impurity model, the interacting resonant level model. We focus on the scaling regime, where the bandwidth of the fermions in the leads is larger than all the other energies, so that the lattice and the continuum versions of the model become equivalent. Using time-dependent density matrix renormalization group simulations initialized with states having different densities in the two leads, we extend the results of Boulat, Saleur, and Schmitteckert [Phys. Rev. Lett. 101, 140601 (2008), 10.1103/PhysRevLett.101.140601] concerning the current-voltage (I -V ) curves, for several values of the interaction strength U . We estimate numerically the Kondo scale TB and the exponent b (U ) associated to the tunneling of the fermions from the leads to the dot. Next, we analyze the quantum entanglement properties of the steady states. We focus in particular on the entropy rate α , describing the linear growth with time of the bipartite entanglement in the system. We show that, as for the current, α /TB is described by some function of U and of the rescaled bias V /TB . Finally, the spatial structure of the entropy profiles is discussed.
On shape dependence of holographic entanglement entropy in AdS{sub 4}/CFT{sub 3}
Energy Technology Data Exchange (ETDEWEB)
Fonda, Piermarco [SISSA and INFN,via Bonomea 265, 34136, Trieste (Italy); Seminara, Domenico [Dipartimento di Fisica, Università di Firenze and INFN,via G. Sansone 1, 50019, Sesto Fiorentino (Italy); Tonni, Erik [SISSA and INFN,via Bonomea 265, 34136, Trieste (Italy)
2015-12-09
We study the finite term of the holographic entanglement entropy of finite domains with smooth shapes and for four dimensional gravitational backgrounds. Analytic expressions depending on the unit vectors normal to the minimal area surface are obtained for both stationary and time dependent spacetimes. The special cases of AdS{sub 4}, asymptotically AdS{sub 4} black holes, domain wall geometries and Vaidya-AdS backgrounds have been analysed explicitly. When the bulk spacetime is AdS{sub 4}, the finite term is the Willmore energy of the minimal area surface viewed as a submanifold of the three dimensional flat Euclidean space. For the static spacetimes, some numerical checks involving spatial regions delimited by ellipses and non convex domains have been performed. In the case of AdS{sub 4}, the infinite wedge has been also considered, recovering the known analytic formula for the coefficient of the logarithmic divergence.
Entanglement and Coherence in Quantum State Merging.
Streltsov, A; Chitambar, E; Rana, S; Bera, M N; Winter, A; Lewenstein, M
2016-06-17
Understanding the resource consumption in distributed scenarios is one of the main goals of quantum information theory. A prominent example for such a scenario is the task of quantum state merging, where two parties aim to merge their tripartite quantum state parts. In standard quantum state merging, entanglement is considered to be an expensive resource, while local quantum operations can be performed at no additional cost. However, recent developments show that some local operations could be more expensive than others: it is reasonable to distinguish between local incoherent operations and local operations which can create coherence. This idea leads us to the task of incoherent quantum state merging, where one of the parties has free access to local incoherent operations only. In this case the resources of the process are quantified by pairs of entanglement and coherence. Here, we develop tools for studying this process and apply them to several relevant scenarios. While quantum state merging can lead to a gain of entanglement, our results imply that no merging procedure can gain entanglement and coherence at the same time. We also provide a general lower bound on the entanglement-coherence sum and show that the bound is tight for all pure states. Our results also lead to an incoherent version of Schumacher compression: in this case the compression rate is equal to the von Neumann entropy of the diagonal elements of the corresponding quantum state.
Quantum entanglement in the one-dimensional spin-orbital SU (2 )⊗XXZ model
You, Wen-Long; Horsch, Peter; Oleś, Andrzej M.
2015-08-01
We investigate the phase diagram and the spin-orbital entanglement of a one-dimensional SU (2 )⊗XXZ model with SU(2) spin exchange and anisotropic XXZ orbital exchange interactions and negative exchange coupling constant. As a unique feature, the spin-orbital entanglement entropy in the entangled ground states increases here linearly with system size. In the case of Ising orbital interactions, we identify an emergent phase with long-range spin-singlet dimer correlations triggered by a quadrupling of correlations in the orbital sector. The peculiar translational-invariant spin-singlet dimer phase has finite von Neumann entanglement entropy and survives when orbital quantum fluctuations are included. It even persists in the isotropic SU (2 )⊗SU (2) limit. Surprisingly, for finite transverse orbital coupling, the long-range spin-singlet correlations also coexist in the antiferromagnetic spin and alternating orbital phase making this phase also unconventional. Moreover, we also find a complementary orbital singlet phase that exists in the isotropic case but does not extend to the Ising limit. The nature of entanglement appears essentially different from that found in the frequently discussed model with positive coupling. Furthermore, we investigate the collective spin and orbital wave excitations of the disentangled ferromagnetic-spin/ferro-orbital ground state and explore the continuum of spin-orbital excitations. Interestingly, one finds among the latter excitations two modes of exciton bound states. Their spin-orbital correlations differ from the remaining continuum states and exhibit logarithmic scaling of the von Neumann entropy with increasing system size. We demonstrate that spin-orbital excitons can be experimentally explored using resonant inelastic x-ray scattering, where the strongly entangled exciton states can be easily distinguished from the spin-orbital continuum.
Thermalization of entanglement
Zhang, Liangsheng; Kim, Hyungwon; Huse, David A.
2015-06-01
We explore the dynamics of the entanglement entropy near equilibrium in highly entangled pure states of two quantum-chaotic spin chains undergoing unitary time evolution. We examine the relaxation to equilibrium from initial states with either less or more entanglement entropy than the equilibrium value, as well as the dynamics of the spontaneous fluctuations of the entanglement that occur in equilibrium. For the spin chain with a time-independent Hamiltonian and thus an extensive conserved energy, we find slow relaxation of the entanglement entropy near equilibration. Such slow relaxation is absent in a Floquet spin chain with a Hamiltonian that is periodic in time and thus has no local conservation law. Therefore, we argue that slow diffusive energy transport is responsible for the slow relaxation of the entanglement entropy in the Hamiltonian system.
Nonequilibrium thermal entanglement
Quiroga, Luis; Rodriguez, Ferney J.; Ramirez, Maria E.; Paris, Roberto
2006-01-01
Results on heat current, entropy production rate and entanglement are reported for a quantum system coupled to two different temperature heat reservoirs. By applying a temperature gradient, different quantum states can be found with exactly the same amount of entanglement but different purity degrees and heat currents. Furthermore, a nonequilibrium enhancement-suppression transition behavior of the entanglement is identified.
Energy Technology Data Exchange (ETDEWEB)
Ma, Chen-Te [Department of Physics and Center for Theoretical Sciences, National Taiwan University, Taipei 10617 (China)
2016-01-13
Entanglement is a physical phenomenon that each state cannot be described individually. Entanglement entropy gives quantitative understanding to the entanglement. We use decomposition of the Hilbert space to discuss properties of the entanglement. Therefore, partial trace operator becomes important to define the reduced density matrix from different centers, which commutes with all elements in the Hilbert space, corresponding to different entanglement choices or different observations on entangling surface. Entanglement entropy is expected to satisfy the strong subadditivity. We discuss decomposition of the Hilbert space for the strong subadditivity and other related inequalities. The entanglement entropy with centers can be computed from the Hamitonian formulations systematically, provided that we know wavefunctional. In the Hamitonian formulation, it is easier to obtain symmetry structure. We consider massless p-form theory as an example. The massless p-form theory in (2p+2)-dimensions has global symmetry, similar to the electric-magnetic duality, connecting centers in ground state. This defines a duality structure in centers. Because it is hard to exactly compute the entanglement entropy from partial trace operator, we propose the Lagrangian formulation from the Hamitonian formulation to compute the entanglement entropy with centers. From the Lagrangian method and saddle point approximation, the codimension two surface term (leading order) in the Einstein gravity theory or holographic entanglement entropy should correspond to non-tensor product decomposition (center is not identity). Finally, we compute the entanglement entropy of the SU(N) Yang-Mills lattice gauge theory in the fundamental representation using the strong coupling expansion in the extended lattice model to obtain spatial area term in total dimensions larger than two for N>1.
Ma, Chen-Te
2016-01-01
Entanglement is a physical phenomenon that each state cannot be described individually. Entanglement entropy gives quantitative understanding to the entanglement. We use decomposition of the Hilbert space to discuss properties of the entanglement. Therefore, partial trace operator becomes important to define the reduced density matrix from different centers, which commutes with all elements in the Hilbert space, corresponding to different entanglement choices or different observations on entangling surface. Entanglement entropy is expected to satisfy the strong subadditivity. We discuss decomposition of the Hilbert space for the strong subadditivity and other related inequalities. The entanglement entropy with centers can be computed from the Hamitonian formulations systematically, provided that we know wavefunctional. In the Hamitonian formulation, it is easier to obtain symmetry structure. We consider massless p-form theory as an example. The massless p-form theory in (2 p + 2)-dimensions has global symmetry, similar to the electric-magnetic duality, connecting centers in ground state. This defines a duality structure in centers. Because it is hard to exactly compute the entanglement entropy from partial trace operator, we propose the Lagrangian formulation from the Hamitonian formulation to compute the entanglement entropy with centers. From the Lagrangian method and saddle point approximation, the codimension two surface term (leading order) in the Einstein gravity theory or holographic entanglement entropy should correspond to non-tensor product decomposition (center is not identity). Finally, we compute the entanglement entropy of the SU( N) Yang-Mills lattice gauge theory in the fundamental representation using the strong coupling expansion in the extended lattice model to obtain spatial area term in total dimensions larger than two for N > 1.
Bródy, F
1995-01-01
After three decades since the first nearly complete edition of John von Neumann's papers, this book is a valuable selection of those papers and excerpts of his books that are most characteristic of his activity, and reveal that of his continuous influence.The results receiving the 1994 Nobel Prizes in economy deeply rooted in Neumann's game theory are only minor traces of his exceptionally broad spectrum of creativity and stimulation.The book is organized by the specific subjects-quantum mechanics, ergodic theory, operator algebra, hydrodynamics, economics, computers, science and society. In a
Quantum entanglement between electronic and vibrational degrees of freedom in molecules.
McKemmish, Laura K; McKenzie, Ross H; Hush, Noel S; Reimers, Jeffrey R
2011-12-28
We consider the quantum entanglement of the electronic and vibrational degrees of freedom in molecules with tendencies towards double welled potentials. In these bipartite systems, the von Neumann entropy of the reduced density matrix is used to quantify the electron-vibration entanglement for the lowest two vibronic wavefunctions obtained from a model Hamiltonian based on coupled harmonic diabatic potential-energy surfaces. Significant entanglement is found only in the region in which the ground vibronic state contains a density profile that is bimodal (i.e., contains two separate local maxima). However, in this region two distinct types of density and entanglement profiles are found: one type arises purely from the degeneracy of energy levels in the two potential wells and is destroyed by slight asymmetry, while the other arises through strong interactions between the diabatic levels of each well and is relatively insensitive to asymmetry. These two distinct types are termed fragile degeneracy-induced entanglement and persistent entanglement, respectively. Six classic molecular systems describable by two diabatic states are considered: ammonia, benzene, BNB, pyridine excited triplet states, the Creutz-Taube ion, and the radical cation of the "special pair" of chlorophylls involved in photosynthesis. These chemically diverse systems are all treated using the same general formalism and the nature of the entanglement that they embody is elucidated.
General polygamy inequality of multi-party quantum entanglement
Kim, Jeong San
2012-01-01
Using entanglement of assistance, we establish a general polygamy inequality of multi-party entanglement in arbitrary dimensional quantum systems. For multi-party closed quantum systems, we relate our result with the monogamy of entanglement to show that the entropy of entanglement is an universal entanglement measure that bounds both monogamy and polygamy of multi-party quantum entanglement.
Entanglement of mixed quantum states for qubits and qudit in double photoionization of atoms
Energy Technology Data Exchange (ETDEWEB)
Chakraborty, M., E-mail: bminakshi@yahoo.com [Department of Physics, Asansol Girls’ College, Asansol 713304 (India); Sen, S. [Department of Physics, Triveni Devi Bhalotia College, Raniganj 713347 (India)
2015-08-15
Highlights: • We study tripartite entanglement between two electronic qubits and an ionic qudit. • We study bipartite entanglement between any two subsystems of a tripartite system. • We have presented a quantitative application of entangled properties in Neon atom. - Abstract: Quantum entanglement and its paradoxical properties are genuine physical resources for various quantum information tasks like quantum teleportation, quantum cryptography, and quantum computer technology. The physical characteristic of the entanglement of quantum-mechanical states, both for pure and mixed, has been recognized as a central resource in various aspects of quantum information processing. In this article, we study the bipartite entanglement of one electronic qubit along with the ionic qudit and also entanglement between two electronic qubits. The tripartite entanglement properties also have been investigated between two electronic qubits and an ionic qudit. All these studies have been done for the single-step double photoionization from an atom following the absorption of a single photon without observing spin orbit interaction. The dimension of the Hilbert space of the qudit depends upon the electronic state of the residual photoion A{sup 2+}. In absence of SOI, when Russell–Saunders coupling (L–S coupling) is applicable, dimension of the qudit is equal to the spin multiplicity of A{sup 2+}. For estimations of entanglement and mixedness, we consider the Peres–Horodecki condition, concurrence, entanglement of formation, negativity, linear and von Neumann entropies. In case of L–S coupling, all the properties of a qubit–qudit system can be predicted merely with the knowledge of the spins of the target atom and the residual photoion.
Entanglement Thermalization and Local Conservation Laws
Zhang, Liangsheng; Kim, Hyungwon; Huse, David
2015-03-01
We study the thermalization of entanglement entropy in one-dimensional spin chains under the unitary dynamics of a nonintegrable Hamiltonian or periodic driving by Floquet operators. Using full diagonalization of the Hamiltonian matrix and the Floquet operators, we analyze the time evolution of entanglement entropy starting from various initial conditions, including initial states with entanglement in excess of the thermal equilibrium value. It is found that the thermalization of entanglement entropy is coupled to local conservation laws when approaching equilibrium, and the absence of conservation laws in the Floquet system allows the entanglement entropy to thermalize more rapidly than it does in the corresponding Hamiltonian.
The Critical Point Entanglement and Chaos in the Dicke Model
Directory of Open Access Journals (Sweden)
Lina Bao
2015-07-01
Full Text Available Ground state properties and level statistics of the Dicke model for a finite number of atoms are investigated based on a progressive diagonalization scheme (PDS. Particle number statistics, the entanglement measure and the Shannon information entropy at the resonance point in cases with a finite number of atoms as functions of the coupling parameter are calculated. It is shown that the entanglement measure defined in terms of the normalized von Neumann entropy of the reduced density matrix of the atoms reaches its maximum value at the critical point of the quantum phase transition where the system is most chaotic. Noticeable change in the Shannon information entropy near or at the critical point of the quantum phase transition is also observed. In addition, the quantum phase transition may be observed not only in the ground state mean photon number and the ground state atomic inversion as shown previously, but also in fluctuations of these two quantities in the ground state, especially in the atomic inversion fluctuation.
Universal quantum computation with little entanglement.
Van den Nest, Maarten
2013-02-08
We show that universal quantum computation can be achieved in the standard pure-state circuit model while the entanglement entropy of every bipartition is small in each step of the computation. The entanglement entropy required for large-scale quantum computation even tends to zero. Moreover we show that the same conclusion applies to many entanglement measures commonly used in the literature. This includes e.g., the geometric measure, localizable entanglement, multipartite concurrence, squashed entanglement, witness-based measures, and more generally any entanglement measure which is continuous in a certain natural sense. These results demonstrate that many entanglement measures are unsuitable tools to assess the power of quantum computers.
Interpolatability distinguishes LOCC from separable von Neumann measurements
Energy Technology Data Exchange (ETDEWEB)
Childs, Andrew M.; Leung, Debbie; Mančinska, Laura [Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario N2L 3G1 (Canada); Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1 (Canada); Ozols, Maris [Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario N2L 3G1 (Canada); Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1 (Canada); IBM TJ Watson Research Center, Yorktown Heights, New York 10598 (United States)
2013-11-15
Local operations with classical communication (LOCC) and separable operations are two classes of quantum operations that play key roles in the study of quantum entanglement. Separable operations are strictly more powerful than LOCC, but no simple explanation of this phenomenon is known. We show that, in the case of von Neumann measurements, the ability to interpolate measurements is an operational principle that sets apart LOCC and separable operations.
Yu, Li-Wei; Ge, Mo-Lin
2017-03-01
The relationships between quantum entangled states and braid matrices have been well studied in recent years. However, most of the results are based on qubits. In this paper, we investigate the applications of 2-qutrit entanglement in the braiding associated with Z3 parafermion. The 2-qutrit entangled state | Ψ (θ) >, generated by the action of the localized unitary solution R ˘ (θ) of YBE on 2-qutrit natural basis, achieves its maximal ℓ1-norm and maximal von Neumann entropy simultaneously at θ = π / 3. Meanwhile, at θ = π / 3, the solutions of YBE reduces braid matrices, which implies the role of ℓ1-norm and entropy plays in determining real physical quantities. On the other hand, we give a new realization of 4-anyon topological basis by qutrit entangled states, then the 9 × 9 localized braid representation in 4-qutrit tensor product space (C3) ⊗ 4 is reduced to Jones representation of braiding in the 4-anyon topological basis. Hence, we conclude that the entangled states are powerful tools in analysing the characteristics of braiding and R ˘ -matrix.
Quantum entanglement and thermal reduced density matrices in fermion and spin systems on ladders
Chen, Xiao; Fradkin, Eduardo
2013-08-01
Numerical studies of the reduced density matrix of a gapped spin-1/2 Heisenberg antiferromagnet on a two-leg ladder find that it has the same form as the Gibbs density matrix of a gapless spin-1/2 Heisenberg antiferromagnetic chain at a finite temperature determined by the spin gap of the ladder. We investigate this interesting result by considering a model of free fermions on a two-leg ladder (gapped by the inter-chain tunneling operator) and in spin systems on a ladder with a gapped ground state using exact solutions and several controlled approximations. We calculate the reduced density matrix and the entanglement entropy for a leg of the ladder (i.e. a cut made between the chains). In the fermionic system we find the exact form of the reduced density matrix for one of the chains and determine the entanglement spectrum explicitly. Here we find that in the weak tunneling limit of the ladder the entanglement entropy of one chain of the gapped ladder has a simple and universal form dictated by conformal invariance. In the case of the spin system, we consider the strong coupling limit by using perturbation theory and get the reduced density matrix by the Schmidt decomposition. The entanglement entropies of a general gapped system of two coupled conformal field theories (in 1 + 1 dimensions) are discussed using the replica trick and scaling arguments. We show that (1) for a system with a bulk gap the reduced density matrix has the form of a thermal density matrix, (2) the long-wavelength modes of one subsystem (a chain) of a gapped coupled system are always thermal, (3) the von Neumann entropy equals the thermodynamic entropy of one chain, and (4) the bulk gap plays the role of effective temperature.
Entanglement and quantum phase diagrams of symmetric multi-qubit systems
Calixto, Manuel; Castaños, Octavio; Romera, Elvira
2017-10-01
For general symmetric multi-qubit systems, the behavior of one- and two-qubit entanglement for Dicke, spin coherent and parity-adapted (even and odd) spin coherent states is determined. These quantum correlations are quantified by linear and von Neumann entropies of the corresponding one- and two-qubit reduced density matrices of the multi-qubit system. These states play a fundamental role in the study of Hamiltonian systems written in terms of collective generators of the angular momentum algebra like, for example, the Lipkin-Meshkov-Glick (LMG) model. Here we shall use these entanglement measures as a signature to characterize the different quantum phases that appear in these models.
DEFF Research Database (Denmark)
Müller-Lennert, Martin; Dupont-Dupuis, Fréderic; Szehr, Oleg
2013-01-01
in information theory and beyond. Various generalizations of Rényi entropies to the quantum setting have been proposed, most prominently Petz's quasi-entropies and Renner's conditional min-, max-, and collision entropy. However, these quantum extensions are incompatible and thus unsatisfactory. We propose a new...... quantum generalization of the family of Rényi entropies that contains the von Neumann entropy, min-entropy, collision entropy, and the max-entropy as special cases, thus encompassing most quantum entropies in use today. We show several natural properties for this definition, including data...
John von Neumann Birthday Centennial
Energy Technology Data Exchange (ETDEWEB)
Grcar, Joseph F.
2004-11-12
In celebration of John von Neumann's 100th birthday, a series of four lectures were presented on the evening of February 10, 2003 during the SIAM Conference on Computational Science and Engineering in San Diego. The venue was appropriate because von Neumann spent much of the later part of his life, in the 1950's, as an unofficial ambassador for computational science. He was then the only senior American scientist who had experience with the new computers (digital, electronic, and programmable) and a vision of their future importance. No doubt he would have relished the chance to attend a meeting such as this. The first speaker, William Aspray, described the ''interesting times'' during which computers were invented. His remarks were based on his history [1] of this period in von Neumann's life. We were honored to have John von Neumann's daughter, Marina von Neumann-Whitman, as our second speaker. Other accounts of von Neumann's life can be found in books by two of his colleagues [2] and [3]. Our third speaker, Peter Lax, provided both mathematical and international perspectives on John von Neumann's career. Finally, Pete Stewart spoke about von Neumann's numerical error analysis [4] in the context of later work; this talk did not lend itself to transcription, but readers may consult the historical notes in [5]. Our thanks to all the speakers for a remarkable evening. We are grateful to the DOE Applied Mathematical Sciences (AMS) program for partially supporting these lectures. Thanks are also due to SIAM and William Kolata, to our emcee, Gene Golub, to Paul Saylor for recording and editing, and to Barbara Lytle for the transcriptions. More about von Neumann's work can be learned from the recent American Mathematical Society proceedings [6].
Entanglement of Exact Excited Eigenstates of the Hubbard Model in Arbitrary Dimension
Directory of Open Access Journals (Sweden)
Oskar Vafek, Nicolas Regnault, B. Andrei Bernevig
2017-12-01
Full Text Available We compute exactly the von Neumann entanglement entropy of the eta-pairing states - a large set of exact excited eigenstates of the Hubbard Hamiltonian. For the singlet eta-pairing states the entropy scales with the logarithm of the spatial dimension of the (smaller partition. For the eta-pairing states with finite spin magnetization density, the leading term can scale as the volume or as the area-times-log, depending on the momentum space occupation of the Fermions with flipped spins. We also compute the corrections to the leading scaling. In order to study the eigenstate thermalization hypothesis (ETH, we also compute the entanglement Renyi entropies of such states and compare them with the corresponding entropies of thermal density matrix in various ensembles. Such states, which we find violate strong ETH, may provide a useful platform for a detailed study of the time-dependence of the onset of thermalization due to perturbations which violate the total pseudospin conservation.
Quantum Kaniadakis entropy under projective measurement
Ourabah, Kamel; Hamici-Bendimerad, Amel Hiba; Tribeche, Mouloud
2015-09-01
It is well known that the von Neumann entropy of a quantum state does not decrease with a projective measurement. This property holds for Tsallis and Rényi entropies as well. We show that the recently introduced quantum version of the Kaniadakis entropy preserves this property.
Deriving covariant holographic entanglement
Energy Technology Data Exchange (ETDEWEB)
Dong, Xi [School of Natural Sciences, Institute for Advanced Study, Princeton, NJ 08540 (United States); Lewkowycz, Aitor [Jadwin Hall, Princeton University, Princeton, NJ 08544 (United States); Rangamani, Mukund [Center for Quantum Mathematics and Physics (QMAP), Department of Physics, University of California, Davis, CA 95616 (United States)
2016-11-07
We provide a gravitational argument in favour of the covariant holographic entanglement entropy proposal. In general time-dependent states, the proposal asserts that the entanglement entropy of a region in the boundary field theory is given by a quarter of the area of a bulk extremal surface in Planck units. The main element of our discussion is an implementation of an appropriate Schwinger-Keldysh contour to obtain the reduced density matrix (and its powers) of a given region, as is relevant for the replica construction. We map this contour into the bulk gravitational theory, and argue that the saddle point solutions of these replica geometries lead to a consistent prescription for computing the field theory Rényi entropies. In the limiting case where the replica index is taken to unity, a local analysis suffices to show that these saddles lead to the extremal surfaces of interest. We also comment on various properties of holographic entanglement that follow from this construction.
Out-of-equilibrium protocol for Rényi entropies via the Jarzynski equality
Alba, Vincenzo
2017-06-01
In recent years entanglement measures, such as the von Neumann and the Rényi entropies, provided a unique opportunity to access elusive features of quantum many-body systems. However, extracting entanglement properties analytically, experimentally, or in numerical simulations can be a formidable task. Here, by combining the replica trick and the Jarzynski equality we devise an alternative effective out-of-equilibrium protocol for measuring the equilibrium Rényi entropies. The key idea is to perform a quench in the geometry of the replicas. The Rényi entropies are obtained as the exponential average of the work performed during the quench. We illustrate an application of the method in classical Monte Carlo simulations, although it could be useful in different contexts, such as in quantum Monte Carlo, or experimentally in cold-atom systems. The method is most effective in the quasistatic regime, i.e., for a slow quench. As a benchmark, we compute the Rényi entropies in the Ising universality class in 1 +1 dimensions. We find perfect agreement with the well-known conformal field theory predictions.
Entanglement and topological interfaces
Energy Technology Data Exchange (ETDEWEB)
Brehm, E.; Brunner, I.; Jaud, D.; Schmidt-Colinet, C. [Arnold Sommerfeld Center, Ludwig-Maximilians-Universitaet, Theresienstrasse 37, 80333, Muenchen (Germany)
2016-06-15
In this paper we consider entanglement entropies in two-dimensional conformal field theories in the presence of topological interfaces. Tracing over one side of the interface, the leading term of the entropy remains unchanged. The interface however adds a subleading contribution, which can be interpreted as a relative (Kullback-Leibler) entropy with respect to the situation with no defect inserted. Reinterpreting boundaries as topological interfaces of a chiral half of the full theory, we rederive the left/right entanglement entropy in analogy with the interface case. We discuss WZW models and toroidal bosonic theories as examples. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Corrections to holographic entanglement plateau
Chen, Bin; Li, Zhibin; Zhang, Jia-ju
2017-09-01
We investigate the robustness of the Araki-Lieb inequality in a two-dimensional (2D) conformal field theory (CFT) on torus. The inequality requires that Δ S = S( L) - | S( L - ℓ) - S( ℓ)| is nonnegative, where S( L) is the thermal entropy and S( L - ℓ), S( ℓ) are the entanglement entropies. Holographically there is an entanglement plateau in the BTZ black hole background, which means that there exists a critical length such that when ℓ ≤ ℓ c the inequality saturates Δ S =0. In thermal AdS background, the holographic entanglement entropy leads to Δ S = 0 for arbitrary ℓ. We compute the next-to-leading order contributions to Δ S in the large central charge CFT at both high and low temperatures. In both cases we show that Δ S is strictly positive except for ℓ = 0 or ℓ = L. This turns out to be true for any 2D CFT. In calculating the single interval entanglement entropy in a thermal state, we develop new techniques to simplify the computation. At a high temperature, we ignore the finite size correction such that the problem is related to the entanglement entropy of double intervals on a complex plane. As a result, we show that the leading contribution from a primary module takes a universal form. At a low temperature, we show that the leading thermal correction to the entanglement entropy from a primary module does not take a universal form, depending on the details of the theory.
Massive Corrections to Entanglement in Minimal E8 Toda Field Theory
Directory of Open Access Journals (Sweden)
Olalla A. Castro-Alvaredo
2017-02-01
Full Text Available In this letter we study the exponentially decaying corrections to saturation of the second R\\'enyi entropy of one interval of length L in minimal E8 Toda field theory. It has been known for some time that the entanglement entropy of a massive quantum field theory in 1+1 dimensions saturates to a constant value for m1 L <<1 where m1 is the mass of the lightest particle in the spectrum. Subsequently, results by Cardy, Castro-Alvaredo and Doyon have shown that there are exponentially decaying corrections to this behaviour which are characterised by Bessel functions with arguments proportional to m1 L. For the von Neumann entropy the leading correction to saturation takes the precise universal form -K0(2m1 L/8 whereas for the R\\'enyi entropies leading corrections which are proportional to K0(m1 L are expected. Recent numerical work by P\\'almai for the second R\\'enyi entropy of minimal E8 Toda has found next-to-leading order corrections decaying as exp(-2m1 L rather than the expected exp(-m1 L. In this paper we investigate the origin of this result and show that it is incorrect. An exact form factor computation of correlators of branch point twist fields reveals that the leading corrections are proportional to K0(m1 L as expected.
Entanglement in valence-bond-solid states and quantum search
Xu, Ying
The present dissertation covers two independent subjects: (i) The quantum entanglement in Valence-Bond-Solid states, and (ii) quantum database search algorithms. Both subjects are presented in a self-contained and pedagogical way. (i) The first chapter is a through introduction to the subject of quantum entanglement in Valence-Bond-Solid (VBS) states defined on a lattice or graph. The VBS state was first introduced as the ground state of the celebrated Affleck-Kennedy-Lieb-Tasaki (AKLT) spin chain model in statistical mechanics. Then it became essential in condensed matter physics, quantum information and measurement-based quantum computation. Recent studies elucidated important entanglement properties of the VBS state. We start with the definition of a general AKLT model and the construction of VBS ground states. A subsystem is introduced and described by the density matrix. Exact spectrum properties of the density matrix are proved and discussed. Density matrices of 1-dimensional models are diagonalized and the entanglement entropies (the von Neumann entropy and Renyi entropy) are calculated. The entropies take saturated value and the density matrix is proportional to a projector in the large subsystem limit. (ii) The second chapter is a detailed introduction to the subject of quantum database search algorithms. The problem of searching a large database (a Hilbert space) for a target item is performed by the famous Grover algorithm which locates the target item with probability 1 and a quadratic speed up compared with the corresponding classical algorithm. If the database is partitioned into blocks and one is searching for the block containing the target item instead of the target item itself, then the problem is referred to as partial search. Partial search trades accuracy for speed and the most efficient version is the Grover-Radhakrishnan-Korepin (GRK) algorithm. The target block can be further partitioned into subblocks so that GRK can be performed in a
Green's functions for Neumann boundary conditions
Franklin, Jerrold
2012-01-01
Green's functions for Neumann boundary conditions have been considered in Math Physics and Electromagnetism textbooks, but special constraints and other properties required for Neumann boundary conditions have generally not been noticed or treated correctly. In this paper, we derive an appropriate Neumann Green's function with these constraints and properties incorporated.
Universal corner contributions to entanglement negativity
Energy Technology Data Exchange (ETDEWEB)
Kim, Keun-Young, E-mail: fortoe@gist.ac.kr [School of Physics and Chemistry, Gwangju Institute of Science and Technology, Gwangju 500-712 (Korea, Republic of); Niu, Chao, E-mail: chaoniu09@gmail.com [School of Physics and Chemistry, Gwangju Institute of Science and Technology, Gwangju 500-712 (Korea, Republic of); Pang, Da-Wei, E-mail: d.pang@soton.ac.uk [Mathematical Sciences and STAG Research Centre, University of Southampton, Southampton SO17 1BJ (United Kingdom)
2016-09-15
It has been realised that corners in entangling surfaces can induce new universal contributions to the entanglement entropy and Rényi entropy. In this paper we study universal corner contributions to entanglement negativity in three- and four-dimensional CFTs using both field theory and holographic techniques. We focus on the quantity χ defined by the ratio of the universal part of the entanglement negativity over that of the entanglement entropy, which may characterise the amount of distillable entanglement. We find that for most of the examples χ takes bigger values for singular entangling regions, which may suggest increase in distillable entanglement. However, there also exist counterexamples where distillable entanglement decreases for singular surfaces. We also explore the behaviour of χ as the coupling varies and observe that for singular entangling surfaces, the amount of distillable entanglement is mostly largest for free theories, while counterexample exists for free Dirac fermion in three dimensions. For holographic CFTs described by higher derivative gravity, χ may increase or decrease, depending on the sign of the relevant parameters. Our results may reveal a more profound connection between geometry and distillable entanglement.
Entanglement area law in superfluid 4He
Herdman, C. M.; Roy, P.-N.; Melko, R. G.; Maestro, A. Del
2017-06-01
Area laws were first discovered by Bekenstein and Hawking, who found that the entropy of a black hole grows proportional to its surface area, and not its volume. Entropy area laws have since become a fundamental part of modern physics, from the holographic principle in quantum gravity to ground-state wavefunctions of quantum matter, where entanglement entropy is generically found to obey area law scaling. As no experiments are currently capable of directly probing the entanglement area law in naturally occurring many-body systems, evidence of its existence is based on studies of simplified qualitative theories. Using new exact microscopic numerical simulations of superfluid 4He, we demonstrate for the first time an area law scaling of entanglement entropy in a real quantum liquid in three dimensions. We validate the fundamental principle that the area law originates from correlations local to the entangling boundary, and present an entanglement equation of state showing how it depends on the density of the superfluid.
Entanglement of Distillation for Lattice Gauge Theories.
Van Acoleyen, Karel; Bultinck, Nick; Haegeman, Jutho; Marien, Michael; Scholz, Volkher B; Verstraete, Frank
2016-09-23
We study the entanglement structure of lattice gauge theories from the local operational point of view, and, similar to Soni and Trivedi [J. High Energy Phys. 1 (2016) 1], we show that the usual entanglement entropy for a spatial bipartition can be written as the sum of an undistillable gauge part and of another part corresponding to the local operations and classical communication distillable entanglement, which is obtained by depolarizing the local superselection sectors. We demonstrate that the distillable entanglement is zero for pure Abelian gauge theories at zero gauge coupling, while it is in general nonzero for the non-Abelian case. We also consider gauge theories with matter, and show in a perturbative approach how area laws-including a topological correction-emerge for the distillable entanglement. Finally, we also discuss the entanglement entropy of gauge fixed states and show that it has no relation to the physical distillable entropy.
Entanglement susceptibility: area laws and beyond
Zanardi, Paolo; Campos Venuti, Lorenzo
2013-04-01
Generic quantum states in the Hilbert space of a many-body system are nearly maximally entangled whereas low-energy physical states are not; the so-called area laws for quantum entanglement are widespread. In this paper we introduce the novel concept of entanglement susceptibility by expanding the 2-Rényi entropy in the boundary couplings. We show how this concept leads to the emergence of area laws for bi-partite quantum entanglement in systems ruled by local gapped Hamiltonians. Entanglement susceptibility also captures quantitatively which violations one should expect when the system becomes gapless. We also discuss an exact series expansion of the 2-Rényi entanglement entropy in terms of connected correlation functions of a boundary term. This is obtained by identifying Rényi entropy with ground state fidelity in a doubled and twisted theory.
John von Neumann selected letters
2005-01-01
John von Neuman was perhaps the most influential mathematician of the twentieth century, especially if his broad influence outside mathematics is included. Not only did he contribute to almost all branches of mathematics and created new fields, but he also changed post-World War II history with his work on the design of computers and with being a sought-after technical advisor to many figures in the U.S. military-political establishment in the 1940s and 1950s. The present volume is the first substantial collection of (previously mainly unpublished) letters written by von Neumann to colleagues, friends, government officials, and others. The letters give us a glimpse of the thinking of John von Neumann about mathematics, physics, computer science, science management, education, consulting, politics, and war. Readers of quite diverse backgrounds will find much of interest in this fascinating first-hand look at one of the towering figures of twentieth century science.
Entanglement Equilibrium and the Einstein Equation.
Jacobson, Ted
2016-05-20
A link between the semiclassical Einstein equation and a maximal vacuum entanglement hypothesis is established. The hypothesis asserts that entanglement entropy in small geodesic balls is maximized at fixed volume in a locally maximally symmetric vacuum state of geometry and quantum fields. A qualitative argument suggests that the Einstein equation implies the validity of the hypothesis. A more precise argument shows that, for first-order variations of the local vacuum state of conformal quantum fields, the vacuum entanglement is stationary if and only if the Einstein equation holds. For nonconformal fields, the same conclusion follows modulo a conjecture about the variation of entanglement entropy.
Entanglement Criteria of Two Two-Level Atoms Interacting with Two Coupled Modes
Baghshahi, Hamid Reza; Tavassoly, Mohammad Kazem; Faghihi, Mohammad Javad
2015-08-01
In this paper, we study the interaction between two two-level atoms and two coupled modes of a quantized radiation field in the form of parametric frequency converter injecting within an optical cavity enclosed by a medium with Kerr nonlinearity. It is demonstrated that, by applying the Bogoliubov-Valatin canonical transformation, the introduced model is reduced to a well-known form of the generalized Jaynes-Cummings model. Then, under particular initial conditions for the atoms (in a coherent superposition of its ground and upper states) and the fields (in a standard coherent state) which may be prepared, the time evolution of state vector of the entire system is analytically evaluated. In order to understand the degree of entanglement between subsystems (atom-field and atom-atom), the dynamics of entanglement through different measures, namely, von Neumann reduced entropy, concurrence and negativity is evaluated. In each case, the effects of Kerr nonlinearity and detuning parameter on the above measures are numerically analyzed, in detail. It is illustrated that the amount of entanglement can be tuned by choosing the evolved parameters, appropriately.
Energy Technology Data Exchange (ETDEWEB)
Estes, John [Blackett Laboratory, Imperial College,London SW7 2AZ (United Kingdom); Jensen, Kristan [Department of Physics and Astronomy, University of Victoria,Victoria, BC V8W 3P6 (Canada); C.N. Yang Institute for Theoretical Physics, SUNY Stony Brook,Stony Brook, NY 11794-3840 (United States); O’Bannon, Andy [Rudolf Peierls Centre for Theoretical Physics, University of Oxford,1 Keble Road, Oxford OX1 3NP (United Kingdom); Tsatis, Efstratios [8 Kotylaiou Street, Athens 11364 (Greece); Wrase, Timm [Stanford Institute for Theoretical Physics, Stanford University,Stanford, CA 94305 (United States)
2014-05-19
We study a number of (3+1)- and (2+1)-dimensional defect and boundary conformal field theories holographically dual to supergravity theories. In all cases the defects or boundaries are planar, and the defects are codimension-one. Using holography, we compute the entanglement entropy of a (hemi-)spherical region centered on the defect (boundary). We define defect and boundary entropies from the entanglement entropy by an appropriate background subtraction. For some (3+1)-dimensional theories we find evidence that the defect/boundary entropy changes monotonically under certain renormalization group flows triggered by operators localized at the defect or boundary. This provides evidence that the g-theorem of (1+1)-dimensional field theories generalizes to higher dimensions.
Estes, John; Jensen, Kristan; O'Bannon, Andy; Tsatis, Efstratios; Wrase, Timm
2014-05-01
We study a number of (3 + 1)- and (2 + 1)-dimensional defect and boundary conformal field theories holographically dual to supergravity theories. In all cases the defects or boundaries are planar, and the defects are codimension-one. Using holography, we compute the entanglement entropy of a (hemi-)spherical region centered on the defect (boundary). We define defect and boundary entropies from the entanglement entropy by an appropriate background subtraction. For some (3 + 1)-dimensional theories we find evidence that the defect/boundary entropy changes monotonically under certain renormalization group flows triggered by operators localized at the defect or boundary. This provides evidence that the g-theorem of (1 + 1)-dimensional field theories generalizes to higher dimensions.
Entanglement temperature with Gauss–Bonnet term
Directory of Open Access Journals (Sweden)
Shesansu Sekhar Pal
2015-09-01
Full Text Available We compute the entanglement temperature using the first law-like of thermodynamics, ΔE=TentΔSEE, up to Gauss–Bonnet term in the Jacobson–Myers entropy functional in any arbitrary spacetime dimension. The computation is done when the entangling region is the geometry of a slab. We also show that such a Gauss–Bonnet term, which becomes a total derivative, when the co-dimension two hypersurface is four dimensional, does not contribute to the finite term in the entanglement entropy. We observe that the Weyl-squared term does not contribute to the entanglement entropy. It is important to note that the calculations are performed when the entangling region is very small and the energy is calculated using the normal Hamiltonian.
On entanglement spreading from holography
Mezei, Márk
2017-05-01
A global quench is an interesting setting where we can study thermalization of subsystems in a pure state. We investigate entanglement entropy (EE) growth in global quenches in holographic field theories and relate some of its aspects to quantities characterizing chaos. More specifically we obtain four key results: 1. We prove holographic bounds on the entanglement velocity v E and the butterfly effect speed v B that arises in the study of chaos.
Entanglement irreversibility from quantum discord and quantum deficit.
Cornelio, Marcio F; de Oliveira, Marcos C; Fanchini, Felipe F
2011-07-08
We relate the problem of irreversibility of entanglement with the recently defined measures of quantum correlation--quantum discord and one-way quantum deficit. We show that the entanglement of formation is always strictly larger than the coherent information and the entanglement cost is also larger in most cases. We prove irreversibility of entanglement under local operations and classical communication for a family of entangled states. This family is a generalization of the maximally correlated states for which we also give an analytic expression for the distillable entanglement, the relative entropy of entanglement, the distillable secret key, and the quantum discord.
Gauge field entanglement in Kitaev's honeycomb model
Dóra, Balázs; Moessner, Roderich
2018-01-01
A spin fractionalizes into matter and gauge fermions in Kitaev's spin liquid on the honeycomb lattice. This follows from a Jordan-Wigner mapping to fermions, allowing for the construction of a minimal entropy ground-state wave function on the cylinder. We use this to calculate the entanglement entropy by choosing several distinct partitionings. First, by partitioning an infinite cylinder into two, the -ln2 topological entanglement entropy is reconfirmed. Second, the reduced density matrix of the gauge sector on the full cylinder is obtained after tracing out the matter degrees of freedom. This allows for evaluating the gauge entanglement Hamiltonian, which contains infinitely long-range correlations along the symmetry axis of the cylinder. The matter-gauge entanglement entropy is (Ny-1 )ln2 , with Ny the circumference of the cylinder. Third, the rules for calculating the gauge sector entanglement of any partition are determined. Rather small correctly chosen gauge partitions can still account for the topological entanglement entropy in spite of long-range correlations in the gauge entanglement Hamiltonian.
Sanz-Vicario, José Luis; Pérez-Torres, Jhon Fredy; Moreno-Polo, Germán
2017-08-01
We compute the entanglement between the electronic and vibrational motions in the simplest molecular system, the hydrogen molecular ion, considering the molecule as a bipartite system, electron and vibrational motion. For that purpose we compute an accurate total non-Born-Oppenheimer wave function in terms of a huge expansion using nonorthogonal B-spline basis sets that expand separately the electronic and nuclear wave functions. According to the Schmidt decomposition theorem for bipartite systems, widely used in quantum-information theory, it is possible to find a much shorter but equivalent expansion in terms of the natural orbitals or Schmidt bases for the electronic and nuclear half spaces. Here we extend the Schmidt decomposition theorem to the case in which nonorthogonal bases are used to span the partitioned Hilbert spaces. This extension is first illustrated with two simple coupled systems, the former without an exact solution and the latter exactly solvable. In these model systems of distinguishable coupled particles it is shown that the entanglement content does not increase monotonically with the excitation energy, but only within the manifold of states that belong to an existing excitation mode, if any. In the hydrogen molecular ion the entanglement content for each non-Born-Oppenheimer vibronic state is quantified through the von Neumann and linear entropies and we show that entanglement serves as a witness to distinguish vibronic states related to different Born-Oppenheimer molecular energy curves or electronic excitation modes.
Poilblanc, Didier; Schuch, Norbert
2013-04-01
Gapped Z2 spin liquids have been proposed as candidates for the ground state of the S=1/2 quantum antiferromagnet on the kagome lattice. We extend the use of projected entangled pair states to construct (on the cylinder) resonating valence bond (RVB) states including both nearest-neighbor and next-nearest-neighbor singlet bonds. Our ansatz—dubbed “simplex spin liquid”—allows for an asymmetry between the two types of triangles (of order 2%-3% in the energy density after optimization) leading to the breaking of inversion symmetry. We show that the topological Z2 structure is still preserved and, by considering the presence or the absence of spinon and vison lines along an infinite cylinder, we explicitly construct four orthogonal RVB minimally entangled states. The spinon and vison coherence lengths are extracted from a finite size scaling with regard to the cylinder perimeter of the energy splittings of the four sectors and are found to be of the order of the lattice spacing. The entanglement spectrum of a partitioned (infinite) cylinder is found to be gapless, suggesting the occurrence, on a cylinder with real open boundaries, of gapless edge modes formally similar to Luttinger liquid (nonchiral) spin and charge modes. When inversion symmetry is spontaneously broken, the RVB spin liquid exhibits an extra Ising degeneracy, which might have been observed in recent exact diagonalization studies.
Bounds for entanglement of formation of two mode squeezed thermal states
Energy Technology Data Exchange (ETDEWEB)
Chen, Xiao-Yu; Qiu, Pei-Liang
2003-07-28
The upper and lower bounds of entanglement of formation are given for two mode squeezed thermal state. The bounds are compared with other entanglement measure or bounds. The entanglement distillation and the relative entropy of entanglement of infinitive squeezed state are obtained at the postulation of hashing inequality.
Gualdi, Giulia; Giampaolo, Salvatore M; Illuminati, Fabrizio
2011-02-04
We introduce and discuss the concept of modular entanglement. This is the entanglement that is established between the end points of modular systems composed by sets of interacting moduli of arbitrarily fixed size. We show that end-to-end modular entanglement scales in the thermodynamic limit and rapidly saturates with the number of constituent moduli. We clarify the mechanisms underlying the onset of entanglement between distant and noninteracting quantum systems and its optimization for applications to quantum repeaters and entanglement distribution and sharing.
Deformed Fredkin Spin Chain with Extensive Entanglement
Salberger, Olof; Zhang, Zhao; Katsura, Hosho; Klich, Israel; Korepin, Vladimir
2016-01-01
We introduce a new spin chain which is a deformation of the Fredkin spin chain and has a phase transition between bounded and extensive entanglement entropy scaling. In this chain, spins have a local interaction of three nearest neighbors. The Hamiltonian is frustration-free and its ground state can be described analytically as a weighted superposition of Dyck paths. In the purely spin $1/2$ case, the entanglement entropy obeys an area law: it is bounded from above by a constant, when the size of the block $n$ increases (and $t>1$). When a local color degree of freedom is introduced the entanglement entropy increases linearly with the size of the block (and $t>1$). The entanglement entropy of half of the chain is tightly bounded by ${ n}\\log s$ where $n$ is the size of the block, and $s$ is the number of colors. Our chain fosters a new example for a significant boost to entropy and for the existence of the associated critical rainbow phase where the entanglement entropy scales with volume that has recently be...
Quantum entanglement in helium-like ions
Lin, Y.-C.; Ho, Y. K.
2012-06-01
Recently, there have been considerable interests to investigate quantum entanglement in two-electron atoms [1-3]. Here we investigate quantum entanglement for the ground and excited states of helium-like ions using correlated wave functions, concentrating on the particle-particle entanglement coming from the continuous spatial degrees of freedom. We use the two-electron wave functions constructed by employing B-spline basis to calculate the linear entropy of the reduced density matrix L=1-TrA(ρA^2 ) as a measure of the spatial entanglement. HereρA=TrB(| >AB ABDehesa et. al., J. Phys. B 45, 015504 (2012)
Entanglement and thermodynamics after a quantum quench in integrable systems.
Alba, Vincenzo; Calabrese, Pasquale
2017-07-25
Entanglement and entropy are key concepts standing at the foundations of quantum and statistical mechanics. Recently, the study of quantum quenches revealed that these concepts are intricately intertwined. Although the unitary time evolution ensuing from a pure state maintains the system at zero entropy, local properties at long times are captured by a statistical ensemble with nonzero thermodynamic entropy, which is the entanglement accumulated during the dynamics. Therefore, understanding the entanglement evolution unveils how thermodynamics emerges in isolated systems. Alas, an exact computation of the entanglement dynamics was available so far only for noninteracting systems, whereas it was deemed unfeasible for interacting ones. Here, we show that the standard quasiparticle picture of the entanglement evolution, complemented with integrability-based knowledge of the steady state and its excitations, leads to a complete understanding of the entanglement dynamics in the space-time scaling limit. We thoroughly check our result for the paradigmatic Heisenberg chain.
Entanglement Properties of a Higher-Integer-Spin AKLT Model with Quantum Group Symmetry
Directory of Open Access Journals (Sweden)
Chikashi Arita
2012-10-01
Full Text Available We study the entanglement properties of a higher-integer-spin Affleck-Kennedy-Lieb-Tasaki model with quantum group symmetry in the periodic boundary condition. We exactly calculate the finite size correction terms of the entanglement entropies from the double scaling limit. We also evaluate the geometric entanglement, which serves as another measure for entanglement. We find the geometric entanglement reaches its maximum at the isotropic point, and decreases with the increase of the anisotropy. This behavior is similar to that of the entanglement entropies.
Quantum discord bounds the amount of distributed entanglement.
Chuan, T K; Maillard, J; Modi, K; Paterek, T; Paternostro, M; Piani, M
2012-08-17
The ability to distribute quantum entanglement is a prerequisite for many fundamental tests of quantum theory and numerous quantum information protocols. Two distant parties can increase the amount of entanglement between them by means of quantum communication encoded in a carrier that is sent from one party to the other. Intriguingly, entanglement can be increased even when the exchanged carrier is not entangled with the parties. However, in light of the defining property of entanglement stating that it cannot increase under classical communication, the carrier must be quantum. Here we show that, in general, the increase of relative entropy of entanglement between two remote parties is bounded by the amount of nonclassical correlations of the carrier with the parties as quantified by the relative entropy of discord. We study implications of this bound, provide new examples of entanglement distribution via unentangled states, and put further limits on this phenomenon.
Liouville-von Neumann molecular dynamics.
Jakowski, Jacek; Morokuma, Keiji
2009-06-14
We present a novel first principles molecular dynamics scheme, called Liouville-von Neumann molecular dynamics, based on Liouville-von Neumann equation for density matrices propagation and Magnus expansion of the time-evolution operator. The scheme combines formally accurate quantum propagation of electrons represented via density matrices and a classical propagation of nuclei. The method requires a few iterations per each time step where the Fock operator is formed and von Neumann equation is integrated. The algorithm (a) is free of constraint and fictitious parameters, (b) avoids diagonalization of the Fock operator, and (c) can be used in the case of fractional occupation as in metallic systems. The algorithm is very stable, and has a very good conservation of energy even in cases when a good quality conventional Born-Oppenheimer molecular dynamics trajectories is difficult to obtain. Test simulations include initial phase of fullerene formation from gaseous C(2) and retinal system.
Entropy Associated with Information Storage and Its Retrieval
Directory of Open Access Journals (Sweden)
Abu Mohamed Alhasan
2015-08-01
Full Text Available We provide an entropy analysis for light storage and light retrieval. In this analysis, entropy extraction and reduction in a typical light storage experiment are identified. The spatiotemporal behavior of entropy is presented for D1 transition in cold sodium atoms. The governing equations are the reduced Maxwell field equations and the Liouville–von Neumann equation for the density matrix of the dressed atom.
Geometric entanglement in the Laughlin wave function
Zhang, Jiang-Min; Liu, Yu
2017-08-01
We study numerically the geometric entanglement in the Laughlin wave function, which is of great importance in condensed matter physics. The Slater determinant having the largest overlap with the Laughlin wave function is constructed by an iterative algorithm. The logarithm of the overlap, which is a geometric quantity, is then taken as a geometric measure of entanglement. It is found that the geometric entanglement is a linear function of the number of electrons to a good extent. This is especially the case for the lowest Laughlin wave function, namely the one with filling factor of 1/3. Surprisingly, the linear behavior extends well down to the smallest possible value of the electron number, namely, N = 2. The constant term does not agree with the expected topological entropy. In view of previous works, our result indicates that the relation between geometric entanglement and topological entropy is very subtle.
Monogamy Inequality for Any Local Quantum Resource and Entanglement.
Camalet, S
2017-09-15
We derive a monogamy inequality for any local quantum resource and entanglement. It results from the fact that there is always a convex measure for a quantum resource, as shown here, and from the relation between entanglement and local entropy. One of its consequences is an entanglement monogamy different from that usually discussed. If the local resource is nonuniformity or coherence, it is satisfied by familiar resource and entanglement measures. The ensuing upper bound for the local coherence, determined by the entanglement, is independent of the basis used to define the coherence.
On quantum Rényi entropies: A new generalization and some properties
Energy Technology Data Exchange (ETDEWEB)
Müller-Lennert, Martin [Department of Mathematics, ETH Zurich, 8092 Zürich (Switzerland); Dupuis, Frédéric [Department of Computer Science, Aarhus University, 8200 Aarhus (Denmark); Szehr, Oleg [Department of Mathematics, Technische Universität München, 85748 Garching (Germany); Fehr, Serge [CWI (Centrum Wiskunde and Informatica), 1090 Amsterdam (Netherlands); Tomamichel, Marco [Centre for Quantum Technologies, National University of Singapore, Singapore 117543 (Singapore)
2013-12-15
The Rényi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies, or mutual information, and have found many applications in information theory and beyond. Various generalizations of Rényi entropies to the quantum setting have been proposed, most prominently Petz's quasi-entropies and Renner's conditional min-, max-, and collision entropy. However, these quantum extensions are incompatible and thus unsatisfactory. We propose a new quantum generalization of the family of Rényi entropies that contains the von Neumann entropy, min-entropy, collision entropy, and the max-entropy as special cases, thus encompassing most quantum entropies in use today. We show several natural properties for this definition, including data-processing inequalities, a duality relation, and an entropic uncertainty relation.
Measurements and von Neumann projection/collapse
Indian Academy of Sciences (India)
unwanted superpositions of (system + apparatus)-states can be shown to be suppressed, leading eventually to the projection/collapse rule postulated in von Neumann's treatment of measurements [3]. In the next section, the measurement problem in quantum mechanics (QM) is recalled. In §3, some proposed improvements ...
Novel quantum phase transition from bounded to extensive entanglement.
Zhang, Zhao; Ahmadain, Amr; Klich, Israel
2017-05-16
The nature of entanglement in many-body systems is a focus of intense research with the observation that entanglement holds interesting information about quantum correlations in large systems and their relation to phase transitions. In particular, it is well known that although generic, many-body states have large, extensive entropy, ground states of reasonable local Hamiltonians carry much smaller entropy, often associated with the boundary length through the so-called area law. Here we introduce a continuous family of frustration-free Hamiltonians with exactly solvable ground states and uncover a remarkable quantum phase transition whereby the entanglement scaling changes from area law into extensively large entropy. This transition shows that entanglement in many-body systems may be enhanced under special circumstances with a potential for generating "useful" entanglement for the purpose of quantum computing and that the full implications of locality and its restrictions on possible ground states may hold further surprises.
Novel quantum phase transition from bounded to extensive entanglement
Zhang, Zhao; Ahmadain, Amr; Klich, Israel
2017-05-01
The nature of entanglement in many-body systems is a focus of intense research with the observation that entanglement holds interesting information about quantum correlations in large systems and their relation to phase transitions. In particular, it is well known that although generic, many-body states have large, extensive entropy, ground states of reasonable local Hamiltonians carry much smaller entropy, often associated with the boundary length through the so-called area law. Here we introduce a continuous family of frustration-free Hamiltonians with exactly solvable ground states and uncover a remarkable quantum phase transition whereby the entanglement scaling changes from area law into extensively large entropy. This transition shows that entanglement in many-body systems may be enhanced under special circumstances with a potential for generating “useful” entanglement for the purpose of quantum computing and that the full implications of locality and its restrictions on possible ground states may hold further surprises.
Baltimaade kunstiajaloo isa : Wilhelm Neumann 150 / Jevgeni Kaljundi
Kaljundi, Jevgeni, 1931-2011
1999-01-01
Wilhelm Neumann ئ iseõppija. Riias: ilmunud uurimused, töö oma projekti järgi ehitatud Läti kunstimuuseumi direktorina. Neumanni vaid Eesti kunstipärandit käsitlevad uurimused. Neumann ئ muinsuskaitsetegevuse algataja Baltimaadel, tema töid muinsuskaitse alal Eestis. W. Neumann arhitektina
Spectral theory and quotients in Von Neumann algebras | West ...
African Journals Online (AJOL)
In this note we consider to what extent the functional calculus and the spectral theory in von Neumann algebras are preserved by the taking of quotients relative to two-sided ideals of the von Neumann algebra. Keywords:von Neumann algebra, functional calculus, spectral theory, quotient algebras. Quaestiones ...
A domain decomposition preconditioner of Neumann-Neumann type for the Stokes equations
Dolean, Victorita; Nataf, Frédéric; Rapin, Gerd
2009-01-01
In this paper we recall a new domain decomposition method for the Stokes problem obtained via the Smith factorization. From the theoretical point of view, this domain decomposition method is optimal in the sense that it converges in two iterations for a decomposition into two equal domains. Previous results illustrated the fast convergence of the proposed algorithm in some cases. Our algorithm has shown a more robust behavior than Neumann- Neumann or FETI type methods for particular decomposi...
Relating quantum coherence and correlations with entropy-based measures.
Wang, Xiao-Li; Yue, Qiu-Ling; Yu, Chao-Hua; Gao, Fei; Qin, Su-Juan
2017-09-21
Quantum coherence and quantum correlations are important quantum resources for quantum computation and quantum information. In this paper, using entropy-based measures, we investigate the relationships between quantum correlated coherence, which is the coherence between subsystems, and two main kinds of quantum correlations as defined by quantum discord as well as quantum entanglement. In particular, we show that quantum discord and quantum entanglement can be well characterized by quantum correlated coherence. Moreover, we prove that the entanglement measure formulated by quantum correlated coherence is lower and upper bounded by the relative entropy of entanglement and the entanglement of formation, respectively, and equal to the relative entropy of entanglement for all the maximally correlated states.
Generalized gravitational entropy from total derivative action
Energy Technology Data Exchange (ETDEWEB)
Dong, Xi [Stanford Institute for Theoretical Physics, Department of Physics, Stanford University,Stanford, CA 94305 (United States); School of Natural Sciences, Institute for Advanced Study,Princeton, NJ 08540 (United States); Miao, Rong-Xin [Max Planck Institute for Gravitational Physics (Albert Einstein Institute),Am Mühlenberg 1, 14476 Golm (Germany)
2015-12-16
We investigate the generalized gravitational entropy from total derivative terms in the gravitational action. Following the method of Lewkowycz and Maldacena, we find that the generalized gravitational entropy from total derivatives vanishes. We compare our results with the work of Astaneh, Patrushev, and Solodukhin. We find that if total derivatives produced nonzero entropy, the holographic and the field-theoretic universal terms of entanglement entropy would not match. Furthermore, the second law of thermodynamics could be violated if the entropy of total derivatives did not vanish.
On holographic entanglement density
Gushterov, Nikola I.; O'Bannon, Andy; Rodgers, Ronnie
2017-10-01
We use holographic duality to study the entanglement entropy (EE) of Conformal Field Theories (CFTs) in various spacetime dimensions d, in the presence of various deformations: a relevant Lorentz scalar operator with constant source, a temperature T , a chemical potential μ, a marginal Lorentz scalar operator with source linear in a spatial coordinate, and a circle-compactified spatial direction. We consider EE between a strip or sphere sub-region and the rest of the system, and define the "entanglement density" (ED) as the change in EE due to the deformation, divided by the sub-region's volume. Using the deformed CFTs above, we show how the ED's dependence on the strip width or sphere radius, L, is useful for characterizing states of matter. For example, the ED's small- L behavior is determined either by the dimension of the perturbing operator or by the first law of EE. For Lorentz-invariant renormalization group (RG) flows between CFTs, the "area theorem" states that the coefficient of the EE's area law term must be larger in the UV than in the IR. In these cases the ED must therefore approach zero from below as L→∞. However, when Lorentz symmetry is broken and the IR fixed point has different scaling from the UV, we find that the ED often approaches the thermal entropy density from above, indicating area theorem violation.
Interuniversal entanglement in a cyclic multiverse
Robles-Pérez, Salvador; Balcerzak, Adam; Dąbrowski, Mariusz P.; Krämer, Manuel
2017-04-01
We study scenarios of parallel cyclic multiverses which allow for a different evolution of the physical constants, while having the same geometry. These universes are classically disconnected, but quantum-mechanically entangled. Applying the thermodynamics of entanglement, we calculate the temperature and the entropy of entanglement. It emerges that the entropy of entanglement is large at big bang and big crunch singularities of the parallel universes as well as at the maxima of the expansion of these universes. The latter seems to confirm earlier studies that quantum effects are strong at turning points of the evolution of the universe performed in the context of the timeless nature of the Wheeler-DeWitt equation and decoherence. On the other hand, the entropy of entanglement at big rip singularities is going to zero despite its presumably quantum nature. This may be an effect of total dissociation of the universe structures into infinitely separated patches violating the null energy condition. However, the temperature of entanglement is large/infinite at every classically singular point and at maximum expansion and seems to be a better measure of quantumness.
Comparing Quantum Entanglement and Topological Entanglement
Kauffman, Louis H.; Lomonaco, Samuel J.
2002-01-01
This paper discusses relationships between topological entanglement and quantum entanglement. Specifically, we propose that for this comparison it is fundamental to view topological entanglements such as braids as "entanglement operators" and to associate to them unitary operators that are capable of creating quantum entanglement.
Spin–momenta entanglement in moving frames: Properties of von ...
Indian Academy of Sciences (India)
well as locality, of information [9–11]. Expressed differently, the von Neumann entropy measures the stored qubits of information per states of the combined system while the reduced one quantifies the qubits per states that may be stored in one of the subsystems. [1]. It is then obvious that a deeper understanding of von ...
Entanglement in the quantum one-dimensional integer spin S Heisenberg antiferromagnet
Lima, L. S.
2017-10-01
We use the modified spin wave theory of Takahashi to study the entanglement entropy in the quantum one-dimensional integer spin Heisenberg antiferromagnet. We calculate the entanglement entropy of this spin system that is well known to be a quantum wire, in the classical limit (N → ∞). We obtain a decreasing the entanglement entropy with the temperature and we obtain none change in the entanglement in the point Δ = 1 at T = 0 where the system presents a quantum phase transition from a gapless phase in the spectrum Δ < 1 to a gapped phase Δ ≥ 1.
Entanglement dynamics in critical random quantum Ising chain with perturbations
Huang, Yichen
2017-05-01
We simulate the entanglement dynamics in a critical random quantum Ising chain with generic perturbations using the time-evolving block decimation algorithm. Starting from a product state, we observe super-logarithmic growth of entanglement entropy with time. The numerical result is consistent with the analytical prediction of Vosk and Altman using a real-space renormalization group technique.
Generalised squeezing and information theory approach to quantum entanglement
Vourdas, A.
1993-01-01
It is shown that the usual one- and two-mode squeezing are based on reducible representations of the SU(1,1) group. Generalized squeezing is introduced with the use of different SU(1,1) rotations on each irreducible sector. Two-mode squeezing entangles the modes and information theory methods are used to study this entanglement. The entanglement of three modes is also studied with the use of the strong subadditivity property of the entropy.
Quantum Entanglement Growth under Random Unitary Dynamics
Directory of Open Access Journals (Sweden)
Adam Nahum
2017-07-01
Full Text Available Characterizing how entanglement grows with time in a many-body system, for example, after a quantum quench, is a key problem in nonequilibrium quantum physics. We study this problem for the case of random unitary dynamics, representing either Hamiltonian evolution with time-dependent noise or evolution by a random quantum circuit. Our results reveal a universal structure behind noisy entanglement growth, and also provide simple new heuristics for the “entanglement tsunami” in Hamiltonian systems without noise. In 1D, we show that noise causes the entanglement entropy across a cut to grow according to the celebrated Kardar-Parisi-Zhang (KPZ equation. The mean entanglement grows linearly in time, while fluctuations grow like (time^{1/3} and are spatially correlated over a distance ∝(time^{2/3}. We derive KPZ universal behavior in three complementary ways, by mapping random entanglement growth to (i a stochastic model of a growing surface, (ii a “minimal cut” picture, reminiscent of the Ryu-Takayanagi formula in holography, and (iii a hydrodynamic problem involving the dynamical spreading of operators. We demonstrate KPZ universality in 1D numerically using simulations of random unitary circuits. Importantly, the leading-order time dependence of the entropy is deterministic even in the presence of noise, allowing us to propose a simple coarse grained minimal cut picture for the entanglement growth of generic Hamiltonians, even without noise, in arbitrary dimensionality. We clarify the meaning of the “velocity” of entanglement growth in the 1D entanglement tsunami. We show that in higher dimensions, noisy entanglement evolution maps to the well-studied problem of pinning of a membrane or domain wall by disorder.
Entanglement quantification by local unitary operations
Energy Technology Data Exchange (ETDEWEB)
Monras, A.; Giampaolo, S. M.; Gualdi, G.; Illuminati, F. [Dipartimento di Matematica e Informatica, Universita degli Studi di Salerno, CNISM, Unita di Salerno, and INFN, Sezione di Napoli-Gruppo Collegato di Salerno, Via Ponte don Melillo, I-84084 Fisciano (Italy); Adesso, G.; Davies, G. B. [School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD (United Kingdom)
2011-07-15
Invariance under local unitary operations is a fundamental property that must be obeyed by every proper measure of quantum entanglement. However, this is not the only aspect of entanglement theory where local unitary operations play a relevant role. In the present work we show that the application of suitable local unitary operations defines a family of bipartite entanglement monotones, collectively referred to as ''mirror entanglement.'' They are constructed by first considering the (squared) Hilbert-Schmidt distance of the state from the set of states obtained by applying to it a given local unitary operator. To the action of each different local unitary operator there corresponds a different distance. We then minimize these distances over the sets of local unitary operations with different spectra, obtaining an entire family of different entanglement monotones. We show that these mirror-entanglement monotones are organized in a hierarchical structure, and we establish the conditions that need to be imposed on the spectrum of a local unitary operator for the associated mirror entanglement to be faithful, i.e., to vanish in and only in separable pure states. We analyze in detail the properties of one particularly relevant member of the family, the ''stellar mirror entanglement'' associated with the traceless local unitary operations with nondegenerate spectra and equispaced eigenvalues in the complex plane. This particular measure generalizes the original analysis of S. M. Giampaolo and F. Illuminati [Phys. Rev. A 76, 042301 (2007)], valid for qubits and qutrits. We prove that the stellar entanglement is a faithful bipartite entanglement monotone in any dimension and that it is bounded from below by a function proportional to the linear entropy and from above by the linear entropy itself, coinciding with it in two- and three-dimensional spaces.
Geometry of two-qubit states with negative conditional entropy
Friis, Nicolai; Bulusu, Sridhar; Bertlmann, Reinhold A.
2017-03-01
We review the geometric features of negative conditional entropy and the properties of the conditional amplitude operator proposed by Cerf and Adami for two qubit states in comparison with entanglement and nonlocality of the states. We identify the region of negative conditional entropy in the tetrahedron of locally maximally mixed two-qubit states. Within this set of states, negative conditional entropy implies nonlocality and entanglement, but not vice versa, and we show that the Cerf–Adami conditional amplitude operator provides an entanglement witness equivalent to the Peres–Horodecki criterion. Outside of the tetrahedron this equivalence is generally not true.
Quantifying entanglement of overlapping indistinguishable particles
Gittings, Joseph R.
This thesis develops the quantitative study of quantum entanglement in systems of identical particles. Understanding this topic is essential for the construction of quantum information processing devices involving identical particles. A brief overview of necessary concepts and methods, such as the density matrix, the entanglement in pure and mixed states of distinguishable particles, and some common applications of entanglement is given in the introduction. Some competing methods of calculating the entanglement in bipartite pure states of indistinguishable particles are examined. It is shown that only the 'site entropy' measure introduced by Zanardi satisfies all the criteria for a correct entanglement measure. A teleportation protocol which utilizes all the entanglement carried (in both the spin and space degrees of freedom) in a doubly- occupied molecular bonding orbital is presented. The output from an interferometer in a thought experiment described by Omar et al. is studied as an example to see whether entanglement can be separated into space-only, spin-only, and space-spin components. A similar exercise is performed for a doubly-occupied molecular bonding orbital. The relationship between these results and the application of superselection rules (SSRs) to the quantification of useful entanglement is discussed. A numerical method for estimating the entanglement of formation of a mixed state of arbitrary dimension by a conjugate gradient algorithm is described. The results of applying an implementation of the algorithm to both random and isotropic states of 2 qutrits (i.e. two three-dimensional systems) is described. Existing work on calculating entanglement between two sites in various spin systems is outlined. New methods for calculating the entanglement between two sites in various types of degenerate quantum gas - a Fermi gas, a Bose condensate, and a BCS superconductor - are described. The results of numerical studies of the entanglement in a normal metal
A Neumann boundary term for gravity
Krishnan, Chethan; Raju, Avinash
2017-05-01
The Gibbons-Hawking-York (GHY) boundary term makes the Dirichlet problem for gravity well-defined, but no such general term seems to be known for Neumann boundary conditions. In this paper, we view Neumann not as fixing the normal derivative of the metric (“velocity”) at the boundary, but as fixing the functional derivative of the action with respect to the boundary metric (“momentum”). This leads directly to a new boundary term for gravity: the trace of the extrinsic curvature with a specific dimension-dependent coefficient. In three dimensions, this boundary term reduces to a “one-half” GHY term noted in the literature previously, and we observe that our action translates precisely to the Chern-Simons action with no extra boundary terms. In four dimensions, the boundary term vanishes, giving a natural Neumann interpretation to the standard Einstein-Hilbert action without boundary terms. We argue that in light of AdS/CFT, ours is a natural approach for defining a “microcanonical” path integral for gravity in the spirit of the (pre-AdS/CFT) work of Brown and York.
Entanglement asymmetry for boosted black branes and the bound
Mishra, Rohit; Singh, Harvendra
2017-06-01
We study the effects of asymmetry in the entanglement thermodynamics of CFT subsystems. It is found that “boosted” Dp-brane backgrounds give rise to the first law of the entanglement thermodynamics where the CFT pressure asymmetry plays a decisive role in the entanglement. Two different strip like subsystems, one parallel to the boost and the other perpendicular, are studied in the perturbative regime Tthermal ≪ TE. We mainly seek to quantify this entanglement asymmetry as a ratio of the first-order entanglement entropies of the excitations. We discuss the AdS-wave backgrounds at zero temperature having maximum asymmetry from where a bound on entanglement asymmetry is obtained. The entanglement asymmetry reduces as we switch on finite temperature in the CFT while it is maximum at zero temperature.
Entanglement of higher-derivative oscillators in holographic systems
Energy Technology Data Exchange (ETDEWEB)
Dimov, Hristo, E-mail: h_dimov@phys.uni-sofia.bg [Department of Physics, Sofia University, 5 J. Bourchier Blvd., 1164 Sofia (Bulgaria); Mladenov, Stefan, E-mail: smladenov@phys.uni-sofia.bg [Department of Physics, Sofia University, 5 J. Bourchier Blvd., 1164 Sofia (Bulgaria); Rashkov, Radoslav C., E-mail: rash@phys.uni-sofia.bg [Department of Physics, Sofia University, 5 J. Bourchier Blvd., 1164 Sofia (Bulgaria); Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstr. 8–10, 1040 Vienna (Austria); Vetsov, Tsvetan, E-mail: vetsov@phys.uni-sofia.bg [Department of Physics, Sofia University, 5 J. Bourchier Blvd., 1164 Sofia (Bulgaria)
2017-05-15
We study the quantum entanglement of coupled Pais–Uhlenbeck oscillators using the formalism of thermo-field dynamics. The entanglement entropy is computed for the specific cases of two and a ring of N coupled Pais–Uhlenbeck oscillators of fourth order. It is shown that the entanglement entropy depends on the temperatures, frequencies and coupling parameters of the different degrees of freedom corresponding to harmonic oscillators. We also make remarks on the appearance of instabilities of higher-derivative oscillators in the context of AdS/CFT correspondence. Finally, we advert to the information geometry theory by calculating the Fisher information metric for the considered system of coupled oscillators.
Entanglement dynamics in critical random quantum Ising chain with perturbations
Energy Technology Data Exchange (ETDEWEB)
Huang, Yichen, E-mail: ychuang@caltech.edu
2017-05-15
We simulate the entanglement dynamics in a critical random quantum Ising chain with generic perturbations using the time-evolving block decimation algorithm. Starting from a product state, we observe super-logarithmic growth of entanglement entropy with time. The numerical result is consistent with the analytical prediction of Vosk and Altman using a real-space renormalization group technique. - Highlights: • We study the dynamical quantum phase transition between many-body localized phases. • We simulate the dynamics of a very long random spin chain with matrix product states. • We observe numerically super-logarithmic growth of entanglement entropy with time.
Directory of Open Access Journals (Sweden)
Bernard S. Kay
2015-12-01
Full Text Available We give a review, in the style of an essay, of the author’s 1998 matter-gravity entanglement hypothesis which, unlike the standard approach to entropy based on coarse-graining, offers a definition for the entropy of a closed system as a real and objective quantity. We explain how this approach offers an explanation for the Second Law of Thermodynamics in general and a non-paradoxical understanding of information loss during black hole formation and evaporation in particular. It also involves a radically different from usual description of black hole equilibrium states in which the total state of a black hole in a box together with its atmosphere is a pure state—entangled in just such a way that the reduced state of the black hole and of its atmosphere are each separately approximately thermal. We also briefly recall some recent work of the author which involves a reworking of the string-theory understanding of black hole entropy consistent with this alternative description of black hole equilibrium states and point out that this is free from some unsatisfactory features of the usual string theory understanding. We also recall the author’s recent arguments based on this alternative description which suggest that the Anti de Sitter space (AdS/conformal field theory (CFT correspondence is a bijection between the boundary CFT and just the matter degrees of freedom of the bulk theory.
Entanglement quantification by local unitary operations
Monras, A.; Adesso, G.; Giampaolo, S. M.; Gualdi, G.; Davies, G. B.; Illuminati, F.
2011-07-01
Invariance under local unitary operations is a fundamental property that must be obeyed by every proper measure of quantum entanglement. However, this is not the only aspect of entanglement theory where local unitary operations play a relevant role. In the present work we show that the application of suitable local unitary operations defines a family of bipartite entanglement monotones, collectively referred to as “mirror entanglement.” They are constructed by first considering the (squared) Hilbert-Schmidt distance of the state from the set of states obtained by applying to it a given local unitary operator. To the action of each different local unitary operator there corresponds a different distance. We then minimize these distances over the sets of local unitary operations with different spectra, obtaining an entire family of different entanglement monotones. We show that these mirror-entanglement monotones are organized in a hierarchical structure, and we establish the conditions that need to be imposed on the spectrum of a local unitary operator for the associated mirror entanglement to be faithful, i.e., to vanish in and only in separable pure states. We analyze in detail the properties of one particularly relevant member of the family, the “stellar mirror entanglement” associated with the traceless local unitary operations with nondegenerate spectra and equispaced eigenvalues in the complex plane. This particular measure generalizes the original analysis of S. M. Giampaolo and F. Illuminati [Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.76.042301 76, 042301 (2007)], valid for qubits and qutrits. We prove that the stellar entanglement is a faithful bipartite entanglement monotone in any dimension and that it is bounded from below by a function proportional to the linear entropy and from above by the linear entropy itself, coinciding with it in two- and three-dimensional spaces.
Entanglement, holography and causal diamonds
Energy Technology Data Exchange (ETDEWEB)
Boer, Jan de [Institute of Physics, Universiteit van Amsterdam,Science Park 904, 1090 GL Amsterdam (Netherlands); Haehl, Felix M. [Centre for Particle Theory & Department of Mathematical Sciences, Durham University,South Road, Durham DH1 3LE (United Kingdom); Heller, Michal P.; Myers, Robert C. [Perimeter Institute for Theoretical Physics,31 Caroline Street North, Waterloo, Ontario N2L 2Y5 (Canada)
2016-08-29
We argue that the degrees of freedom in a d-dimensional CFT can be re-organized in an insightful way by studying observables on the moduli space of causal diamonds (or equivalently, the space of pairs of timelike separated points). This 2d-dimensional space naturally captures some of the fundamental nonlocality and causal structure inherent in the entanglement of CFT states. For any primary CFT operator, we construct an observable on this space, which is defined by smearing the associated one-point function over causal diamonds. Known examples of such quantities are the entanglement entropy of vacuum excitations and its higher spin generalizations. We show that in holographic CFTs, these observables are given by suitably defined integrals of dual bulk fields over the corresponding Ryu-Takayanagi minimal surfaces. Furthermore, we explain connections to the operator product expansion and the first law of entanglement entropy from this unifying point of view. We demonstrate that for small perturbations of the vacuum, our observables obey linear two-derivative equations of motion on the space of causal diamonds. In two dimensions, the latter is given by a product of two copies of a two-dimensional de Sitter space. For a class of universal states, we show that the entanglement entropy and its spin-three generalization obey nonlinear equations of motion with local interactions on this moduli space, which can be identified with Liouville and Toda equations, respectively. This suggests the possibility of extending the definition of our new observables beyond the linear level more generally and in such a way that they give rise to new dynamically interacting theories on the moduli space of causal diamonds. Various challenges one has to face in order to implement this idea are discussed.
$E_{6}$ and the bipartite entanglement of three qutrits
Duff, M J
2007-01-01
Recent investigations have established an analogy between the entropy of four-dimensional supersymmetric black holes in string theory and entanglement in quantum information theory. Examples include: (1) N=2 STU black holes and the tripartite entanglement of three qubits (2-state systems), where the common symmetry is [SL(2)]^3 and (2) N=8 black holes and the tripartite entanglement of seven qubits where the common symmetry is E_7 which contains [SL(2)]^7. Here we present another example: N=8 black holes (or black strings) in five dimensions and the bipartite entanglement of three qutrits (3-state systems), where the common symmetry is E_6 which contains [SL(3)]^3. Both the black hole (or black string) entropy and the entanglement measure are provided by the Cartan cubic E_6 invariant. Similar analogies exist for ``magic'' N=2 supergravity black holes in both four and five dimensions.
Entanglement in Lifshitz-type quantum field theories
Mohammadi Mozaffar, M. Reza; Mollabashi, Ali
2017-07-01
We study different aspects of quantum entanglement and its measures, including entanglement entropy in the vacuum state of a certain Lifshitz free scalar theory. We present simple intuitive arguments based on "non-local" effects of this theory that the scaling of entanglement entropy depends on the dynamical exponent as a characteristic parameter of the theory. The scaling is such that in the massless theory for small entangling regions it leads to area law in the Lorentzian limit and volume law in the z → ∞ limit. We present strong numerical evidences in (1+1) and (2+1)-dimensions in support of this behavior. In (2 + 1)-dimensions we also study some shape dependent aspects of entanglement. We argue that in the massless limit corner contributions are no more additive for large enough dynamical exponent due to non-local effects of Lifshitz theories. We also comment on possible holographic duals of such theories based on the sign of tripartite information.
$E_7$ and the tripartite entanglement of seven qubits
Duff, Michael J
2007-01-01
In quantum information theory, it is well known that the tripartite entanglement of three qubits is described by the group [SL(2,C)]^3 and that the entanglement measure is given by Cayley's hyperdeterminant. This has provided an analogy with certain N=2 supersymmetric black holes in string theory, whose entropy is also given by the hyperdeterminant. In this paper, we extend the analogy to N=8. We propose that a particular tripartite entanglement of seven qubits is described by the exceptional group E_7(C) and that the entanglement measure is given by Cartan's quartic E_7 invariant.
Conditional steering under the von Neumann scenario
Mukherjee, Kaushiki; Paul, Biswajit; Karmakar, Sumana; Sarkar, Debasis; Mukherjee, Amit; Bhattacharya, Some Sankar; Roy, Arup
2017-08-01
In Phys. Lett. A 166, 293 (1992), 10.1016/0375-9601(92)90711-T, Popescu and Rohrlich characterized nonlocality of pure n -partite entangled systems by studying bipartite violation of local realism when n -2 number of parties perform projective measurements on their particles. A pertinent question in this scenario is whether similar characterization is possible for n -partite mixed entangled states also. In the present work we have followed an analogous approach so as to explore whether given a tripartite mixed entangled state the conditional bipartite states obtained by performing projective measurement on the third party demonstrate a weaker form of nonlocality, quantum steering. We also compare this phenomenon of conditional steering with existing notions of tripartite correlations.
Adjoint entropy vs topological entropy
Giordano Bruno, Anna
2012-01-01
Recently the adjoint algebraic entropy of endomorphisms of abelian groups was introduced and studied. We generalize the notion of adjoint entropy to continuous endomorphisms of topological abelian groups. Indeed, the adjoint algebraic entropy is defined using the family of all finite-index subgroups, while we take only the subfamily of all open finite-index subgroups to define the topological adjoint entropy. This allows us to compare the (topological) adjoint entropy with the known topologic...
Detecting Quantum Entanglement
Terhal, Barbara M
2001-01-01
We review the criteria for separability and quantum entanglement, both in a bipartite as well as a multipartite setting. We discuss Bell inequalities, entanglement witnesses, entropic inequalities, bound entanglement and several features of multipartite entanglement. We indicate how these criteria bear on the experimental detection of quantum entanglement.
Bit Threads and Holographic Entanglement
Freedman, Michael; Headrick, Matthew
2017-05-01
The Ryu-Takayanagi (RT) formula relates the entanglement entropy of a region in a holographic theory to the area of a corresponding bulk minimal surface. Using the max flow-min cut principle, a theorem from network theory, we rewrite the RT formula in a way that does not make reference to the minimal surface. Instead, we invoke the notion of a "flow", defined as a divergenceless norm-bounded vector field, or equivalently a set of Planck-thickness "bit threads". The entanglement entropy of a boundary region is given by the maximum flux out of it of any flow, or equivalently the maximum number of bit threads that can emanate from it. The threads thus represent entanglement between points on the boundary, and naturally implement the holographic principle. As we explain, this new picture clarifies several conceptual puzzles surrounding the RT formula. We give flow-based proofs of strong subadditivity and related properties; unlike the ones based on minimal surfaces, these proofs correspond in a transparent manner to the properties' information-theoretic meanings. We also briefly discuss certain technical advantages that the flows offer over minimal surfaces. In a mathematical appendix, we review the max flow-min cut theorem on networks and on Riemannian manifolds, and prove in the network case that the set of max flows varies Lipshitz continuously in the network parameters.
Von Neumann's quantization of general relativity
Arbuzov, A. B.; Cherny, A. Yu.; Cirilo-Lombardo, D. J.; Nazmitdinov, R. G.; Han, Nguyen Suan; Pavlov, A. E.; Pervushin, V. N.; Zakharov, A. F.
2017-05-01
Von Neumann's procedure is applied to quantizing general relativity. Initial data for dynamical variables in the Planck epoch, where the Hubble parameter value coincided with the Planck mass are quantized. These initial data are defined in terms of the Fock orthogonal simplex in the tangent Minkowski spacetime and the Dirac conformal interval. The Einstein cosmological principle is used to average the logarithm of the determinant of the spatial metric over the spatial volume of the visible Universe. The splitting of general coordinate transformations into diffeomorphisms and transformations of the initial data is introduced. In accordance with von Neumann's procedure, the vacuum state is treated is a quantum ensemble that is degenerate in quantum numbers of nonvacuum states. The distribution of the vacuum state leads to the Casimir effect in gravidynamics in just the same way as in electrodynamics. The generating functional for perturbation theory in gravidynamics is found by solving the quantum energy constraint. The applicability range of gravidynamics is discussed along with the possibility of employing this theory to interpret modern observational data.
An accurate von Neumann's law for three-dimensional foams
Hilgenfeldt, Sascha; Kraynik, Andrew M.; Koehler, Stephan A.; Stone, Howard A.
2001-01-01
The diffusive coarsening of 2D soap froths is governed by von Neumann's law. A statistical version of this law for dry 3D foams has long been conjectured. A new derivation, based on a theorem by Minkowski, yields an explicit analytical von Neumann's law in 3D which is in very good agreement with
Minimum Moduli in Von Neumann Algebras | Gopalraj | Quaestiones ...
African Journals Online (AJOL)
Minimum Moduli in Von Neumann Algebras. Perumal Gopalraj, Anton Ströh. Abstract. In this paper we answer a question raised in [12] in the affirmative, namely that the essential minimum modulus of an element in a von. Neumann algebra, relative to any norm closed two-sided ideal, is equal to the minimum modulus of the ...
Entanglement branes in a two-dimensional string theory
Donnelly, William; Wong, Gabriel
2017-09-01
What is the meaning of entanglement in a theory of extended objects such as strings? To address this question we consider the spatial entanglement between two intervals in the Gross-Taylor model, the string theory dual to two-dimensional Yang-Mills theory at large N . The string diagrams that contribute to the entanglement entropy describe open strings with endpoints anchored to the entangling surface, as first argued by Susskind. We develop a canonical theory of these open strings, and describe how closed strings are divided into open strings at the level of the Hilbert space. We derive the modular Hamiltonian for the Hartle-Hawking state and show that the corresponding reduced density matrix describes a thermal ensemble of open strings ending on an object at the entangling surface that we call an entanglement brane, or E-brane.
Liu, Zhao; Bhatt, R N
2016-11-11
We investigate the disorder-driven phase transition from a fractional quantum Hall state to an Anderson insulator using quantum entanglement methods. We find that the transition is signaled by a sharp increase in the sensitivity of a suitably averaged entanglement entropy with respect to disorder-the magnitude of its disorder derivative appears to diverge in the thermodynamic limit. We also study the level statistics of the entanglement spectrum as a function of disorder. However, unlike the dramatic phase-transition signal in the entanglement entropy derivative, we find a gradual reduction of level repulsion only deep in the Anderson insulating phase.
Quantum Entanglement in Neural Network States
Deng, Dong-Ling; Li, Xiaopeng; Das Sarma, S.
2017-04-01
Machine learning, one of today's most rapidly growing interdisciplinary fields, promises an unprecedented perspective for solving intricate quantum many-body problems. Understanding the physical aspects of the representative artificial neural-network states has recently become highly desirable in the applications of machine-learning techniques to quantum many-body physics. In this paper, we explore the data structures that encode the physical features in the network states by studying the quantum entanglement properties, with a focus on the restricted-Boltzmann-machine (RBM) architecture. We prove that the entanglement entropy of all short-range RBM states satisfies an area law for arbitrary dimensions and bipartition geometry. For long-range RBM states, we show by using an exact construction that such states could exhibit volume-law entanglement, implying a notable capability of RBM in representing quantum states with massive entanglement. Strikingly, the neural-network representation for these states is remarkably efficient, in the sense that the number of nonzero parameters scales only linearly with the system size. We further examine the entanglement properties of generic RBM states by randomly sampling the weight parameters of the RBM. We find that their averaged entanglement entropy obeys volume-law scaling, and the meantime strongly deviates from the Page entropy of the completely random pure states. We show that their entanglement spectrum has no universal part associated with random matrix theory and bears a Poisson-type level statistics. Using reinforcement learning, we demonstrate that RBM is capable of finding the ground state (with power-law entanglement) of a model Hamiltonian with a long-range interaction. In addition, we show, through a concrete example of the one-dimensional symmetry-protected topological cluster states, that the RBM representation may also be used as a tool to analytically compute the entanglement spectrum. Our results uncover the
Quantum Entanglement in Neural Network States
Directory of Open Access Journals (Sweden)
Dong-Ling Deng
2017-05-01
Full Text Available Machine learning, one of today’s most rapidly growing interdisciplinary fields, promises an unprecedented perspective for solving intricate quantum many-body problems. Understanding the physical aspects of the representative artificial neural-network states has recently become highly desirable in the applications of machine-learning techniques to quantum many-body physics. In this paper, we explore the data structures that encode the physical features in the network states by studying the quantum entanglement properties, with a focus on the restricted-Boltzmann-machine (RBM architecture. We prove that the entanglement entropy of all short-range RBM states satisfies an area law for arbitrary dimensions and bipartition geometry. For long-range RBM states, we show by using an exact construction that such states could exhibit volume-law entanglement, implying a notable capability of RBM in representing quantum states with massive entanglement. Strikingly, the neural-network representation for these states is remarkably efficient, in the sense that the number of nonzero parameters scales only linearly with the system size. We further examine the entanglement properties of generic RBM states by randomly sampling the weight parameters of the RBM. We find that their averaged entanglement entropy obeys volume-law scaling, and the meantime strongly deviates from the Page entropy of the completely random pure states. We show that their entanglement spectrum has no universal part associated with random matrix theory and bears a Poisson-type level statistics. Using reinforcement learning, we demonstrate that RBM is capable of finding the ground state (with power-law entanglement of a model Hamiltonian with a long-range interaction. In addition, we show, through a concrete example of the one-dimensional symmetry-protected topological cluster states, that the RBM representation may also be used as a tool to analytically compute the entanglement spectrum. Our
Quantum entanglement in strong-field ionization
Majorosi, Szilárd; Benedict, Mihály G.; Czirják, Attila
2017-10-01
We investigate the time evolution of quantum entanglement between an electron, liberated by a strong few-cycle laser pulse, and its parent ion core. Since the standard procedure is numerically prohibitive in this case, we propose a method to quantify the quantum correlation in such a system: we use the reduced density matrices of the directional subspaces along the polarization of the laser pulse and along the transverse directions as building blocks for an approximate entanglement entropy. We present our results, based on accurate numerical simulations, in terms of several of these entropies, for selected values of the peak electric-field strength and the carrier-envelope phase difference of the laser pulse. The time evolution of the mutual entropy of the electron and the ion-core motion along the direction of the laser polarization is similar to our earlier results based on a simple one-dimensional model. However, taking into account also the dynamics perpendicular to the laser polarization reveals a surprisingly different entanglement dynamics above the laser intensity range corresponding to pure tunneling: the quantum entanglement decreases with time in the over-the-barrier ionization regime.
Quantum entanglement: theory and applications
Energy Technology Data Exchange (ETDEWEB)
Schuch, N.
2007-10-10
This thesis deals with various questions concerning the quantification, the creation, and the application of quantum entanglement. Entanglement arises due to the restriction to local operations and classical communication. We investigate how the notion of entanglement changes if additional restrictions in form of a superselection rule are imposed and show that they give rise to a new resource. We characterize this resource and demonstrate that it can be used to overcome the restrictions, very much as entanglement can overcome the restriction to local operations by teleportation. We next turn towards the optimal generation of resources. We show how squeezing can be generated as efficiently as possible from noisy squeezing operations supplemented by noiseless passive operations, and discuss the implications of this result to the optimal generation of entanglement. The difficulty in describing the behaviour of correlated quantum many-body systems is ultimately due to the complicated entanglement structure of multipartite states. Using quantum information techniques, we investigate the ground state properties of lattices of harmonic oscillators. We derive an exponential decay of correlations for gapped systems, compute the dependence of correlation length and gap, and investigate the notion of criticality by relating a vanishing energy gap to an algebraic decay of correlations. Recently, ideas from entanglement theory have been applied to the description of many-body systems. Matrix Product States (MPS), which have a particularly simple interpretation from the point of quantum information, perform extremely well in approximating the ground states of local Hamiltonians. It is generally believed that this is due to the fact that both ground states and MPS obey an entropic area law. We clarify the relation between entropy scaling laws and approximability by MPS, and in particular find that an area law does not necessarily imply approximability. Using the quantum
Clausius entropy for arbitrary bifurcate null surfaces
Baccetti, Valentina; Visser, Matt
2014-02-01
Jacobson’s thermodynamic derivation of the Einstein equations was originally applied only to local Rindler horizons. But at least some parts of that construction can usefully be extended to give meaningful results for arbitrary bifurcate null surfaces. As presaged in Jacobson’s original article, this more general construction sharply brings into focus the questions: is entropy objectively ‘real’? Or is entropy in some sense subjective and observer-dependent? These innocent questions open a Pandora’s box of often inconclusive debate. A consensus opinion, though certainly not universally held, seems to be that Clausius entropy (thermodynamic entropy, defined via a Clausius relation {\\rm{d}}S = \\unicode{x111} Q/T) should be objectively real, but that the ontological status of statistical entropy (Shannon or von Neumann entropy) is much more ambiguous, and much more likely to be observer-dependent. This question is particularly pressing when it comes to understanding Bekenstein entropy (black hole entropy). To perhaps further add to the confusion, we shall argue that even the Clausius entropy can often be observer-dependent. In the current article we shall conclusively demonstrate that one can meaningfully assign a notion of Clausius entropy to arbitrary bifurcate null surfaces—effectively defining a ‘virtual Clausius entropy’ for arbitrary ‘virtual (local) causal horizons’. As an application, we see that we can implement a version of the generalized second law (GSL) for this virtual Clausius entropy. This version of GSL can be related to certain (nonstandard) integral variants of the null energy condition. Because the concepts involved are rather subtle, we take some effort in being careful and explicit in developing our framework. In future work we will apply this construction to generalize Jacobson’s derivation of the Einstein equations.
Entanglement and area laws in weakly correlated gaussian states
Matera, Juan Mauricio; Rossignoli, Raúl Dante; Canosa, Norma B.
2012-01-01
We examine the evaluation of entanglement measures in weakly correlated gaussian states. It is shown that they can be expressed in terms of the singular values of a particular block of the generalized contraction matrix. This result enables to obtain in a simple way asymptotic expressions and related area laws for the entanglement entropy of bipartitions in pure states, as well as for the logarithmic negativity associated with bipartitions and also pairs of arbitrary subsystems. As illustrati...
Lai, Hsin-Hua; Yang, Kun; Bonesteel, N E
2013-11-22
We show the violation of the entanglement area law for bosonic systems with Bose surfaces. For bosonic systems with gapless factorized energy dispersions on an N(d) Cartesian lattice in d dimensions, e.g., the exciton Bose liquid in two dimensions, we explicitly show that a belt subsystem with width L preserving translational symmetry along d-1 Cartesian axes has leading entanglement entropy (N(d-1)/3)lnL. Using this result, the strong subadditivity inequality, and lattice symmetries, we bound the entanglement entropy of a rectangular subsystem from below and above showing a logarithmic violation of the area law. For subsystems with a single flat boundary, we also bound the entanglement entropy from below showing a logarithmic violation, and argue that the entanglement entropy of subsystems with arbitrary smooth boundaries are similarly bounded.
Von Neumann's impossibility proof: Mathematics in the service of rhetorics
Dieks, Dennis
2017-11-01
According to what has become a standard history of quantum mechanics, in 1932 von Neumann persuaded the physics community that hidden variables are impossible as a matter of principle, after which leading proponents of the Copenhagen interpretation put the situation to good use by arguing that the completeness of quantum mechanics was undeniable. This state of affairs lasted, so the story continues, until Bell in 1966 exposed von Neumann's proof as obviously wrong. The realization that von Neumann's proof was fallacious then rehabilitated hidden variables and made serious foundational research possible again. It is often added in recent accounts that von Neumann's error had been spotted almost immediately by Grete Hermann, but that her discovery was of no effect due to the dominant Copenhagen Zeitgeist. We shall attempt to tell a story that is more historically accurate and less ideologically charged. Most importantly, von Neumann never claimed to have shown the impossibility of hidden variables tout court, but argued that hidden-variable theories must possess a structure that deviates fundamentally from that of quantum mechanics. Both Hermann and Bell appear to have missed this point; moreover, both raised unjustified technical objections to the proof. Von Neumann's argument was basically that hidden-variables schemes must violate the ;quantum principle; that physical quantities are to be represented by operators in a Hilbert space. As a consequence, hidden-variables schemes, though possible in principle, necessarily exhibit a certain kind of contextuality. As we shall illustrate, early reactions to Bohm's theory are in agreement with this account. Leading physicists pointed out that Bohm's theory has the strange feature that pre-existing particle properties do not generally reveal themselves in measurements, in accordance with von Neumann's result. They did not conclude that the ;impossible was done; and that von Neumann had been shown wrong.
Stabilization of a scroll ring by a cylindrical Neumann boundary.
Paulau, P V; Löber, J; Engel, H
2013-12-01
We study the interaction of phase singularities with homogeneous Neumann boundaries in one, two, and three spatial dimensions for the complex Ginzburg-Landau equation. The existence of a boundary-induced drift attractor, well known for spiral waves in two spatial dimensions, is demonstrated for scroll waves in three spatial dimensions. We find that a cylindrical Neumann boundary can lock a scroll ring, thus preventing the collapse of its closed filament.
Nash y von Neumann: mundos posibles y juegos de lenguaje
Directory of Open Access Journals (Sweden)
Salazar , Boris
2004-06-01
Full Text Available Este ensayo emplea las nociones de juego de lenguaje y de equivalencia entre juegos para examinar la decisión de John Nash de no jugar el juego coalicional que propuso John von Neumann. El argumento central es que Nash concibió una clase de mundos posibles incompatible con la de von Neumann, y que en el origen de esa divergencia estarían sus distintas nociones de racionalidad.
Deformed Fredkin spin chain with extensive entanglement
Salberger, Olof; Udagawa, Takuma; Zhang, Zhao; Katsura, Hosho; Klich, Israel; Korepin, Vladimir
2017-06-01
We introduce a new spin chain which is a deformation of the Fredkin spin chain and has a phase transition between bounded and extensive entanglement entropy scaling. In this chain, spins have a local interaction of three nearest neighbors. The Hamiltonian is frustration-free and its ground state can be described analytically as a weighted superposition of Dyck paths that depends on a deformation parameter t. In the purely spin 1/2 case, whenever t\
Lechner, Joseph H.
1999-10-01
This report describes two classroom activities that help students visualize the abstract concept of entropy and apply the second law of thermodynamics to real situations. (i) A sealed "rainbow tube" contains six smaller vessels, each filled with a different brightly colored solution (low entropy). When the tube is inverted, the solutions mix together and react to form an amorphous precipitate (high entropy). The change from low entropy to high entropy is irreversible as long as the tube remains sealed. (ii) When U.S. currency is withdrawn from circulation, intact bills (low entropy) are shredded into small fragments (high entropy). Shredding is quick and easy; the reverse process is clearly nonspontaneous. It is theoretically possible, but it is time-consuming and energy-intensive, to reassemble one bill from a pile that contains fragments of hundreds of bills. We calculate the probability P of drawing pieces of only one specific bill from a mixture containing one pound of bills, each shredded into n fragments. This result can be related to Boltzmann's entropy formula S?=klnW.
Entanglement spectroscopy on a quantum computer
Johri, Sonika; Steiger, Damian S.; Troyer, Matthias
2017-11-01
We present a quantum algorithm to compute the entanglement spectrum of arbitrary quantum states. The interesting universal part of the entanglement spectrum is typically contained in the largest eigenvalues of the density matrix which can be obtained from the lower Renyi entropies through the Newton-Girard method. Obtaining the p largest eigenvalues (λ1>λ2⋯>λp ) requires a parallel circuit depth of O [p (λ1/λp) p] and O [p log(N )] qubits where up to p copies of the quantum state defined on a Hilbert space of size N are needed as the input. We validate this procedure for the entanglement spectrum of the topologically ordered Laughlin wave function corresponding to the quantum Hall state at filling factor ν =1 /3 . Our scaling analysis exposes the tradeoffs between time and number of qubits for obtaining the entanglement spectrum in the thermodynamic limit using finite-size digital quantum computers. We also illustrate the utility of the second Renyi entropy in predicting a topological phase transition and in extracting the localization length in a many-body localized system.
Quantum thermalization through entanglement in an isolated many-body system.
Kaufman, Adam M; Tai, M Eric; Lukin, Alexander; Rispoli, Matthew; Schittko, Robert; Preiss, Philipp M; Greiner, Markus
2016-08-19
Statistical mechanics relies on the maximization of entropy in a system at thermal equilibrium. However, an isolated quantum many-body system initialized in a pure state remains pure during Schrödinger evolution, and in this sense it has static, zero entropy. We experimentally studied the emergence of statistical mechanics in a quantum state and observed the fundamental role of quantum entanglement in facilitating this emergence. Microscopy of an evolving quantum system indicates that the full quantum state remains pure, whereas thermalization occurs on a local scale. We directly measured entanglement entropy, which assumes the role of the thermal entropy in thermalization. The entanglement creates local entropy that validates the use of statistical physics for local observables. Our measurements are consistent with the eigenstate thermalization hypothesis. Copyright © 2016, American Association for the Advancement of Science.
The Conditional Entropy Power Inequality for Bosonic Quantum Systems
DEFF Research Database (Denmark)
de Palma, Giacomo; Trevisan, Dario
2018-01-01
We prove the conditional Entropy Power Inequality for Gaussian quantum systems. This fundamental inequality determines the minimum quantum conditional von Neumann entropy of the output of the beam-splitter or of the squeezing among all the input states where the two inputs are conditionally...... achieved by a suitable sequence of quantum Gaussian input states. Our proof of the conditional Entropy Power Inequality is based on a new Stam inequality for the quantum conditional Fisher information and on the determination of the universal asymptotic behaviour of the quantum conditional entropy under...... the heat semigroup evolution. The beam-splitter and the squeezing are the central elements of quantum optics, and can model the attenuation, the amplification and the noise of electromagnetic signals. This conditional Entropy Power Inequality will have a strong impact in quantum information and quantum...
Invariant Correlation Entropy and Complexity of Quantum States
Sokolov, V V; Zelevinsky, V; Sokolov, Valentin V.; Zelevinsky, Vladimir
1998-01-01
We define correlational (von Neumann) entropy for an individual quantum state of a system whose time-independent hamiltonian contains random parameters and is treated as a member of a statistical ensemble. This entropy is representation independent and can be calculated as a trace functional of the density matrix which describes the system in its interaction with the noise source. We analyze perturbation theory in order to show the evolution from the pure state to the mixed one. Exactly solvable examples illustrate the use of correlational entropy as a measure of the degree of complexity in comparison with other available suggestions such as basis-dependent information entropy. It is shown in particular that a harmonic oscillator in a uniform field of random strength comes to a quasithermal equilibrium; we discuss the relation between effective temperature and canonical equilibrium temperature. The notion of correlational entropy is applied to a realistic numerical caculation in the framework of the nuclear s...
The Conditional Entropy Power Inequality for Bosonic Quantum Systems
De Palma, Giacomo; Trevisan, Dario
2018-01-01
We prove the conditional Entropy Power Inequality for Gaussian quantum systems. This fundamental inequality determines the minimum quantum conditional von Neumann entropy of the output of the beam-splitter or of the squeezing among all the input states where the two inputs are conditionally independent given the memory and have given quantum conditional entropies. We also prove that, for any couple of values of the quantum conditional entropies of the two inputs, the minimum of the quantum conditional entropy of the output given by the conditional Entropy Power Inequality is asymptotically achieved by a suitable sequence of quantum Gaussian input states. Our proof of the conditional Entropy Power Inequality is based on a new Stam inequality for the quantum conditional Fisher information and on the determination of the universal asymptotic behaviour of the quantum conditional entropy under the heat semigroup evolution. The beam-splitter and the squeezing are the central elements of quantum optics, and can model the attenuation, the amplification and the noise of electromagnetic signals. This conditional Entropy Power Inequality will have a strong impact in quantum information and quantum cryptography. Among its many possible applications there is the proof of a new uncertainty relation for the conditional Wehrl entropy.
Dynamics of Rényi entropy and applications in detecting quantum non-Markovianity
Song, Hongting; Mao, Yuanyuan
2017-09-01
Exploiting the master equations in the Lindblad form, we establish a sufficient and necessary condition for a Markovian dynamics to be unital. Based on this condition, we analyze the dynamical property of quantum Rényi entropy and propose a characterization of quantum non-Markovianity for unital dynamics in terms of Rényi entropy, which contains the previous criteria of non-Markovianity via von Neumann entropy and linear entropy as particular cases. The effectiveness of this measure in capturing the backflow of information from the environment is illustrated through several typical unital dynamics.
Von-Neumann and Beyond: Memristor Architectures
Naous, Rawan
2017-05-01
An extensive reliance on technology, an abundance of data, and increasing processing requirements have imposed severe challenges on computing and data processing. Moreover, the roadmap for scaling electronic components faces physical and reliability limits that hinder the utilization of the transistors in conventional systems and promotes the need for faster, energy-efficient, and compact nano-devices. This work thus capitalizes on emerging non-volatile memory technologies, particularly the memristor for steering novel design directives. Moreover, aside from the conventional deterministic operation, a temporal variability is encountered in the devices functioning. This inherent stochasticity is addressed as an enabler for endorsing the stochastic electronics field of study. We tackle this approach of design by proposing and verifying a statistical approach to modelling the stochastic memristors behaviour. This mode of operation allows for innovative computing designs within the approximate computing and beyond Von-Neumann domains. In the context of approximate computing, sacrificing functional accuracy for the sake of energy savings is proposed based on inherently stochastic electronic components. We introduce mathematical formulation and probabilistic analysis for Boolean logic operators and correspondingly incorporate them into arithmetic blocks. Gate- and system-level accuracy of operation is presented to convey configurability and the different effects that the unreliability of the underlying memristive components has on the intermediary and overall output. An image compression application is presented to reflect the efficiency attained along with the impact on the output caused by the relative precision quantification. In contrast, in neuromorphic structures the memristors variability is mapped onto abstract models of the noisy and unreliable brain components. In one approach, we propose using the stochastic memristor as an inherent source of variability in
Wang, Xin; Duan, Runyao
2017-11-01
We demonstrate the irreversibility of asymptotic entanglement manipulation under quantum operations that completely preserve the positivity of partial transpose (PPT), resolving a major open problem in quantum information theory. Our key tool is a new efficiently computable additive lower bound for the asymptotic relative entropy of entanglement with respect to PPT states, which can be used to evaluate the entanglement cost under local operations and classical communication (LOCC). We find that for any rank-two mixed state supporting on the 3 ⊗3 antisymmetric subspace, the amount of distillable entanglement by PPT operations is strictly smaller than one entanglement bit (ebit) while its entanglement cost under PPT operations is exactly one ebit. As a by-product, we find that for this class of states, both the Rains's bound and its regularization are strictly less than the asymptotic relative entropy of entanglement. So, in general, there is no unique entanglement measure for the manipulation of entanglement by PPT operations. We further show a computable sufficient condition for the irreversibility of entanglement distillation by LOCC (or PPT) operations.
Average subentropy, coherence and entanglement of random mixed quantum states
Energy Technology Data Exchange (ETDEWEB)
Zhang, Lin, E-mail: godyalin@163.com [Institute of Mathematics, Hangzhou Dianzi University, Hangzhou 310018 (China); Singh, Uttam, E-mail: uttamsingh@hri.res.in [Harish-Chandra Research Institute, Allahabad, 211019 (India); Pati, Arun K., E-mail: akpati@hri.res.in [Harish-Chandra Research Institute, Allahabad, 211019 (India)
2017-02-15
Compact expressions for the average subentropy and coherence are obtained for random mixed states that are generated via various probability measures. Surprisingly, our results show that the average subentropy of random mixed states approaches the maximum value of the subentropy which is attained for the maximally mixed state as we increase the dimension. In the special case of the random mixed states sampled from the induced measure via partial tracing of random bipartite pure states, we establish the typicality of the relative entropy of coherence for random mixed states invoking the concentration of measure phenomenon. Our results also indicate that mixed quantum states are less useful compared to pure quantum states in higher dimension when we extract quantum coherence as a resource. This is because of the fact that average coherence of random mixed states is bounded uniformly, however, the average coherence of random pure states increases with the increasing dimension. As an important application, we establish the typicality of relative entropy of entanglement and distillable entanglement for a specific class of random bipartite mixed states. In particular, most of the random states in this specific class have relative entropy of entanglement and distillable entanglement equal to some fixed number (to within an arbitrary small error), thereby hugely reducing the complexity of computation of these entanglement measures for this specific class of mixed states.
Entanglement of the quantum system with spin-spin coupling created by optical excitation
Fu, Chenghua
2017-12-01
In this paper, we investigate the quantum entanglement characteristics of the system consisting an intermediary molecule with an optically excited triplet and two bilateral spin-1/2 nucleons. The two nuclear spins both couple to the excitation state which is caused by a pulsed laser. We study the linear entropy and entangling power of the evolution operator acting on the product state of the system. We deduce the entangling power when the energy state has a uniform distribution, and we find that the entanglement of the system shows a certain stability. In this paper, several standard expressions are analyzed and calculated in detail, including the detailed solution for the quantum entropy as well as the calculation of the linear entropy and entangling power, which are based on this solution. In comparing the linear entropy and entangling power, we find that the latter is the average of the former. Subsequently, we present an alternative derivation of the evolution operator and find that the result is consistent with that of the traditional method. When the evolution operator acts on the average of the product states, the entangling power of the evolution operator presents a distinct changing trend.
Nuclear quadrupole resonance of spin 3/2 and entangled two-qubit states
Furman, G.; Goren, S. D.; Meerovich, V.; Sokolovsky, V.
2015-10-01
A single spin-3/2, possessing a quadrupole moment and placed in a non-uniform electric field, is isomorphic to a system of two spins of 1/2, which can be represented as two qubits. To create these qubits, the degeneracy of the energy levels is removed by applying two radio-frequency fields with different phases and directions. The properties of entanglement between two qubits are studied. We analyze the concurrence, the entropy of entanglement, and fluctuations of the entropy in the pure and mixed states. Concurrence and entropy of entanglement in a mixed state increase with decreasing temperature and approach to their values in a pure state. For a nucleus Cu in high temperature superconductor {{YBa}}2{{Cu}}3{{{O}}}7-δ , the estimation of the temperature, at which entanglement appears, gives T ≤slant 0.8 μK.
Quantum Entanglement Swapping between Two Multipartite Entangled States.
Su, Xiaolong; Tian, Caixing; Deng, Xiaowei; Li, Qiang; Xie, Changde; Peng, Kunchi
2016-12-09
Quantum entanglement swapping is one of the most promising ways to realize the quantum connection among local quantum nodes. In this Letter, we present an experimental demonstration of the entanglement swapping between two independent multipartite entangled states, each of which involves a tripartite Greenberger-Horne-Zeilinger (GHZ) entangled state of an optical field. The entanglement swapping is implemented deterministically by means of a joint measurement on two optical modes coming from the two multipartite entangled states respectively and the classical feedforward of the measurement results. After entanglement swapping the two independent multipartite entangled states are merged into a large entangled state in which all unmeasured quantum modes are entangled. The entanglement swapping between a tripartite GHZ state and an Einstein-Podolsky-Rosen entangled state is also demonstrated and the dependence of the resultant entanglement on transmission loss is investigated. The presented experiment provides a feasible technical reference for constructing more complicated quantum networks.
Regularity of spectral fractional Dirichlet and Neumann problems
DEFF Research Database (Denmark)
Grubb, Gerd
2016-01-01
Consider the fractional powers and of the Dirichlet and Neumann realizations of a second-order strongly elliptic differential operator A on a smooth bounded subset Ω of . Recalling the results on complex powers and complex interpolation of domains of elliptic boundary value problems by Seeley...... in the 1970's, we demonstrate how they imply regularity properties in full scales of -Sobolev spaces and Hölder spaces, for the solutions of the associated equations. Extensions to nonsmooth situations for low values of s are derived by use of recent results on -calculus. We also include an overview...... of the various Dirichlet- and Neumann-type boundary problems associated with the fractional Laplacian....
Excess Entropy Production in Quantum System: Quantum Master Equation Approach
Nakajima, Satoshi; Tokura, Yasuhiro
2017-10-01
For open systems described by the quantum master equation (QME), we investigate the excess entropy production under quasistatic operations between nonequilibrium steady states. The average entropy production is composed of the time integral of the instantaneous steady entropy production rate and the excess entropy production. We propose to define average entropy production rate using the average energy and particle currents, which are calculated by using the full counting statistics with QME. The excess entropy production is given by a line integral in the control parameter space and its integrand is called the Berry-Sinitsyn-Nemenman (BSN) vector. In the weakly nonequilibrium regime, we show that BSN vector is described by ln \\breve{ρ }_0 and ρ _0 where ρ _0 is the instantaneous steady state of the QME and \\breve{ρ }_0 is that of the QME which is given by reversing the sign of the Lamb shift term. If the system Hamiltonian is non-degenerate or the Lamb shift term is negligible, the excess entropy production approximately reduces to the difference between the von Neumann entropies of the system. Additionally, we point out that the expression of the entropy production obtained in the classical Markov jump process is different from our result and show that these are approximately equivalent only in the weakly nonequilibrium regime.
Excess Entropy Production in Quantum System: Quantum Master Equation Approach
Nakajima, Satoshi; Tokura, Yasuhiro
2017-12-01
For open systems described by the quantum master equation (QME), we investigate the excess entropy production under quasistatic operations between nonequilibrium steady states. The average entropy production is composed of the time integral of the instantaneous steady entropy production rate and the excess entropy production. We propose to define average entropy production rate using the average energy and particle currents, which are calculated by using the full counting statistics with QME. The excess entropy production is given by a line integral in the control parameter space and its integrand is called the Berry-Sinitsyn-Nemenman (BSN) vector. In the weakly nonequilibrium regime, we show that BSN vector is described by ln \\breve{ρ }_0 and ρ _0 where ρ _0 is the instantaneous steady state of the QME and \\breve{ρ }_0 is that of the QME which is given by reversing the sign of the Lamb shift term. If the system Hamiltonian is non-degenerate or the Lamb shift term is negligible, the excess entropy production approximately reduces to the difference between the von Neumann entropies of the system. Additionally, we point out that the expression of the entropy production obtained in the classical Markov jump process is different from our result and show that these are approximately equivalent only in the weakly nonequilibrium regime.
Entropic Entanglement: Information Prison Break
Directory of Open Access Journals (Sweden)
Alexander Y. Yosifov
2017-01-01
Full Text Available We argue that certain nonviolent local quantum field theory (LQFT modification considered at the global horizon (r=2M of a static spherically symmetric black hole can lead to adiabatic leakage of quantum information in the form of Hawking particles. The source of the modification is (i smooth at r=2M and (ii rapidly vanishing at r≫2M. Furthermore, we restore the unitary evolution by introducing extra quanta which departs slightly from the generic Hawking emission without changing the experience of an infalling observer (no drama. Also, we suggest that a possible interpretation of the Bekenstein-Hawking bound as entanglement entropy may yield a nonsingular dynamical horizon behavior described by black hole thermodynamics. Hence, by treating gravity as a field theory and considering its coupling to the matter fields in the Minkowski vacuum, we derive the conjectured fluctuations of the background geometry of a black hole.
Stationary solutions and Neumann boundary conditions in the Sivashinsky equation.
Denet, Bruno
2006-09-01
New stationary solutions of the (Michelson) Sivashinsky equation of premixed flames are obtained numerically in this paper. Some of these solutions, of the bicoalescent type recently described by Guidi and Marchetti, are stable with Neumann boundary conditions. With these boundary conditions, the time evolution of the Sivashinsky equation in the presence of a moderate white noise is controlled by jumps between stationary solutions.
On Neumann and Poincare problems for Laplace equation
Ryazanov, Vladimir
2017-09-01
It is proved the existence of nonclassical solutions of the Neumann problem for the harmonic functions in the Jordan rectifiable domains with arbitrary measurable boundary distributions of normal derivatives. The same is stated for a special case of the Poincare problem on directional derivatives. Moreover, it is shown that the spaces of the found solutions have the infinite dimension.
A Duality Approach for the Boundary Variation of Neumann Problems
DEFF Research Database (Denmark)
Bucur, Dorin; Varchon, Nicolas
2002-01-01
In two dimensions, we study the stability of the solution of an elliptic equation with Neumann boundary conditions for nonsmooth perturbations of the geometric domain. Using harmonic conjugates, we relate this problem to the shape stability of the solution of an elliptic equation with Dirichlet...
A duality approach or the boundary variation of Neumann problems
DEFF Research Database (Denmark)
Bucur, D.; Varchon, Nicolas
2002-01-01
In two dimensions, we study the stability of the solution of an elliptic equation with Neumann boundary conditions for nonsmooth perturbations of the geometric domain. Using harmonic conjugates, we relate this problem to the shape stability of the solution of an elliptic equation with Dirichlet...
The degenerate C. Neumann system I: symmetry reduction and convexity
Dullin, H.R.; Hanssmann, H.|info:eu-repo/dai/nl/107757435
2012-01-01
The C. Neumann system describes a particle on the sphere Sn under the influence of a potential that is a quadratic form. We study the case that the quadratic form has ` +1 distinct eigenvalues with multiplicity. Each group of m equal eigenvalues gives rise to an O(m )-symmetry in configuration
Nonclassicality versus entanglement in a noncommutative space
Dey, Sanjib; Fring, Andreas; Hussin, Véronique
2017-01-01
Nonclassicality is an interesting property of light having applications in many different contexts of quantum optics, quantum information and computation. Nonclassical states produce substantial amount of reduced noise in optical communications. Furthermore, they often behave as sources of entangled quantum states, which are the most elementary requirement for quantum teleportation. We study various nonclassical properties of coherent states and Schrödinger cat states in a setting of noncommutative space resulting from the generalized uncertainty relation, first, in a complete analytical fashion and, later, by computing their entanglement entropies, which in turn provide supporting arguments behind our analytical results. By using standard theoretical frameworks, they are shown to produce considerably improved squeezing and nonclassicality and, hence, significantly higher amount of entanglement in comparison to the usual quantum mechanical models. Both the nonclassicality and the entanglement can be enhanced further by increasing the noncommutativity of the underlying space. In addition, we find as a by-product some rare explicit minimum uncertainty quadrature and number squeezed states, i.e., ideal squeezed states.
Relating Out-of-Time-Order Correlations to Entanglement via Multiple-Quantum Coherences
Gärttner, Martin; Hauke, Philipp; Rey, Ana Maria
2018-01-01
Out-of-time-order correlations (OTOCs) characterize the scrambling, or delocalization, of quantum information over all the degrees of freedom of a system and thus have been proposed as a proxy for chaos in quantum systems. Recent experimental progress in measuring OTOCs calls for a more thorough understanding of how these quantities characterize complex quantum systems, most importantly in terms of the buildup of entanglement. Although a connection between OTOCs and entanglement entropy has been derived, the latter only quantifies entanglement in pure systems and is hard to access experimentally. In this work, we formally demonstrate that the multiple-quantum coherence spectra, a specific family of OTOCs well known in NMR, can be used as an entanglement witness and as a direct probe of multiparticle entanglement. Our results open a path to experimentally testing the fascinating idea that entanglement is the underlying glue that links thermodynamics, statistical mechanics, and quantum gravity.
Interface contributions to topological entanglement in abelian Chern-Simons theory
Fliss, Jackson R.; Wen, Xueda; Parrikar, Onkar; Hsieh, Chang-Tse; Han, Bo; Hughes, Taylor L.; Leigh, Robert G.
2017-09-01
We study the entanglement entropy between (possibly distinct) topological phases across an interface using an Abelian Chern-Simons description with topological boundary conditions (TBCs) at the interface. From a microscopic point of view, these TBCs correspond to turning on particular gapping interactions between the edge modes across the interface. However, in studying entanglement in the continuum Chern-Simons description, we must confront the problem of non-factorization of the Hilbert space, which is a standard property of gauge theories. We carefully define the entanglement entropy by using an extended Hilbert space construction directly in the continuum theory. We show how a given TBC isolates a corresponding gauge invariant state in the extended Hilbert space, and hence compute the resulting entanglement entropy. We find that the sub-leading correction to the area law remains universal, but depends on the choice of topological boundary conditions. This agrees with the microscopic calculation of [1]. Additionally, we provide a replica path integral calculation for the entropy. In the case when the topological phases across the interface are taken to be identical, our construction gives a novel explanation of the equivalence between the left-right entanglement of (1+1)d Ishibashi states and the spatial entanglement of (2+1)d topological phases.
Thermality and excited state Rényi entropy in two-dimensional CFT
Energy Technology Data Exchange (ETDEWEB)
Lin, Feng-Li [Department of Physics, National Taiwan Normal University,Taipei 11677, Taiwan (China); Wang, Huajia [Department of Physics, University of Illinois,Urbana-Champaign, IL 61801 (United States); Zhang, Jia-ju [Dipartimento di Fisica, Università degli Studi di Milano-Bicocca,Piazza della Scienza 3, I-20126 Milano (Italy); Theoretical Physics Division, Institute of High Energy Physics, Chinese Academy of Sciences,19B Yuquan Rd, Beijing 100049 (China); Theoretical Physics Center for Science Facilities, Chinese Academy of Sciences,19B Yuquan Rd, Beijing 100049 (China)
2016-11-21
We evaluate one-interval Rényi entropy and entanglement entropy for the excited states of two-dimensional conformal field theory (CFT) on a cylinder, and examine their differences from the ones for the thermal state. We assume the interval to be short so that we can use operator product expansion (OPE) of twist operators to calculate Rényi entropy in terms of sum of one-point functions of OPE blocks. We find that the entanglement entropy for highly excited state and thermal state behave the same way after appropriate identification of the conformal weight of the state with the temperature. However, there exists no such universal identification for the Rényi entropy in the short-interval expansion. Therefore, the highly excited state does not look thermal when comparing its Rényi entropy to the thermal state one. As the Rényi entropy captures the higher moments of the reduced density matrix but the entanglement entropy only the average, our results imply that the emergence of thermality depends on how refined we look into the entanglement structure of the underlying pure excited state.
Entangled de Sitter from stringy axionic Bell pair I: an analysis using Bunch-Davies vacuum
Choudhury, Sayantan; Panda, Sudhakar
2018-01-01
In this work, we study the quantum entanglement and compute entanglement entropy in de Sitter space for a bipartite quantum field theory driven by an axion originating from Type IIB string compactification on a Calabi-Yau three fold (CY^3) and in the presence of an NS5 brane. For this computation, we consider a spherical surface S^2, which divides the spatial slice of de Sitter (dS_4) into exterior and interior sub-regions. We also consider the initial choice of vacuum to be Bunch-Davies state. First we derive the solution of the wave function of the axion in a hyperbolic open chart by constructing a suitable basis for Bunch-Davies vacuum state using Bogoliubov transformation. We then derive the expression for density matrix by tracing over the exterior region. This allows us to compute the entanglement entropy and Rényi entropy in 3+1 dimension. Furthermore, we quantify the UV-finite contribution of the entanglement entropy which contain the physics of long range quantum correlations of our expanding universe. Finally, our analysis complements the necessary condition for generating non-vanishing entanglement entropy in primordial cosmology due to the axion.
Quantum Entanglement and Teleportation
Yates, Brent R.
2011-01-01
Even Einstein has to be wrong sometimes. However, when Einstein was wrong he created a 70 year debate about the strange behavior of quantum mechanics. His debate helped prove topics such as the indeterminacy of particle states, quantum entanglement, and a rather clever use of quantum entanglement known as quantum teleportation.
Facets of tripartite entanglement
Indian Academy of Sciences (India)
Tripartite entangled states of systems 1, 2 and 3 involving nonorthogonal states are used to reveal two hitherto unexplored quantum effects. The ﬁrst shows that kinematic entanglement between the states of 1 and 2 can affect the result of dynamical interaction between 2 and 3, though 1 and 2 may be spatially separated so ...
Facets of tripartite entanglement
Indian Academy of Sciences (India)
Abstract. Tripartite entangled states of systems 1, 2 and 3 involving nonorthogonal states are used to reveal two hitherto unexplored quantum effects. The first shows that kinematic entanglement between the states of 1 and 2 can affect the result of dynamical interaction between 2 and 3, though. 1 and 2 may be spatially ...
Consistent histories: Description of a world with increasing entropy
Directory of Open Access Journals (Sweden)
C. H. Woo
2000-07-01
Full Text Available A distinction is made between two kinds of consistent histories: (1 robust histories consistent by virtue of decoherence, and (2 verifiable histories consistent through the existence of accessible records. It is events in verifiable histories which describe amplified quantum fluctuations. If the consistent-histories formalism is to improve on the Copenhagen interpretation by providing a self-contained quantum representation of the quasi-classical world, the appropriate quantum state must track closely all macroscopic phenomena, and the von Neumann entropy of that quantum state ought to change in the same direction as the statistical entropy of the macro-world. Since the von Neumann entropy tends to decrease under successive branchings, the evolution of an entropy-increasing quasi-classical world is not described by a process of branchings only: mergings of previously separate histories must also occur. As a consequence, the number of possible quasi-classical worlds does not have to grow indefinitely as in the many-world picture.
The Entropy-Based Quantum Metric
Directory of Open Access Journals (Sweden)
Roger Balian
2014-07-01
Full Text Available The von Neumann entropy S( D ^ generates in the space of quantum density matrices D ^ the Riemannian metric ds2 = −d2S( D ^ , which is physically founded and which characterises the amount of quantum information lost by mixing D ^ and D ^ + d D ^ . A rich geometric structure is thereby implemented in quantum mechanics. It includes a canonical mapping between the spaces of states and of observables, which involves the Legendre transform of S( D ^ . The Kubo scalar product is recovered within the space of observables. Applications are given to equilibrium and non equilibrium quantum statistical mechanics. There the formalism is specialised to the relevant space of observables and to the associated reduced states issued from the maximum entropy criterion, which result from the exact states through an orthogonal projection. Von Neumann’s entropy specialises into a relevant entropy. Comparison is made with other metrics. The Riemannian properties of the metric ds2 = −d2S( D ^ are derived. The curvature arises from the non-Abelian nature of quantum mechanics; its general expression and its explicit form for q-bits are given, as well as geodesics.
Krenn, Mario; Hochrainer, Armin; Lahiri, Mayukh; Zeilinger, Anton
2017-02-01
Quantum entanglement is one of the most prominent features of quantum mechanics and forms the basis of quantum information technologies. Here we present a novel method for the creation of quantum entanglement in multipartite and high-dimensional systems. The two ingredients are (i) superposition of photon pairs with different origins and (ii) aligning photons such that their paths are identical. We explain the experimentally feasible creation of various classes of multiphoton entanglement encoded in polarization as well as in high-dimensional Hilbert spaces—starting only from nonentangled photon pairs. For two photons, arbitrary high-dimensional entanglement can be created. The idea of generating entanglement by path identity could also apply to quantum entities other than photons. We discovered the technique by analyzing the output of a computer algorithm. This shows that computer designed quantum experiments can be inspirations for new techniques.
Information geometry of entanglement renormalization for free quantum fields
Energy Technology Data Exchange (ETDEWEB)
Molina-Vilaplana, J. [Universidad Politécnica de Cartagena,C/Dr Fleming S/N 30202, Cartagena (Spain)
2015-09-01
We provide an explicit connection between the differential generation of entanglement entropy in a tensor network representation of the ground states of two field theories, and a geometric description of these states based on the Fisher information metric. We show how the geometrical description remains invariant despite there is an irreducible gauge freedom in the definition of the tensor network. The results might help to understand how spacetimes may emerge from distributions of quantum states, or more concretely, from the structure of the quantum entanglement concomitant to those distributions.
An Information Geometric Analysis of Entangled Continuous Variable Quantum Systems
Energy Technology Data Exchange (ETDEWEB)
Kim, D-H [Institute for the Early Universe, Ewha Womans University, Seoul 120-750 (Korea, Republic of); Ali, S A [Department of Physics, State University of New York at Albany, 1400 Washington Avenue, Albany, NY 12222 (United States); Cafaro, C; Mancini, S [School of Science and Technology, Physics Division, University of Camerino, I-62032 Camerino (Italy)
2011-07-08
In this work, using information geometric (IG) techniques, we investigate the effects of micro-correlations on the evolution of maximal probability paths on statistical manifolds induced by systems whose microscopic degrees of freedom are Gaussian distributed. Analytical estimates of the information geometric entropy (IGE) as well as the IG analogue of the Lyapunov exponents are presented. It is shown that the entanglement duration is related to the scattering potential and incident particle energies. Finally, the degree of entanglement generated by an s-wave scattering event between minimum uncertainty wave-packets is computed in terms of the purity of the system.
Neumann spectral problem in a domain with very corrugated boundary
Cardone, Giuseppe; Khrabustovskyi, Andrii
2015-09-01
Let Ω ⊂Rn be a bounded domain. We perturb it to a domain Ωε attaching a family of small protuberances with "room-and-passage"-like geometry (ε > 0 is a small parameter). Peculiar spectral properties of Neumann problems in so perturbed domains were observed for the first time by R. Courant and D. Hilbert. We study the case, when the number of protuberances tends to infinity as ε → 0 and they are ε-periodically distributed along a part of ∂Ω. Our goal is to describe the behavior of the spectrum of the operator Aε = -(ρε) - 1ΔΩε, where ΔΩε is the Neumann Laplacian in Ωε, and the positive function ρε is equal to 1 in Ω. We prove that the spectrum of Aε converges as ε → 0 to the "spectrum" of a certain boundary value problem for the Neumann Laplacian in Ω with boundary conditions containing the spectral parameter in a nonlinear manner. Its eigenvalues may accumulate to a finite point.
An Introduction to Entanglement Theory
Markham, Damian J. H.
2008-04-01
We introduce the theory of entanglement intended for an audience of physicists, computer scientists and mathematicians not necessarily having a background in quantum mechanics. We cover the main concepts of entanglement theory such as separability, entanglement witnesses, LOCC and entanglement measures. Along the way we will see many interesting questions arise spanning mathematics, physics and information science amongst other disciplines.
Quantifying and exploiting entanglement
Ali Khan, Irfan
The aim of this work is to explore the characterization of various entangled parameters of the two-photon state that is created in the process of spontaneous parametric down-conversion, as well as to investigate the potential application of these two-photon states to quantum communication and quantum information processing. The parameters fall into two natural divisions, the discrete-variable and continuous-variable regimes. Polarization-correlated photon pairs are used to explore the discrete-variable regime. Using these polarization-correlated photon pairs we investigate phase-covariant quantum cloning, sum-variance entanglement measures, and unambiguous state-discrimination. Phase-covariant quantum cloning is experimentally demonstrated to provide higher cloning fidelity than a universal quantum cloner. The simplicity of the practical implementation of this cloning method makes this cloner a useful addition to the quantum information and communication toolbox. Next, it is experimentally demonstrated that three, concatenating, sum-variance entanglement measures possess higher sensitivities than the popular Bell entanglement measure, while each requires fewer measurements than a Bell measurement to obtain. Finally, it is demonstrated that unambiguous state-discrimination of nonorthogonal, bipartite entangled-states involves an analogous physical mechanism to that of entanglement distillation of bipartite entangled states. This physical mechanism is the basis of a two-qudit, three-party secret sharing protocol. In the continuous variable regime, two-photon position-momentum entanglement and two-photon time-energy entanglement is explored. Entanglement between discrete regions of space (pixels) is demonstrated using transverse momentum and position entanglement. Each photon is mapped onto as many as six pixels, where each pixel represents one level of a qudit state. Next, the number of information eigenmodes K of time-energy entanglement is investigated. Explicit
Long-range entanglement is necessary for a topological storage of quantum information.
Kim, Isaac H
2013-08-23
A general inequality between entanglement entropy and a number of topologically ordered states is derived, even without using the properties of the parent Hamiltonian or the formalism of topological quantum field theory. Given a quantum state |ψ], we obtain an upper bound on the number of distinct states that are locally indistinguishable from |ψ]. The upper bound is determined only by the entanglement entropy of some local subsystems. As an example, we show that log N≤2γ for a large class of topologically ordered systems on a torus, where N is the number of topologically protected states and γ is the constant subcorrection term of the entanglement entropy. We discuss applications to quantum many-body systems that do not have any low-energy topological quantum field theory description, as well as tradeoff bounds for general quantum error correcting codes.
More on the rainbow chain: entanglement, space-time geometry and thermal states
Rodríguez-Laguna, Javier; Dubail, Jérôme; Ramírez, Giovanni; Calabrese, Pasquale; Sierra, Germán
2017-04-01
The rainbow chain is an inhomogenous exactly solvable local spin model that, in its ground state, displays a half-chain entanglement entropy growing linearly with the system size. Although many exact results about the rainbow chain are known, the structure of the underlying quantum field theory has not yet been unraveled. Here we show that the universal scaling features of this model are captured by a massless Dirac fermion in a curved space-time with constant negative curvature R = -h 2 (h is the amplitude of the inhomogeneity). This identification allows us to use recently developed techniques to study inhomogeneous conformal systems and to analytically characterise the entanglement entropies of more general bipartitions. These results are carefully tested against exact numerical calculations. Finally, we study the entanglement entropies of the rainbow chain in thermal states, and find that there is a non-trivial interplay between the rainbow effective temperature T R and the physical temperature T.
Hierarchies of geometric entanglement
Blasone, M.; Dell'Anno, F.; de Siena, S.; Illuminati, F.
2008-06-01
We introduce a class of generalized geometric measures of entanglement. For pure quantum states of N elementary subsystems, they are defined as the distances from the sets of K -separable states (K=2,…,N) . The entire set of generalized geometric measures provides a quantification and hierarchical ordering of the different bipartite and multipartite components of the global geometric entanglement, and allows discrimination among the different contributions. The extended measures are applied to the study of entanglement in different classes of N -qubit pure states. These classes include W and Greenberger-Horne-Zeilinger (GHZ) states, and their symmetric superpositions; symmetric multimagnon states; cluster states; and, finally, asymmetric generalized W -like superposition states. We discuss in detail a general method for the explicit evaluation of the multipartite components of geometric entanglement, and we show that the entire set of geometric measures establishes an ordering among the different types of bipartite and multipartite entanglement. In particular, it determines a consistent hierarchy between GHZ and W states, clarifying the original result of Wei and Goldbart that W states possess a larger global entanglement than GHZ states. Furthermore, we show that all multipartite components of geometric entanglement in symmetric states obey a property of self-similarity and scale invariance with the total number of qubits and the number of qubits per party.
Entanglement Growth in Quench Dynamics with Variable Range Interactions
Directory of Open Access Journals (Sweden)
J. Schachenmayer
2013-09-01
Full Text Available Studying entanglement growth in quantum dynamics provides both insight into the underlying microscopic processes and information about the complexity of the quantum states, which is related to the efficiency of simulations on classical computers. Recently, experiments with trapped ions, polar molecules, and Rydberg excitations have provided new opportunities to observe dynamics with long-range interactions. We explore nonequilibrium coherent dynamics after a quantum quench in such systems, identifying qualitatively different behavior as the exponent of algebraically decaying spin-spin interactions in a transverse Ising chain is varied. Computing the buildup of bipartite entanglement as well as mutual information between distant spins, we identify linear growth of entanglement entropy corresponding to propagation of quasiparticles for shorter-range interactions, with the maximum rate of growth occurring when the Hamiltonian parameters match those for the quantum phase transition. Counterintuitively, the growth of bipartite entanglement for long-range interactions is only logarithmic for most regimes, i.e., substantially slower than for shorter-range interactions. Experiments with trapped ions allow for the realization of this system with a tunable interaction range, and we show that the different phenomena are robust for finite system sizes and in the presence of noise. These results can act as a direct guide for the generation of large-scale entanglement in such experiments, towards a regime where the entanglement growth can render existing classical simulations inefficient.
Entanglement distribution and quantum discord
Streltsov, Alexander; Kampermann, Hermann; Bruß, Dagmar
2016-01-01
Establishing entanglement between distant parties is one of the most important problems of quantum technology, since long-distance entanglement is an essential part of such fundamental tasks as quantum cryptography or quantum teleportation. In this lecture we review basic properties of entanglement and quantum discord, and discuss recent results on entanglement distribution and the role of quantum discord therein. We also review entanglement distribution with separable states, and discuss imp...
Quantifying entanglement resources
Eltschka, Christopher; Siewert, Jens
2014-10-01
We present an overview of the quantitative theory of single-copy entanglement in finite-dimensional quantum systems. In particular we emphasize the point of view that different entanglement measures quantify different types of resources, which leads to a natural interdependence of entanglement classification and quantification. Apart from the theoretical basis, we outline various methods for obtaining quantitative results on arbitrary mixed states. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘50 years of Bell’s theorem’.
Characterizing Genuine Multilevel Entanglement
Kraft, Tristan; Ritz, Christina; Brunner, Nicolas; Huber, Marcus; Gühne, Otfried
2018-02-01
Entanglement of high-dimensional quantum systems has become increasingly important for quantum communication and experimental tests of nonlocality. However, many effects of high-dimensional entanglement can be simulated by using multiple copies of low-dimensional systems. We present a general theory to characterize those high-dimensional quantum states for which the correlations cannot simply be simulated by low-dimensional systems. Our approach leads to general criteria for detecting multilevel entanglement in multiparticle quantum states, which can be used to verify these phenomena experimentally.
Renyi entropies for classical string-net models
Hermanns, M.; Trebst, S.
2014-05-01
In quantum mechanics, string-net condensed states—a family of prototypical states exhibiting nontrivial topological order—can be classified via their long-range entanglement properties, in particular, topological corrections to the prevalent area law of the entanglement entropy. Here we consider classical analogs of such string-net models whose partition function is given by an equal-weight superposition of classical string-net configurations. Our analysis of the Shannon and Renyi entropies for a bipartition of a given system reveals that the prevalent volume law for these classical entropies is augmented by subleading topological corrections that are intimately linked to the anyonic theories underlying the construction of the classical models. We determine the universal values of these topological corrections for a number of underlying anyonic theories including SU(2)k,SU(N)1, and SU(N)2 theories.
Kruglikov, Boris; Rypdal, Martin
2005-01-01
The topological entropy of piecewise affine maps is studied. It is shown that singularities may contribute to the entropy only if there is angular expansion and we bound the entropy via the expansion rates of the map. As a corollary we deduce that non-expanding conformal piecewise affine maps have zero topological entropy. We estimate the entropy of piecewise affine skew-products. Examples of abnormal entropy growth are provided.
DEFF Research Database (Denmark)
Ateniese, Giuseppe; Dagdelen, Özgür; Damgård, Ivan Bjerre
2012-01-01
Entangled cloud storage enables a set of clients {P_i} to “entangle” their files {f_i} into a single clew c to be stored by a (potentially malicious) cloud provider S. The entanglement makes it impossible to modify or delete significant part of the clew without affecting all files in c. A clew...... keeps the files in it private but still lets each client P_i recover his own data by interacting with S; no cooperation from other clients is needed. At the same time, the cloud provider is discouraged from altering or overwriting any significant part of c as this will imply that none of the clients can...... recover their files. We provide theoretical foundations for entangled cloud storage, introducing the notion of an entangled encoding scheme that guarantees strong security requirements capturing the properties above. We also give a concrete construction based on privacy-preserving polynomial interpolation...
Multipartite Entanglement and Firewalls
Luo, Shengqiao; Albrecht, Andreas
2016-01-01
Black holes offer an exciting area to explore the nature of quantum gravity. The classic work on Hawking radiation indicates that black holes should decay via quantum effects, but our ideas about how this might work at a technical level are incomplete. Recently Almheiri-Marolf-Polchinski-Sully (AMPS) have noted an apparent paradox in reconciling fundamental properties of quantum mechanics with standard beliefs about black holes. One way to resolve the paradox is to postulate the existence of a "firewall" inside the black hole horizon which prevents objects from falling smoothly toward the singularity. A fundamental limitation on the behavior of quantum entanglement known as "monogamy" plays a key role in the AMPS argument. Our goal is to study and apply many-body entanglement theory to consider the entanglement among different parts of Hawking radiation and black holes. Using the multipartite entanglement measure called negativity, we identify an example which could change the AMPS accounting of quantum entan...
Entanglement in neutrino oscillations
Energy Technology Data Exchange (ETDEWEB)
Blasone, M.; Dell' Anno, F.; De Siena, S.; Illuminati, F. [Universita degli Studi di Salerno Via Ponte don Melillon, Dipt. di Matematica e Informatica, Fisciano SA (Italy); INFN Sezione di Napoli, Gruppo collegato di Salerno - Baronissi SA (Italy); Dell' Anno, F.; De Siena, S.; Illuminati, F. [CNR-INFM Coherentia - Napoli (Italy); Blasone, M. [ISI Foundation for Scientific Interchange, Torino (Italy)
2009-03-15
Flavor oscillations in elementary particle physics are related to multimode entanglement of single-particle states. We show that mode entanglement can be expressed in terms of flavor transition probabilities, and therefore that single-particle entangled states acquire a precise operational characterization in the context of particle mixing. We treat in detail the physically relevant cases of two- and three-flavor neutrino oscillations, including the effective measure of CP violation. We discuss experimental schemes for the transfer of the quantum information encoded in single-neutrino states to spatially delocalized two-flavor charged-lepton states, thus showing, at least in principle, that single-particle entangled states of neutrino mixing are legitimate physical resources for quantum information tasks. (authors)
Damped driven coupled oscillators: entanglement, decoherence and the classical limit
Energy Technology Data Exchange (ETDEWEB)
Mancilla, R D Guerrero; Rey-Gonzalez, R R; Fonseca-Romero, K M [Grupo de Optica e Informacion Cuantica, Departamento de Fisica, Universidad Nacional de Colombia, Bogota (Colombia)], E-mail: rdguerrerom@unal.edu.co, E-mail: rrreyg@unal.edu.co, E-mail: kmfonsecar@unal.edu.co
2009-03-13
We investigate the quantum-classical border, the entanglement and decoherence of an analytically solvable model, comprising a first subsystem (a harmonic oscillator) coupled to a driven and damped second subsystem (another harmonic oscillator). We choose initial states whose dynamics is confined to a couple of two-level systems, and show that the maximum value of entanglement between the two subsystems, as measured by concurrence, depends on the dissipation rate to the coupling-constant ratio and the initial state. While in a related model the entropy of the first subsystem (a two-level system) never grows appreciably (for large dissipation rates), in our model it reaches a maximum before decreasing. Although both models predict small values of entanglement and dissipation, for fixed times of the order of the inverse of the coupling constant and large dissipation rates, these quantities decrease faster, as a function of the ratio of the dissipation rate to the coupling constant, in our model.
Comments on entanglement negativity in holographic field theories
Rangamani, Mukund; Rota, Massimiliano
2014-10-01
We explore entanglement negativity, a measure of the distillable entanglement contained in a quantum state, in relativistic field theories in various dimensions. We first give a general overview of negativity and its properties and then explain a well known result relating (logarithmic) negativity of pure quantum states to the Rényi entropy (at index 1/2), by exploiting the simple features of entanglement in thermal states. In particular, we show that the negativity of the thermofield double state is given by the free energy difference of the system at temperature T and 2 T respectively. We then use this result to compute the negativity in the vacuum state of conformal field theories in various dimensions, utilizing results that have been derived for free and holographic CFTs in the literature. We also comment upon general lessons to be learnt about negativity in holographic field theories.
Erol, Volkan; Ozaydin, Fatih; Altintas, Azmi Ali
2014-06-24
Entanglement has been studied extensively for unveiling the mysteries of non-classical correlations between quantum systems. In the bipartite case, there are well known measures for quantifying entanglement such as concurrence, relative entropy of entanglement (REE) and negativity, which cannot be increased via local operations. It was found that for sets of non-maximally entangled states of two qubits, comparing these entanglement measures may lead to different entanglement orderings of the states. On the other hand, although it is not an entanglement measure and not monotonic under local operations, due to its ability of detecting multipartite entanglement, quantum Fisher information (QFI) has recently received an intense attraction generally with entanglement in the focus. In this work, we revisit the state ordering problem of general two qubit states. Generating a thousand random quantum states and performing an optimization based on local general rotations of each qubit, we calculate the maximal QFI for each state. We analyze the maximized QFI in comparison with concurrence, REE and negativity and obtain new state orderings. We show that there are pairs of states having equal maximized QFI but different values for concurrence, REE and negativity and vice versa.
Energy Technology Data Exchange (ETDEWEB)
Erol, V. [Department of Computer Engineering, Institute of Science, Okan University, Istanbul (Turkey); Netas Telecommunication Inc., Istanbul (Turkey)
2016-04-21
Entanglement has been studied extensively for understanding the mysteries of non-classical correlations between quantum systems. In the bipartite case, there are well known monotones for quantifying entanglement such as concurrence, relative entropy of entanglement (REE) and negativity, which cannot be increased via local operations. The study on these monotones has been a hot topic in quantum information [1-7] in order to understand the role of entanglement in this discipline. It can be observed that from any arbitrary quantum pure state a mixed state can obtained. A natural generalization of this observation would be to consider local operations classical communication (LOCC) transformations between general pure states of two parties. Although this question is a little more difficult, a complete solution has been developed using the mathematical framework of the majorization theory [8]. In this work, we analyze the relation between entanglement monotones concurrence and negativity with respect to majorization for general two-level quantum systems of two particles.
Adesso, Gerardo; Giampaolo, Salvatore M.; Illuminati, Fabrizio
2007-10-01
We present a geometric approach to the characterization of separability and entanglement in pure Gaussian states of an arbitrary number of modes. The analysis is performed adapting to continuous variables a formalism based on single subsystem unitary transformations that has been recently introduced to characterize separability and entanglement in pure states of qubits and qutrits [S. M. Giampaolo and F. Illuminati, Phys. Rev. A 76, 042301 (2007)]. In analogy with the finite-dimensional case, we demonstrate that the 1×M bipartite entanglement of a multimode pure Gaussian state can be quantified by the minimum squared Euclidean distance between the state itself and the set of states obtained by transforming it via suitable local symplectic (unitary) operations. This minimum distance, corresponding to a , uniquely determined, extremal local operation, defines an entanglement monotone equivalent to the entropy of entanglement, and amenable to direct experimental measurement with linear optical schemes.
Momentum-Space Entanglement and Loschmidt Echo in Luttinger Liquids after a Quantum Quench.
Dóra, Balázs; Lundgren, Rex; Selover, Mark; Pollmann, Frank
2016-07-01
Luttinger liquids (LLs) arise by coupling left- and right-moving particles through interactions in one dimension. This most natural partitioning of LLs is investigated by the momentum-space entanglement after a quantum quench using analytical and numerical methods. We show that the momentum-space entanglement spectrum of a LL possesses many universal features both in equilibrium and after a quantum quench. The largest entanglement eigenvalue is identical to the Loschmidt echo, i.e., the overlap of the disentangled and final wave functions of the system. The second largest eigenvalue is the overlap of the first excited state of the disentangled system with zero total momentum and the final wave function. The entanglement gap is universal both in equilibrium and after a quantum quench. The momentum-space entanglement entropy is always extensive and saturates fast to a time independent value after the quench, in sharp contrast to a spatial bipartitioning.
Spin torque oscillator neuroanalog of von Neumann's microwave computer.
Hoppensteadt, Frank
2015-10-01
Frequency and phase of neural activity play important roles in the behaving brain. The emerging understanding of these roles has been informed by the design of analog devices that have been important to neuroscience, among them the neuroanalog computer developed by O. Schmitt and A. Hodgkin in the 1930s. Later J. von Neumann, in a search for high performance computing using microwaves, invented a logic machine based on crystal diodes that can perform logic functions including binary arithmetic. Described here is an embodiment of his machine using nano-magnetics. Electrical currents through point contacts on a ferromagnetic thin film can create oscillations in the magnetization of the film. Under natural conditions these properties of a ferromagnetic thin film may be described by a nonlinear Schrödinger equation for the film's magnetization. Radiating solutions of this system are referred to as spin waves, and communication within the film may be by spin waves or by directed graphs of electrical connections. It is shown here how to formulate a STO logic machine, and by computer simulation how this machine can perform several computations simultaneously using multiplexing of inputs, that this system can evaluate iterated logic functions, and that spin waves may communicate frequency, phase and binary information. Neural tissue and the Schmitt-Hodgkin, von Neumann and STO devices share a common bifurcation structure, although these systems operate on vastly different space and time scales; namely, all may exhibit Andronov-Hopf bifurcations. This suggests that neural circuits may be capable of the computational functionality as described by von Neumann. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.
Structure and coarsening of foams: Beyond von Neumann's law
Roth, Adam E.
We report on the statistics of bubble size, topology, and shape and on their role in the coarsening dynamics for foams consisting of bubbles compressed between two parallel plates. We find that in the scaling regime, all bubble distributions are independent not only of time, but also of liquid content. For coarsening, the average rate decreases with liquid content due to the blocking of gas diffusion by Plateau borders inflated with liquid. By observing the growth rate of individual bubbles, we find that von Neumann's law becomes progressively violated with increasing wetness and decreasing bubble size. We successfully model this behavior by explicitly incorporating the border-blocking effect into the von Neumann argument. We report on bubble growth rates and on the statistics of bubble topology for the coarsening of a dry foam contained in the gap between two hemispheres. By contrast with coarsening in flat space, we observe that six-sided bubbles grow with time at a rate that depends on their size. We measure the statistics of bubble topology, and find distributions that differ from the scaling state of a flat two dimensional foam. We report on the statistics of bubble distribution and coarsening of the two dimensional surface of a three dimensional foam. The surface of a three dimensional foam obeys Plateau's laws, but does not obey von Neumann's law on the individual bubble level, although it holds on average. We measure bubble distributions, which to not change with time, but have different values from an ordinary two dimensional foam. We report on a method for optical tomography of three dimensional foams. Using a bottle filled with dry foam that is mounted on a rotation stage, we take pictures of the foam at many different angles. Using these images, it is possible to reconstruct horizontal slices of the foam. By controlling the parameters of this system, it is possible to get good slices, for possible use in reconstruction of the foam structure.
Wave packet dynamics of entangled two-mode states
Sudheesh, C.; Lakshmibala, S.; Balakrishnan, V.
2006-08-01
We consider a model Hamiltonian describing the interaction of a single-mode radiation field with the atoms of a nonlinear medium and study the dynamics of entanglement for specific non-entangled initial states of interest: namely, those in which the field mode is initially in a Fock state, a coherent state or a photon-added coherent state. The counterparts of near-revivals and fractional revivals are shown to be clearly identifiable in the entropy of entanglement. The 'overlap fidelity' of the system is another such indicator, and its behaviour corroborates that of the entropy of entanglement in the vicinity of near-revivals. The expectation values and higher moments of suitable quadrature variables are also examined, with reference to possible squeezing and higher order squeezing. The power spectra of the time series generated by the mean photon number are presented for initial states corresponding, respectively, to a coherent state and a photon-added coherent state. When the nonlinearity in the Hamiltonian is weak, these show signatures of quasiperiodicity.
Approximate solution of fourth order differential equation in Neumann problem
Directory of Open Access Journals (Sweden)
Jalil Rashidinia
2014-07-01
Full Text Available Generalized solution on Neumann problem of the fourth order ordinary differential equation in space $ W^{2}_{\\alpha} (0, b $ has been discussed , we obtain the condition on B.V.P when the solution is in classical form. Formulation of Quintic Spline Function has been derived and the consistency relations are given.Numerical method,based on Quintic spline approximation has been developed .Spline solution of the given problem has been considered for a certain value of $\\alpha.$ Error analysis of the spline method is given and it has been tested by an example
Driven Liouville von Neumann Equation in Lindblad Form.
Hod, Oded; Rodríguez-Rosario, César A; Zelovich, Tamar; Frauenheim, Thomas
2016-05-19
The Driven Liouville von Neumann approach [J. Chem. Theory Comput. 2014, 10, 2927-2941] is a computationally efficient simulation method for modeling electron dynamics in molecular electronics junctions. Previous numerical simulations have shown that the method can reproduce the exact single-particle dynamics while avoiding density matrix positivity violation found in previous implementations. In this study we prove that in the limit of infinite lead models the underlying equation of motion can be cast in Lindblad form. This provides a formal justification for the numerically observed density matrix positivity conservation.
Contiguity and Entire Separability of States on von Neumann Algebras
Haliullin, Samigulla
2017-12-01
We introduce the notions of the contiguity and entirely separability for two sequences of states on von Neumann algebras. The ultraproducts technique allows us to reduce the study of the contiguity to investigation of the equivalence for two states. Here we apply the Ocneanu ultraproduct and the Groh-Raynaud ultraproduct (see Ocneanu (1985), Groh (J. Operator Theory, 11, 2, 395-404 1984), Raynaud (J. Operator Theory, 48, 1, 41-68, 2002), Ando and Haagerup (J. Funct. Anal., 266, 12, 6842-6913, 2014)), as well as the technique developed in Mushtari and Haliullin (Lobachevskii J. Math., 35, 2, 138-146, 2014).
Rényi formulation of entanglement criteria for continuous variables
Rastegin, Alexey E.
2017-04-01
Entanglement criteria for an n -partite quantum system with continuous variables are formulated in terms of Rényi entropies. Rényi entropies are widely used as a good information measure due to many nice properties. Derived entanglement criteria are based on several mathematical results such as the Hausdorff-Young inequality, Young's inequality for convolution and its converse. From the historical viewpoint, the formulations of these results with sharp constants were obtained comparatively recently. Using the position and momentum observables of subsystems, one can build two total-system measurements with the following property. For product states, the final density in each global measurement appears as a convolution of n local densities. Hence, restrictions in terms of two Rényi entropies with constrained entropic indices are formulated for n -separable states of an n -partite quantum system with continuous variables. Experimental results are typically sampled into bins between prescribed discrete points. For these aims, we give appropriate reformulations of the derived entanglement criteria.
Quantum Rényi relative entropies affirm universality of thermodynamics
Misra, Avijit; Singh, Uttam; Bera, Manabendra Nath; Rajagopal, A. K.
2015-10-01
We formulate a complete theory of quantum thermodynamics in the Rényi entropic formalism exploiting the Rényi relative entropies, starting from the maximum entropy principle. In establishing the first and second laws of quantum thermodynamics, we have correctly identified accessible work and heat exchange in both equilibrium and nonequilibrium cases. The free energy (internal energy minus temperature times entropy) remains unaltered, when all the entities entering this relation are suitably defined. Exploiting Rényi relative entropies we have shown that this "form invariance" holds even beyond equilibrium and has profound operational significance in isothermal process. These results reduce to the Gibbs-von Neumann results when the Rényi entropic parameter α approaches 1. Moreover, it is shown that the universality of the Carnot statement of the second law is the consequence of the form invariance of the free energy, which is in turn the consequence of maximum entropy principle. Further, the Clausius inequality, which is the precursor to the Carnot statement, is also shown to hold based on the data processing inequalities for the traditional and sandwiched Rényi relative entropies. Thus, we find that the thermodynamics of nonequilibrium state and its deviation from equilibrium together determine the thermodynamic laws. This is another important manifestation of the concepts of information theory in thermodynamics when they are extended to the quantum realm. Our work is a substantial step towards formulating a complete theory of quantum thermodynamics and corresponding resource theory.
Quantum Rényi relative entropies affirm universality of thermodynamics.
Misra, Avijit; Singh, Uttam; Bera, Manabendra Nath; Rajagopal, A K
2015-10-01
We formulate a complete theory of quantum thermodynamics in the Rényi entropic formalism exploiting the Rényi relative entropies, starting from the maximum entropy principle. In establishing the first and second laws of quantum thermodynamics, we have correctly identified accessible work and heat exchange in both equilibrium and nonequilibrium cases. The free energy (internal energy minus temperature times entropy) remains unaltered, when all the entities entering this relation are suitably defined. Exploiting Rényi relative entropies we have shown that this "form invariance" holds even beyond equilibrium and has profound operational significance in isothermal process. These results reduce to the Gibbs-von Neumann results when the Rényi entropic parameter α approaches 1. Moreover, it is shown that the universality of the Carnot statement of the second law is the consequence of the form invariance of the free energy, which is in turn the consequence of maximum entropy principle. Further, the Clausius inequality, which is the precursor to the Carnot statement, is also shown to hold based on the data processing inequalities for the traditional and sandwiched Rényi relative entropies. Thus, we find that the thermodynamics of nonequilibrium state and its deviation from equilibrium together determine the thermodynamic laws. This is another important manifestation of the concepts of information theory in thermodynamics when they are extended to the quantum realm. Our work is a substantial step towards formulating a complete theory of quantum thermodynamics and corresponding resource theory.
Teleporting entanglement during black hole evaporation
Energy Technology Data Exchange (ETDEWEB)
Brustein, Ram [Department of Physics, Ben-Gurion University,Beer-Sheva 84105 (Israel); Medved, A.J.M. [Department of Physics & Electronics, Rhodes University,Grahamstown 6140 (South Africa); National Institute for Theoretical Physics (NITheP),Western Cape 7602 (South Africa)
2016-10-06
The unitary evaporation of a black hole (BH) in an initially pure state must lead to the eventual purification of the emitted radiation. It follows that the late radiation has to be entangled with the early radiation and, as a consequence, the entanglement among the Hawking pair partners has to decrease continuously from maximal to vanishing during the BH’s life span. Starting from the basic premise that both the horizon radius and the center of mass of a finite-mass BH are fluctuating quantum mechanically, we show how this process is realized. First, it is shown that the horizon fluctuations induce a small amount of variance in the total linear momentum of each created pair. This is in contrast to the case of an infinitely massive BH, for which the total momentum of the produced pair vanishes exactly on account of momentum conservation. This variance leads to a random recoil of the BH during each emission and, as a result, the center of mass of the BH undergoes a quantum random walk. Consequently, the uncertainty in its momentum grows as the square root of the number of emissions. We then show that this uncertainty controls the amount of deviation from maximal entanglement of the produced pairs and that this deviation is determined by the ratio of the cumulative number of emitted particles to the initial BH entropy. Thus, the interplay between the horizon and center-of-mass fluctuations provides a mechanism for teleporting entanglement from the pair partners to the BH and the emitted radiation.
Sparavigna, Amelia Carolina
2015-01-01
Entropy has a relevant role in several applications of information theory and in the image processing. Here, we discuss the Kaniadakis entropy for images. An example of bi-level image thresholding obtained by means of this entropy is also given. Keywords: Kaniadakis Entropy, Data Segmentation, Image processing, Thresholding
Energy Technology Data Exchange (ETDEWEB)
Letessier, J.; Tounsi, A. [Paris-7 Univ., 75 (France); Rafelski, J. [Arizona Univ., Tucson, AZ (United States). Dept. of Physics
1994-04-01
Entropy is a quantity characterizing the arrow of time in the evolution of a physical system - in every irreversible process the entropy increases. In elementary interactions such as relativistic collision of two atomic nuclei there is considerable particle production and hence entropy production. We address here a number of questions which arise naturally in this context. When and how is entropy produced in a quantum process, such as is a nuclear collision? How is the particle production related to entropy production? How does one measure the entropy produced in the reaction? We also consider certain fundamental approaches to the problem of entropy definition in quantum physics. (author). 15 refs., 5 figs.
Supersymmetric Renyi entropy in CFT{sub 2} and AdS{sub 3}
Energy Technology Data Exchange (ETDEWEB)
Giveon, Amit [Racah Institute of Physics, The Hebrew University,Jerusalem 91904 (Israel); Kutasov, David [EFI and Department of Physics, University of Chicago,5640 S. Ellis Av., Chicago, IL 60637 (United States)
2016-01-08
We show that in any two dimensional conformal field theory with (2,2) supersymmetry one can define a supersymmetric analog of the usual Renyi entropy of a spatial region A. It differs from the Renyi entropy by a universal function (which we compute) of the central charge, Renyi parameter n and the geometric parameters of A. In the limit n→1 it coincides with the entanglement entropy. Thus, it contains the same information as the Renyi entropy but its computation only involves correlation functions of chiral and anti-chiral operators. We also show that this quantity appears naturally in string theory on AdS{sub 3}.
Multipartite entanglement in neutrino oscillations
Energy Technology Data Exchange (ETDEWEB)
Blasone, Massimo; Dell' Anno, Fabio; De Siena, Silvio; Illuminati, Fabrizio, E-mail: blasone@sa.infn.i [Dipartimento di Matematica e Informatica, Universita degli Studi di Salerno, Via Ponte don Melillo, I-84084 Fisciano (Italy)
2009-06-01
Particle mixing is related to multi-mode entanglement of single-particle states The occupation number of both flavor eigenstates and mass eigenstates can be used to define a multiqubit space. In such a framework, flavor neutrino states can be interpreted as multipartite mode-entangled states. By using two different entanglement measures, we analyze the behavior of multipartite entanglement in the phenomenon of neutrino oscillations.
Entanglement in the Bogoliubov vacuum
DEFF Research Database (Denmark)
Poulsen, Uffe Vestergaard; Meyer, T.; Lewenstein, M.
2005-01-01
We analyze the entanglement properties of the Bogoliubov vacuum, which is obtained as a second-order approximation to the ground state of an interacting Bose-Einstein condensate. We work in one- and two-dimensional lattices and study the entanglement between two groups of sites as a function...... and to be favoured by strong interactions. Conversely, long-range entanglement is favoured by relatively weak interactions. No examples of bound entanglement are found....
Von Neumann algebras as complemented subspaces of B(H)
DEFF Research Database (Denmark)
Christensen, Erik; Wang, Liguang
2014-01-01
Let M be a von Neumann algebra of type II1 which is also a complemented subspace of B( H). We establish an algebraic criterion, which ensures that M is an injective von Neumann algebra. As a corollary we show that if M is a complemented factor of type II1 on a Hilbert space H, then M is injective...
Directory of Open Access Journals (Sweden)
Charyyar Ashyralyyev
2015-07-01
Full Text Available This article studies the numerical solution of inverse problems for the multidimensional elliptic equation with Dirichlet-Neumann boundary conditions and Neumann type overdetermination. We present first and second order accuracy difference schemes. The stability and almost coercive stability inequalities for the solution are obtained. Numerical examples with explanation on the implementation illustrate the theoretical results.
Entanglement versus disentanglement: Quantum Cryptography
Mitra, Arindam
2000-01-01
In quantum information, the role of entanglement and disentanglement is itself a subject of research and debate. Earlier works on quantum cryptography have almost established that entanglement has no special advantage in quantum cryptography. In this paper we reveal that entanglement is better ingredient than disentanglement for our alternative quantum cryptography.
Lithography using quantum entangled particles
Williams, Colin (Inventor); Dowling, Jonathan (Inventor)
2001-01-01
A system of etching using quantum entangled particles to get shorter interference fringes. An interferometer is used to obtain an interference fringe. N entangled photons are input to the interferometer. This reduces the distance between interference fringes by n, where again n is the number of entangled photons.
Fermionic entanglement in itinerant systems
Energy Technology Data Exchange (ETDEWEB)
Zanardi, Paolo [Institute for Scientific Interchange (ISI) Foundation, Torino (Italy); Wang Xiaoguang [Department of Physics and Centre for Advanced Computing-Algorithms and Cryptography, Macquarie University, Sydney, NSW (Australia)
2002-09-20
We study pairwise quantum entanglement in systems of fermions itinerant in a lattice from a second-quantized perspective. Entanglement in the grand-canonical ensemble is studied, both for energy eigenstates and for the thermal state. Relations between entanglement and superconducting correlations are discussed in a BCS-like model and for {eta}-pair superconductivity. (author)
Verifying bound entanglement of dephased Werner states
Thomas, P.; Bohmann, M.; Vogel, W.
2017-10-01
The verification of quantum entanglement under the influence of realistic noise and decoherence is crucial for the development of quantum technologies. Unfortunately, a full entanglement characterization is generally not possible with most entanglement criteria such as entanglement witnesses or the partial transposition criterion. In particular, so-called bound entanglement cannot be certified via the partial transposition criterion. Here we present the full entanglement verification of dephased qubit and qutrit Werner states via entanglement quasiprobabilities. Remarkably, we are able to reveal bound entanglement for noisy mixed states in the qutrit case. This example demonstrates the strength of the entanglement quasiprobabilities for verifying the full entanglement of quantum states suffering from noise.
Torsion and entropy driven denaturation of DNA
Energy Technology Data Exchange (ETDEWEB)
Roy, Subhamoy Singha, E-mail: ssroy.science@gmail.com [Department of Physics, JIS College of Engineering (Autonomous), West Bengal University of Technology, Kalyani, Nadia 741235 (India); Bandyopadhyay, Pratul, E-mail: b_pratul@yahoo.co.in [Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata 700108 (India)
2013-11-29
A unified theory of the denaturation transition having torsion energy as the control parameter has been formulated here in the framework of the mapping of a DNA molecule onto a Heisenberg spin system. The torsion energy incorporates the torque, tension and temperature, the latter being associated with the twist angle. The denaturation transition can be mapped onto the quantum phase transition induced by a quench when the temperature effect is incorporated in the quench time and torsion takes the role of the external field. The denaturation transition occurs when the entanglement entropy of the spin system vanishes.
Evolution of entropy in different types of non-Markovian three-level ...
Indian Academy of Sciences (India)
atoms in a single reservoir. We write the entropy evolution of the atoms in single reser- voirs to measure the degree of entanglement in §3.3 and then we compare entanglement in different types of atoms for two different states in §3.4. In §4, we do the above men- tioned procedures for three-level atoms in two independent ...
Economical and feasible controlled teleportation of an arbitrary unknown N-qubit entangled state
Energy Technology Data Exchange (ETDEWEB)
Man Zhongxiao [College of Physics and Engineering, Qufu Normal University, Qufu 273165 (China); Xia Yunjie [College of Physics and Engineering, Qufu Normal University, Qufu 273165 (China); Nguyen Ba An [Institute of Physics and Electronics, 10 Dao Tan, Thu Le, Ba Dinh, Hanoi (Viet Nam)
2007-05-28
We propose a new quantum protocol to teleport an arbitrary unknown N-qubit entangled state from a sender to a fixed receiver under the control of M (M < N) controllers. In comparison with other existing protocols, ours is more economical and more feasible. The quantum resource required is just M Greenberger-Horne-Zeilinger trios plus (N - M) Einstein-Podolsky-Rosen pairs. The techniques required are only N Bell measurements by the sender, a von Neumann measurement by a controller and N single-qubit transformations by the receiver. The rule for the receiver to reconstruct the desired state is derived explicitly in the most general case.
Quantum entanglement and criticality of the antiferromagnetic Heisenberg model in an external field
Liu, Guang-Hua; Li, Ruo-Yan; Tian, Guang-Shan
2012-06-01
By Lanczos exact diagonalization and the infinite time-evolving block decimation (iTEBD) technique, the two-site entanglement as well as the bipartite entanglement, the ground state energy, the nearest-neighbor correlations, and the magnetization in the antiferromagnetic Heisenberg (AFH) model under an external field are investigated. With increasing external field, the small size system shows some distinct upward magnetization stairsteps, accompanied synchronously with some downward two-site entanglement stairsteps. In the thermodynamic limit, the two-site entanglement, as well as the bipartite entanglement, the ground state energy, the nearest-neighbor correlations, and the magnetization are calculated, and the critical magnetic field hc = 2.0 is determined exactly. Our numerical results show that the quantum entanglement is sensitive to the subtle changing of the ground state, and can be used to describe the magnetization and quantum phase transition. Based on the discontinuous behavior of the first-order derivative of the entanglement entropy and fidelity per site, we think that the quantum phase transition in this model should belong to the second-order category. Furthermore, in the magnon existence region (h behavior of block entanglement which can be described by a free bosonic field theory is observed, and the central charge c is determined to be 1.
Quantum entanglement and criticality of the antiferromagnetic Heisenberg model in an external field.
Liu, Guang-Hua; Li, Ruo-Yan; Tian, Guang-Shan
2012-06-27
By Lanczos exact diagonalization and the infinite time-evolving block decimation (iTEBD) technique, the two-site entanglement as well as the bipartite entanglement, the ground state energy, the nearest-neighbor correlations, and the magnetization in the antiferromagnetic Heisenberg (AFH) model under an external field are investigated. With increasing external field, the small size system shows some distinct upward magnetization stairsteps, accompanied synchronously with some downward two-site entanglement stairsteps. In the thermodynamic limit, the two-site entanglement, as well as the bipartite entanglement, the ground state energy, the nearest-neighbor correlations, and the magnetization are calculated, and the critical magnetic field h(c) = 2.0 is determined exactly. Our numerical results show that the quantum entanglement is sensitive to the subtle changing of the ground state, and can be used to describe the magnetization and quantum phase transition. Based on the discontinuous behavior of the first-order derivative of the entanglement entropy and fidelity per site, we think that the quantum phase transition in this model should belong to the second-order category. Furthermore, in the magnon existence region (h entanglement which can be described by a free bosonic field theory is observed, and the central charge c is determined to be 1.
The limiting equation for Neumann Laplacians on shrinking domains
Directory of Open Access Journals (Sweden)
Yoshimi Saito
2000-04-01
Full Text Available Let ${Omega_{epsilon} }_{0 < epsilon le1}$ be an indexed family of connected open sets in ${mathbb R}^2$, that shrinks to a tree $Gamma$ as $epsilon$ approaches zero. Let $H_{Omega_{epsilon}}$ be the Neumann Laplacian and $f_{epsilon}$ be the restriction of an $L^2(Omega_1$ function to $Omega_{epsilon} $. For $z in {mathbb C}Backslash [0, infty$, set $u_{epsilon} = (H_{Omega_{epsilon}} - z^{-1}f_{epsilon} $. Under the assumption that all the edges of $Gamma$ are line segments, and some additional conditions on $Omega_{epsilon}$, we show that the limit function $u_0 = lim_{epsilono 0} u_{epsilon}$ satisfies a second-order ordinary differential equation on $Gamma$ with Kirchhoff boundary conditions on each vertex of $Gamma $.
Solution of the Classical Stefan Problem: Neumann Condition
Kot, V. A.
2017-07-01
A polynomial solution of the classical one-phase Stefan problem with a Neumann boundary condition is presented. As a result of the multiple integration of the heat-conduction equation, a sequence of identical equalities has been obtained. On the basis of these equalities, solutions were constructed in the form of the second-, third-, fourth-, and fifth-degree polynomials. It is shown by test examples that the approach proposed is highly efficient and that the approximation errors of the solutions in the form of the fourth- and fifth-degree polynomials are negligible small, which allows them to be considered in fact as exact. The polynomial solutions obtained substantially surpass the analogous numerical solutions in the accuracy of determining the position of the moving interphase boundary in a body and are in approximate parity with them in the accuracy of determining the temperature profile in it.
Modeling Groundwater Flow using both Neumann and Dirichlet Boundary Conditions
Zijl, Wouter; El-Rawy, Mustafa; Batelaan, Okke
2013-04-01
In groundwater flow models it is customary to use the recharge rate, obtained from measured precipitation minus run off and evapotranspiration, as the top boundary condition (a Neumann boundary condition). However, as has been emphasized by Tóth (1962; 2009), the topography of the water table offers a better boundary condition (a Dirichlet boundary condition), because it leads to the delineation of flow systems and stagnation zones. However, in practical modeling studies the recharge rates obtained when using the Dirichlet boundary condition may turn out to be unrealistically small or large. To remediate this we have developed an unconventional modeling procedure that is based on both the Neumann and the Dirichlet boundary condition on the phreatic surface. Such a model does not only calculate the heads and fluxes, but also an update of the initially perceived hydraulic conductivities, in such a way that the initially perceived conductivity model is preserved as much as possible. For given grid block conductivities, numerical groundwater models (e.g. MODFLOW) are linear in the heads. However, for given heads the numerical models are not linear in the grid block conductivities. Mohammed et al. (2009) have developed a MODFLOW-compatible numerical model that is linear in the stream functions for given grid block conductivities, while it is also linear in the grid block resistivities (inverse of conductivities) if the heads are given. Unconventional modeling is based on this bi-linearity. Assume we specify a reasonable perception of the hydraulic conductivities and determine the numerical solution with Neumann boundary conditions. The resulting fluxes are then substituted into the stream function model, together with Dirichlet boundary conditions, and the grid block resistivities can then be determined by a standard routine for solving systems of linear algebraic equations. The thus calibrated grid block conductivities do not deviate much from the initially perceived
Implementing the quantum von Neumann architecture with superconducting circuits.
Mariantoni, Matteo; Wang, H; Yamamoto, T; Neeley, M; Bialczak, Radoslaw C; Chen, Y; Lenander, M; Lucero, Erik; O'Connell, A D; Sank, D; Weides, M; Wenner, J; Yin, Y; Zhao, J; Korotkov, A N; Cleland, A N; Martinis, John M
2011-10-07
The von Neumann architecture for a classical computer comprises a central processing unit and a memory holding instructions and data. We demonstrate a quantum central processing unit that exchanges data with a quantum random-access memory integrated on a chip, with instructions stored on a classical computer. We test our quantum machine by executing codes that involve seven quantum elements: Two superconducting qubits coupled through a quantum bus, two quantum memories, and two zeroing registers. Two vital algorithms for quantum computing are demonstrated, the quantum Fourier transform, with 66% process fidelity, and the three-qubit Toffoli-class OR phase gate, with 98% phase fidelity. Our results, in combination especially with longer qubit coherence, illustrate a potentially viable approach to factoring numbers and implementing simple quantum error correction codes.
John von Neumann and Klaus Fuchs: an Unlikely Collaboration
Bernstein, Jeremy
2010-03-01
I discuss the origin of the idea of making a fusion (hydrogen) bomb and the physics involved in it, and then turn to the design proposed for one by the unlikely collaborators John von Neumann and Klaus Fuchs in a patent application they filed at Los Alamos in May 1946, which Fuchs passed on to the Russians in March 1948, and which with substantial modifications was tested on the island of Eberiru on the Eniwetok atoll in the South Pacific on May 8, 1951. This test showed that the fusion of deuterium and tritium nuclei could be ignited, but that the ignition would not propagate because the heat produced was rapidly radiated away. Meanwhile, Stanislaw Ulam and C.J. Everett had shown that Edward Teller’s Classical Super could not work, and at the end of December 1950, Ulam had conceived the idea of super compression, using the energy of a fission bomb to compress the fusion fuel to such a high density that it would be opaque to the radiation produced. Once Teller understood this, he invented a greatly improved, new method of compression using radiation, which then became the heart of the Ulam-Teller bomb design, which was tested, also in the South Pacific, on November 1, 1952. The Russians have freely acknowledged that Fuchs gave them the fission bomb, but they have insisted that no one gave them the fusion bomb, which grew out of design involving a fission bomb surrounded by alternating layers of fusion and fission fuels, and which they tested on November 22, 1955. Part of the irony of this story is that neither the American nor the Russian hydrogen-bomb programs made any use of the brilliant design that von Neumann and Fuchs had conceived as early as 1946, which could have changed the entire course of development of both programs.
Excited-state entanglement and thermal mutual information in random spin chains
Huang, Yichen; Moore, Joel E.
2014-12-01
Entanglement properties of excited eigenstates (or of thermal mixed states) are difficult to study with conventional analytical methods. We approach this problem for random spin chains using a recently developed real-space renormalization group technique for excited states ("RSRG-X"). For the random XX and quantum Ising chains, which have logarithmic divergences in the entanglement entropy of their (infinite-randomness) critical ground states, we show that the entanglement entropy of excited eigenstates retains a logarithmic divergence while the mutual information of thermal mixed states does not. However, in the XX case the coefficient of the logarithmic divergence extends from the universal ground-state value to a universal interval due to the degeneracy of excited eigenstates. These models are noninteracting in the sense of having free-fermion representations, allowing strong numerical checks of our analytical predictions.
Sang, Nguyen Anh; Thu Thuy, Do Thi; Loan, Nguyen Thi Ha; Lan, Nguyen Tri; Viet, Nguyen Ai
2017-06-01
Using the simple deformed three-level model (D3L model) proposed in our early work, we study the entanglement problem of composite bosons. Consider three first energy levels are known, we can get two energy separations, and can define the level deformation parameter δ. Using connection between q-deformed harmonic oscillator and Morse-like anharmonic potential, the deform parameter q also can be derived explicitly. Like the Einstein’s theory of special relativity, we introduce the observer e˙ects: out side observer (looking from outside the studying system) and inside observer (looking inside the studying system). Corresponding to those observers, the outside entanglement entropy and inside entanglement entropy will be defined.. Like the case of Foucault pendulum in the problem of Earth rotation, our deformation energy level investigation might be useful in prediction the environment e˙ect outside a confined box.
Topological Entanglement Entropy of a Bose-Hubbard Spin Liquid
Isakov, Sergei V.; Hastings, Matthew B.; Melko, Roger G.
2011-01-01
The Landau paradigm of classifying phases by broken symmetries was demonstrated to be incomplete when it was realized that different quantum Hall states could only be distinguished by more subtle, topological properties. Today, the role of topology as an underlying description of order has branched out to include topological band insulators, and certain featureless gapped Mott insulators with a topological degeneracy in the groundstate wavefunction. Despite intense focus, very few candidates ...
Energy Technology Data Exchange (ETDEWEB)
Blasone, Massimo [Dipartimento di Fisica, Università degli Studi di Salerno, Via Ponte don Melillo, I-84084 Fisciano (Italy); INFN Sezione di Napoli, Gruppo collegato di Salerno (Italy); Dell' Anno, Fabio; De Siena, Silvio; Illuminati, Fabrizio [Dipartimento di Ingegneria Industriale, Università degli Studi di Salerno, Via Ponte don Melillo, I-84084 Fisciano (Italy)
2013-04-15
Neutrino oscillations can be equivalently described in terms of (dynamical) entanglement of neutrino flavor modes. We review previous results derived in the context of quantum mechanics and extend them to the quantum field theory framework, were a rich structure of quantum correlations appears.
Postcolonial Entanglements: Unruling Stories
Pacini-Ketchabaw, Veronica
2012-01-01
In this article, I use Donna Haraway's philosophy to think about postcolonial encounters between different species. I follow entangled stories of the deer/settler-child figure to trouble colonialisms and untangle the histories and trajectories that we inhabit with other species through colonial histories. I shy away from generalizations and…
Soltani, M.; Tavassoly, M. K.; Pakniat, R.
2017-10-01
In this paper, we outline a scheme for the entanglement swapping procedure based on cavity quantum electrodynamics using the Jaynes-Cummings model consisting of the coherent and photon-added coherent states. In particular, utilizing the photon-added coherent states (|α,m〉≃â†m|α〉, where |α〉 is the Glauber coherent state) in the scheme, enables us to investigate the effect of m, i.e., the number of excitations corresponding to the photon-added coherent field on the entanglement swapping process. In the scheme, two two-level atoms A1 and A2 are initially entangled together, and distinctly two exploited cavity fields F1 and F2 are prepared in an entangled state (a combination of coherent and photon-added coherent states). Interacting the atom A2 with field F1 (via the Jaynes-Cummings model) and then making detection on them, transfers the entanglement from the two atoms A1, A2 and the two fields F1, F2 to the atom-field “A1-F2”, i.e., entanglement swapping occurs. In the continuation, we pay our attention to the evaluation of the fidelity of the swapped entangled state relative to a suitable maximally entangled state, success probability of the performed detections and linear entropy as the degree of entanglement of the swapped entangled state. It is demonstrated that, an increase in the number of excitations, m, leads to the increment of fidelity as well as the amount of entanglement. According to our numerical results, the maximum values of fidelity (linear entropy) 0.98 (0.46) is obtained for m = 9, however, the maximum value of success probability does not significantly change by increasing m.
Mutual Information and Nonadditive Entropies: A Method for Kaniadakis Entropy
Sparavigna, Amelia Carolina
2015-01-01
In [10.18483/ijSci.8451], we have discussed the mutual information of two random variables and how it can be obtained from entropies. We considered the Shannon entropy and the nonadditive Tsallis entropy. Here, following the same approach used in the Tsallis case, we propose a method for discussing the mutual entropy of another nonadditive entropy, the Kaniadakis entropy
Ben-Naim, Arieh
2011-01-01
Changes in entropy can "sometimes" be interpreted in terms of changes in disorder. On the other hand, changes in entropy can "always" be interpreted in terms of changes in Shannon's measure of information. Mixing and demixing processes are used to highlight the pitfalls in the association of entropy with disorder. (Contains 3 figures.)
Hierarchy of graph-diagonal states based on quantum discord and entanglement classification
Jafarizadeh, Mohammad Ali; Karimi, Naser; Sahlan, Davood Amidi; Heshmati, Ahmad; Yahyavi, Marziyeh
2017-10-01
For the relative entropy-based measure of quantum discord the key idea is to find the closest classical state (CCS) for a given state ρ, which is in general a more complicated problem. In this work, we study three and four qubit graph-diagonal states and give the explicit expressions of CCS for these states. Using the CCS, we compute the quantum discord of graph-diagonal states of three and four qubit systems and show that there is a hierarchy for the quantum discord of graph-diagonal states of any three and four qubit systems. Then we classify the entanglement of graph-diagonal states of three and four qubit systems and draw the hierarchy of entanglement of these graph-diagonal states. Finally, we compare the hierarchy of quantum discord and quantum entanglement of the these graph-diagonal states and show that the hierarchy of quantum entanglement is at least in equivalence of quantum discord.
On n-flat modules and n-Von Neumann regular rings
Directory of Open Access Journals (Sweden)
Najib Mahdou
2006-01-01
Full Text Available We show that each R-module is n-flat (resp., weakly n-flat if and only if R is an (n,n−1-ring (resp., a weakly (n,n−1-ring. We also give a new characterization of n-Von Neumann regular rings and a characterization of weak n-Von Neumann regular rings for (CH-rings and for local rings. Finally, we show that in a class of principal rings and a class of local Gaussian rings, a weak n-Von Neumann regular ring is a (CH-ring.
Stability estimates for the anisotropic wave equation from the Dirichlet-to-Neumann map
Bellassoued, Mourad; Ferreira, David Dos Santos
2010-01-01
In this article we seek stability estimates in the inverse problem of determining the potential or the velocity in a wave equation in an anisotropic medium from measured Neumann boundary observations. This information is enclosed in the dynamical Dirichlet-to-Neumann map associated to the wave equation. We prove in dimension $n\\geq 2$ that the knowledge of the Dirichlet-to-Neumann map for the wave equation uniquely determines the electric potential and we prove H\\"older-type stability in dete...
Maximal entanglement entanglement-assisted quantum codes of distance three
Guo, Luobin; Fu, Qiang; Li, Ruihu; Lu, Liangdong
2015-02-01
Entanglement-assisted quantum error correcting code (EAQECC) is a generalization of standard stabilizer quantum code. Maximal entanglement EAQECCs can achieve the EA-hashing bound asymptotically. In this work, we give elementary recursive constructions of quaternary zero radical codes with dual distance three for all n ≥ 4. Consequently, good maximal entanglement EAQECCs of minimum distance three for such length n are obtained. Almost all of these EAQECCs are optimal or near optimal according to the EA-quantum Hamming bound.
Entanglement-assisted state discrimination and entanglement preservation
Güngör, Özenç; Turgut, Sadi
In this study, the following scenario is considered: there are two qubits possessed by two parties at different locations. Qubits have been prepared in one of a maximum of four, mutually-orthogonal, entangled states and the parties wish to distinguish between the states by using local operations and classical communication. Although in general it is not possible to distinguish between four arbitrary states, the parties can spend some pre-shared entanglement to achieve perfect discrimination between four qubit states and can also preserve the entanglement of the states after discrimination. This is shown by employing the theory of majorization and the connections between entanglement transformations and state discrimination protocols.
Canonical distillation of entanglement
Das, Tamoghna; Kumar, Asutosh; Kumar Pal, Amit; Shukla, Namrata; Sen(De), Aditi; Sen, Ujjwal
2017-11-01
Distilling highly entangled quantum states from weaker ones is a process that is crucial for efficient and long-distance quantum communication, and has implications for several other quantum information protocols. We introduce the notion of distillation under limited resources, and specifically focus on the energy constraint. The corresponding protocol, which we call the canonical distillation of entanglement, naturally leads to the set of canonically distillable states. We show that for non-interacting Hamiltonians, almost no states are canonically distillable, while the situation can be drastically different for interacting ones. Several paradigmatic Hamiltonians are considered for bipartite as well as multipartite canonical distillability. The results have potential applications for practical quantum communication devices.
Spread of entanglement for small subsystems in holographic CFTs
Kundu, Sandipan; Pedraza, Juan F.
2017-04-01
We develop an analytic perturbative expansion to study the propagation of entanglement entropy for small subsystems after a global quench, in the context of the AdS /CFT correspondence. Opposite to the large interval limit, in this case the evolution of the system takes place at time scales that are shorter in comparison to the local equilibration scale and, thus, different physical mechanisms govern the dynamics and subsequent thermalization. In particular, we show that the heuristic picture in terms of an "entanglement tsunami" does not apply in this regime. We find two crucial differences: First, that the instantaneous rate of growth of the entanglement is not constrained by causality, but rather its time average and, second, that the approach to saturation is always continuous, regardless of the shape of the entangling surface. Our analytic expansion also enables us to verify some previous numerical results, namely, that the saturation time is nonmonotonic with respect to the chemical potential. All of our results are pertinent to CFTs with a classical gravity dual formulation.
RNA Thermodynamic Structural Entropy.
Garcia-Martin, Juan Antonio; Clote, Peter
2015-01-01
Conformational entropy for atomic-level, three dimensional biomolecules is known experimentally to play an important role in protein-ligand discrimination, yet reliable computation of entropy remains a difficult problem. Here we describe the first two accurate and efficient algorithms to compute the conformational entropy for RNA secondary structures, with respect to the Turner energy model, where free energy parameters are determined from UV absorption experiments. An algorithm to compute the derivational entropy for RNA secondary structures had previously been introduced, using stochastic context free grammars (SCFGs). However, the numerical value of derivational entropy depends heavily on the chosen context free grammar and on the training set used to estimate rule probabilities. Using data from the Rfam database, we determine that both of our thermodynamic methods, which agree in numerical value, are substantially faster than the SCFG method. Thermodynamic structural entropy is much smaller than derivational entropy, and the correlation between length-normalized thermodynamic entropy and derivational entropy is moderately weak to poor. In applications, we plot the structural entropy as a function of temperature for known thermoswitches, such as the repression of heat shock gene expression (ROSE) element, we determine that the correlation between hammerhead ribozyme cleavage activity and total free energy is improved by including an additional free energy term arising from conformational entropy, and we plot the structural entropy of windows of the HIV-1 genome. Our software RNAentropy can compute structural entropy for any user-specified temperature, and supports both the Turner'99 and Turner'04 energy parameters. It follows that RNAentropy is state-of-the-art software to compute RNA secondary structure conformational entropy. Source code is available at https://github.com/clotelab/RNAentropy/; a full web server is available at http
RNA Thermodynamic Structural Entropy.
Directory of Open Access Journals (Sweden)
Juan Antonio Garcia-Martin
Full Text Available Conformational entropy for atomic-level, three dimensional biomolecules is known experimentally to play an important role in protein-ligand discrimination, yet reliable computation of entropy remains a difficult problem. Here we describe the first two accurate and efficient algorithms to compute the conformational entropy for RNA secondary structures, with respect to the Turner energy model, where free energy parameters are determined from UV absorption experiments. An algorithm to compute the derivational entropy for RNA secondary structures had previously been introduced, using stochastic context free grammars (SCFGs. However, the numerical value of derivational entropy depends heavily on the chosen context free grammar and on the training set used to estimate rule probabilities. Using data from the Rfam database, we determine that both of our thermodynamic methods, which agree in numerical value, are substantially faster than the SCFG method. Thermodynamic structural entropy is much smaller than derivational entropy, and the correlation between length-normalized thermodynamic entropy and derivational entropy is moderately weak to poor. In applications, we plot the structural entropy as a function of temperature for known thermoswitches, such as the repression of heat shock gene expression (ROSE element, we determine that the correlation between hammerhead ribozyme cleavage activity and total free energy is improved by including an additional free energy term arising from conformational entropy, and we plot the structural entropy of windows of the HIV-1 genome. Our software RNAentropy can compute structural entropy for any user-specified temperature, and supports both the Turner'99 and Turner'04 energy parameters. It follows that RNAentropy is state-of-the-art software to compute RNA secondary structure conformational entropy. Source code is available at https://github.com/clotelab/RNAentropy/; a full web server is available at http
Entanglement in Nonunitary Quantum Critical Spin Chains
Couvreur, Romain; Jacobsen, Jesper Lykke; Saleur, Hubert
2017-07-01
Entanglement entropy has proven invaluable to our understanding of quantum criticality. It is natural to try to extend the concept to "nonunitary quantum mechanics," which has seen growing interest from areas as diverse as open quantum systems, noninteracting electronic disordered systems, or nonunitary conformal field theory (CFT). We propose and investigate such an extension here, by focusing on the case of one-dimensional quantum group symmetric or supergroup symmetric spin chains. We show that the consideration of left and right eigenstates combined with appropriate definitions of the trace leads to a natural definition of Rényi entropies in a large variety of models. We interpret this definition geometrically in terms of related loop models and calculate the corresponding scaling in the conformal case. This allows us to distinguish the role of the central charge and effective central charge in rational minimal models of CFT, and to define an effective central charge in other, less well-understood cases. The example of the s l (2 |1 ) alternating spin chain for percolation is discussed in detail.
Existence and uniqueness of solutions for a Neumann boundary-value problem
Directory of Open Access Journals (Sweden)
Safia Benmansour
2011-09-01
Full Text Available In this article, we show the existence and uniqueness of positive solutions for perturbed Neumann boundary-value problems of second-order differential equations. We use a fixed point theorem for general $alpha$-concave operators.
DEFF Research Database (Denmark)
Flindt, Christian; Sørensen, A. S.; Lukin, M. D.
2007-01-01
We propose a semiconductor device that can electrically generate entangled electron spin-photon states, providing a building block for entanglement of distant spins. The device consists of a p-i-n diode structure that incorporates a coupled double quantum dot. We show that electronic control...... of the diode bias and local gating allow for the generation of single photons that are entangled with a robust quantum memory based on the electron spins. Practical performance of this approach to controlled spin-photon entanglement is analyzed....
Higher-order quantum entanglement
Zeilinger, Anton; Horne, Michael A.; Greenberger, Daniel M.
1992-01-01
In quantum mechanics, the general state describing two or more particles is a linear superposition of product states. Such a superposition is called entangled if it cannot be factored into just one product. When only two particles are entangled, the stage is set for Einstein-Podolsky-Rosen (EPR) discussions and Bell's proof that the EPR viewpoint contradicts quantum mechanics. If more than two particles are involved, new possibilities and phenomena arise. For example, the Greenberger, Horne, and Zeilinger (GHZ) disproof of EPR applies. Furthermore, as we point out, with three or more particles even entanglement itself can be an entangled property.
Multiple von Neumann computers: an evolutionary approach to functional emergence.
Suzuki, H
1997-01-01
A novel system composed of multiple von Neumann computers and an appropriate problem environment is proposed and simulated. Each computer has a memory to store the machine instruction program, and when a program is executed, a series of machine codes in the memory is sequentially decoded, leading to register operations in the central processing unit (CPU). By means of these operations, the computer not only can handle its generally used registers but also can read and write the environmental database. Simulation is driven by genetic algorithms (GAs) performed on the population of program memories. Mutation and crossover create program diversity in the memory, and selection facilitates the reproduction of appropriate programs. Through these evolutionary operations, advantageous combinations of machine codes are created and fixed in the population one by one, and the higher function, which enables the computer to calculate an appropriate number from the environment, finally emerges in the program memory. In the latter half of the article, the performance of GAs on this system is studied. Under different sets of parameters, the evolutionary speed, which is determined by the time until the domination of the final program, is examined and the conditions for faster evolution are clarified. At an intermediate mutation rate and at an intermediate population size, crossover helps create novel advantageous sets of machine codes and evidently accelerates optimization by GAs.
Using the Neumann series expansion for assembling Reduced Order Models
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Nasisi S.
2014-06-01
Full Text Available An efficient method to remove the limitation in selecting the master degrees of freedom in a finite element model by means of a model order reduction is presented. A major difficulty of the Guyan reduction and IRS method (Improved Reduced System is represented by the need of appropriately select the master and slave degrees of freedom for the rate of convergence to be high. This study approaches the above limitation by using a particular arrangement of the rows and columns of the assembled matrices K and M and employing a combination between the IRS method and a variant of the analytical selection of masters presented in (Shah, V. N., Raymund, M., Analytical selection of masters for the reduced eigenvalue problem, International Journal for Numerical Methods in Engineering 18 (1 1982 in case first lowest frequencies had to be sought. One of the most significant characteristics of the approach is the use of the Neumann series expansion that motivates this particular arrangement of the matrices’ entries. The method shows a higher rate of convergence when compared to the standard IRS and very accurate results for the lowest reduced frequencies. To show the effectiveness of the proposed method two testing structures and the human vocal tract model employed in (Vampola, T., Horacek, J., Svec, J. G., FE modeling of human vocal tract acoustics. Part I: Prodution of Czech vowels, Acta Acustica United with Acustica 94 (3 2008 are presented.
Cornering Gapless Quantum States via Their Torus Entanglement.
Witczak-Krempa, William; Hayward Sierens, Lauren E; Melko, Roger G
2017-02-17
The entanglement entropy (EE) has emerged as an important window into the structure of complex quantum states of matter. We analyze the universal part of the EE for gapless systems on tori in 2D and 3D, denoted by χ. Focusing on scale-invariant systems, we derive general nonperturbative properties for the shape dependence of χ and reveal surprising relations to the EE associated with corners in the entangling surface. We obtain closed-form expressions for χ in 2D and 3D within a model that arises in the study of conformal field theories (CFTs), and we use them to obtain Ansätze without fitting parameters for the 2D and 3D free boson CFTs. Our numerical lattice calculations show that the Ansätze are highly accurate. Finally, we discuss how the torus EE can act as a fingerprint of exotic states such as gapless quantum spin liquids, e.g., Kitaev's honeycomb model.
Cornering Gapless Quantum States via Their Torus Entanglement
Witczak-Krempa, William; Hayward Sierens, Lauren E.; Melko, Roger G.
2017-02-01
The entanglement entropy (EE) has emerged as an important window into the structure of complex quantum states of matter. We analyze the universal part of the EE for gapless systems on tori in 2D and 3D, denoted by χ . Focusing on scale-invariant systems, we derive general nonperturbative properties for the shape dependence of χ and reveal surprising relations to the EE associated with corners in the entangling surface. We obtain closed-form expressions for χ in 2D and 3D within a model that arises in the study of conformal field theories (CFTs), and we use them to obtain Ansätze without fitting parameters for the 2D and 3D free boson CFTs. Our numerical lattice calculations show that the Ansätze are highly accurate. Finally, we discuss how the torus EE can act as a fingerprint of exotic states such as gapless quantum spin liquids, e.g., Kitaev's honeycomb model.
Dirichlet forms and symmetric Markovian semigroups on Z_2-graded von Neumann algebras
Bahn, C; Moon-Park, Y
2003-01-01
We extend the construction of Dirichlet forms and symmetric Markovian semigroups on standard forms of von Neumann algebras given in [Infin. Dimens. Anal. Quantum Probab. Relat Top. Vol. 3, 1-14 (2000)] to the case of Z_2-graded von Neumann algebras. We apply the extension to construct symmetric Markovian semigroups on CAR algebras with respect to gauge invariant quasi-free states and also investigate detailed properties such as ergodicity of the semigroups.
Directory of Open Access Journals (Sweden)
Zhang Jing
2011-01-01
Full Text Available Abstract We discuss Neumann and Robin problems driven by the -Laplacian with jumping nonlinearities. Using sub-sup solution method, Fucík spectrum, mountain pass theorem, degree theorem together with suitable truncation techniques, we show that the Neumann problem has infinitely many nonconstant solutions and the Robin problem has at least four nontrivial solutions. Furthermore, we study oscillating equations with Robin boundary and obtain infinitely many nontrivial solutions.
Configurational Entropy Revisited
Lambert, Frank L.
2007-09-01
Entropy change is categorized in some prominent general chemistry textbooks as being either positional (configurational) or thermal. In those texts, the accompanying emphasis on the dispersal of matter—independent of energy considerations and thus in discord with kinetic molecular theory—is most troubling. This article shows that the variants of entropy can be treated from a unified viewpoint and argues that to decrease students' confusion about the nature of entropy change these variants of entropy should be merged. Molecular energy dispersal in space is implicit but unfortunately tacit in the cell models of statistical mechanics that develop the configurational entropy change in gas expansion, fluids mixing, or the addition of a non-volatile solute to a solvent. Two factors are necessary for entropy change in chemistry. An increase in thermodynamic entropy is enabled in a process by the motional energy of molecules (that, in chemical reactions, can arise from the energy released from a bond energy change). However, entropy increase is only actualized if the process results in a larger number of arrangements for the system's energy, that is, a final state that involves the most probable distribution for that energy under the new constraints. Positional entropy should be eliminated from general chemistry instruction and, especially benefiting "concrete minded" students, it should be replaced by emphasis on the motional energy of molecules as enabling entropy change.
Relative entropy of excited states in conformal field theories of arbitrary dimensions
Energy Technology Data Exchange (ETDEWEB)
Sárosi, Gábor [Theoretische Natuurkunde, Vrije Universiteit Brussels and International Solvay Institutes,Pleinlaan 2, Brussels, B-1050 (Belgium); David Rittenhouse Laboratory, University of Pennsylvania,Philadelphia, PA 19104 (United States); Ugajin, Tomonori [Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106 (United States)
2017-02-10
Extending our previous work, we study the relative entropy between the reduced density matrices obtained from globally excited states in conformal field theories of arbitrary dimensions. We find a general formula in the small subsystem size limit. When one of the states is the vacuum of the CFT, our result matches with the holographic entanglement entropy computations in the corresponding bulk geometries, including AdS black branes. We also discuss the first asymmetric part of the relative entropy and comment on some implications of the results on the distinguishability of black hole microstates in AdS/CFT.
Entropy of Reissner–Nordström–de Sitter black hole
Directory of Open Access Journals (Sweden)
Li-Chun Zhang
2016-10-01
Full Text Available Based on the consideration that the black hole horizon and the cosmological horizon of Reissner–Nordström black hole in de Sitter space are not independent each other, we conjecture the total entropy of the system should have an extra term contributed from the entanglement between the two horizons, except for the sum of the two horizon entropies. Making use of the globally effective first law and the effective thermodynamic quantities, we derive the total entropy and find that it will diverge as the two horizons tend to coincide.
Information Entropy of Fullerenes.
Sabirov, Denis Sh; Ōsawa, Eiji
2015-08-24
The reasons for the formation of the highly symmetric C60 molecule under nonequilibrium conditions are widely discussed as it dominates over numerous similar fullerene structures. In such conditions, evolution of structure rather than energy defines the processes. We have first studied the diversity of fullerenes in terms of information entropy. Sorting 2079 structures from An Atlas of Fullerenes [ Fowler , P. W. ; Manolopoulos , D. E. An Atlas of Fullerenes ; Oxford : Clarendon , 1995 . ], we have found that the information entropies of only 14 fullerenes (fullerenes. Interestingly, buckminsterfullerene is the only fullerene with zero information entropy, i.e., an exclusive compound among the other members of the fullerene family. Such an efficient sorting demonstrates possible relevance of information entropy to chemical processes. For this reason, we have introduced an algorithm for calculating changes in information entropy at chemical transformations. The preliminary calculations of changes in information entropy at the selected fullerene reactions show good agreement with thermochemical data.
Gaussian classical-quantum channels: gain of entanglement-assistance
Holevo, A. S.
2012-01-01
In the present paper we introduce and study Bosonic Gaussian classical-quantum (c-q) channels; the embedding of the classical input into quantum is always possible and therefore the classical entanglement-assisted capacity C_{ea} under appropriate input constraint is well defined. We prove a general property of entropy increase for weak complementary channel, that implies the equality C_{ea}=C (where C is the unassisted capacity) for certain class of c-q Gaussian channel under appropriate ene...
Relative entropy, mixed gauge-gravitational anomaly and causality
Energy Technology Data Exchange (ETDEWEB)
Bhattacharyya, Arpan [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); Centre For High Energy Phsyics, Indian Institute of Science,560012 Bangalore (India); Cheng, Long [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); Hung, Ling-Yan [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); Collaborative Innovation Center of Advanced Microstructures, Fudan University,220 Handan Road, 200433 Shanghai (China)
2016-07-25
In this note we explored the holographic relative entropy in the presence of the 5d Chern-Simons term, which introduces a mixed gauge-gravity anomaly to the dual CFT. The theory trivially satisfies an entanglement first law. However, to quadratic order in perturbations of the stress tensor T and current density J, there is a mixed contribution to the relative entropy bi-linear in T and J, signalling a potential violation of the positivity of the relative entropy. Miraculously, the term vanishes up to linear order in a derivative expansion. This prompted a closer inspection on a different consistency check, that involves time-delay of a graviton propagating in a charged background, scattered via a coupling supplied by the Chern-Simons term. The analysis suggests that the time-delay can take either sign, potentially violating causality for any finite value of the CS coupling.
Area law for localization-entropy in local quantum physics
Energy Technology Data Exchange (ETDEWEB)
Schroer, Bert [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)]. E-mail: schroer@cbpf.br
2002-02-01
The previously developed algebraic lightfront holography is used in conjunction with the tensor splitting of the chiral theory on the causal horizon. In this way a universal area law for the entanglement entropy of the vacuum relative to the split (tensor factorized) vacuum is obtained. The universality of the area law is a result of the kinematical structure of the properly defined lightfront degrees of freedom. We consider this entropy associated with causal horizon of the wedge algebra in Minkowski spacetime as an analog of the quantum Bekenstein black hole entropy similar to the way in which the Unruh temperature for the wedge algebra may be viewed as an analog in Minkowski spacetime of the Hawking thermal behavior. My more recent preprint hep-th/20202085 presents other aspects of the same problem. (author)
Entanglement for All Quantum States
de la Torre, A. C.; Goyeneche, D.; Leitao, L.
2010-01-01
It is shown that a state that is factorizable in the Hilbert space corresponding to some choice of degrees of freedom becomes entangled for a different choice of degrees of freedom. Therefore, entanglement is not a special case but is ubiquitous in quantum systems. Simple examples are calculated and a general proof is provided. The physical…
Generic entangling through quantum indistinguishability
Indian Academy of Sciences (India)
it exploits quantum indistinguishability as an important entangling mechanism, rather than using explicit interactions. The basic idea is as follows: Two identical particles in orthogonal states of the degree of freedom to be entangled (for example, opposite orientations in the case of spin) are mixed at a beamsplitter. Then the ...
Purified discord and multipartite entanglement
Energy Technology Data Exchange (ETDEWEB)
Brown, Eric G. [Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1 (Canada); Webster, Eric J. [Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1 (Canada); Martín-Martínez, Eduardo, E-mail: emmfis@gmail.com [Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1 (Canada); Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1 (Canada); Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5 (Canada); Kempf, Achim [Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1 (Canada); Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1 (Canada); Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1 (Canada); Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5 (Canada); Centre for Quantum Computing Technology, Department of Physics, University of Queensland, St. Lucia, Queensland 4072 (Australia)
2013-10-15
We study bipartite quantum discord as a manifestation of a multipartite entanglement structure in the tripartite purified system. In particular, we find that bipartite quantum discord requires the presence of both bipartite and tripartite entanglement in the purification. This allows one to understand the asymmetry of quantum discord, D(A,B)≠D(B,A) in terms of entanglement monogamy. As instructive special cases, we study discord for qubits and Gaussian states in detail. As a result of this we shed new light on a counterintuitive property of Gaussian states: the presence of classical correlations necessarily requires the presence of quantum correlations. Finally, our results also shed new light on a protocol for remote activation of entanglement by a third party. -- Highlights: •Bipartite quantum discord as a manifestation of multipartite entanglement. •Relevance of quantum discord as a utilizable resource for quantum info. tasks. •Quantum discord manifests itself in entanglement in the purified state. •Relation between asymmetry of discord and entanglement monogamy. •Protocol for remote activation of entanglement by a third party.
Emergence of Symmetries from Entanglement
CERN. Geneva
2016-01-01
Maximal Entanglement appears to be a key ingredient for the emergence of symmetries. We first illustrate this phenomenon using two examples: the emergence of conformal symmetry in condensed matter systems and the relation of tensor networks to holography. We further present a Principle of Maximal Entanglement that seems to dictate to a large extend the structure of gauge symmetry.
Energy Technology Data Exchange (ETDEWEB)
Santos, A.P., E-mail: alysonpaulo@dfte.ufrn.br [Universidade Federal do Rio Grande do Norte, Departamento de Fisica, Natal, RN 59072-970 (Brazil); Silva, R., E-mail: raimundosilva@dfte.ufrn.br [Universidade Federal do Rio Grande do Norte, Departamento de Fisica, Natal, RN 59072-970 (Brazil); Universidade do Estado Rio Grande do Norte, Departamento de Fisica, Mossoro, RN 59610-210 (Brazil); Alcaniz, J.S., E-mail: alcaniz@on.br [Observatorio Nacional, Rio de Janeiro, RJ 20921-400 (Brazil); Anselmo, D.H.A.L., E-mail: doryh@dfte.ufrn.br [Universidade Federal do Rio Grande do Norte, Departamento de Fisica, Natal, RN 59072-970 (Brazil)
2011-08-15
A deduction of generalized quantum entropies within the Tsallis and Kaniadakis frameworks is derived using a generalization of the ordinary multinomial coefficient. This generalization is based on the respective deformed multiplication and division. We show that the two above entropies are consistent with ones arbitrarily assumed at other contexts. -- Highlights: → Derivation of generalized quantum entropies. → Generalized combinatorial method. → Non-Gaussian quantum statistics.
Some Relations Among Entropy Measures
Sparavigna, Amelia Carolina
2015-01-01
Several entropies are generalizing the Shannon entropy and have it as their limit as entropic indices approach specific values. Here we discuss some relations existing among Rényi, Tsallis and Kaniadakis entropies and show how the Shannon entropy becomes the limit of Kaniadakis entropy
Energy Technology Data Exchange (ETDEWEB)
Nomura, Yasunori [Berkeley Center for Theoretical Physics, Department of Physics, University of California, Berkeley, CA 94720 (United States); Theoretical Physics Group, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study, Kashiwa 277-8583 (Japan); Salzetta, Nico, E-mail: nsalzetta@berkeley.edu [Berkeley Center for Theoretical Physics, Department of Physics, University of California, Berkeley, CA 94720 (United States); Theoretical Physics Group, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Sanches, Fabio; Weinberg, Sean J. [Berkeley Center for Theoretical Physics, Department of Physics, University of California, Berkeley, CA 94720 (United States); Theoretical Physics Group, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States)
2016-12-10
We study the Hilbert space structure of classical spacetimes under the assumption that entanglement in holographic theories determines semiclassical geometry. We show that this simple assumption has profound implications; for example, a superposition of classical spacetimes may lead to another classical spacetime. Despite its unconventional nature, this picture admits the standard interpretation of superpositions of well-defined semiclassical spacetimes in the limit that the number of holographic degrees of freedom becomes large. We illustrate these ideas using a model for the holographic theory of cosmological spacetimes.
CSIR Research Space (South Africa)
Mc
2012-07-01
Full Text Available stream_source_info McLaren_2012.pdf.txt stream_content_type text/plain stream_size 2190 Content-Encoding ISO-8859-1 stream_name McLaren_2012.pdf.txt Content-Type text/plain; charset=ISO-8859-1 High dimensional... entanglement M. McLAREN1,2, F.S. ROUX1 & A. FORBES1,2,3 1. CSIR National Laser Centre, PO Box 395, Pretoria 0001 2. School of Physics, University of the Stellenbosch, Private Bag X1, 7602, Matieland 3. School of Physics, University of Kwazulu...
Experimental entanglement of four particles
Sackett; Kielpinski; King; Langer; Meyer; Myatt; Rowe; Turchette; Itano; Wineland; Monroe
2000-03-16
Quantum mechanics allows for many-particle wavefunctions that cannot be factorized into a product of single-particle wavefunctions, even when the constituent particles are entirely distinct. Such 'entangled' states explicitly demonstrate the non-local character of quantum theory, having potential applications in high-precision spectroscopy, quantum communication, cryptography and computation. In general, the more particles that can be entangled, the more clearly nonclassical effects are exhibited--and the more useful the states are for quantum applications. Here we implement a recently proposed entanglement technique to generate entangled states of two and four trapped ions. Coupling between the ions is provided through their collective motional degrees of freedom, but actual motional excitation is minimized. Entanglement is achieved using a single laser pulse, and the method can in principle be applied to any number of ions.
Global and short-range entanglement properties in excited, many-body localized spin chains
West, Colin; Wei, Tzu-Chieh
Many-body localization is a manifestation of the violation of the eigenstate thermalization hypothesis. As one of many characteristic features, eigenstates in a many-body localized regime have been observed to obey an area law in the scaling of the entanglement entropy. Consequently, such states can be efficiently represented by matrix product states (MPS). Here, we use the SIMPS algorithm proposed by Yu, Pekker, and Clark to numerically access these excited states in spin chains with disorder, and study them from the perspective of their global and short range entanglement properties, as well as through other local observables. We compare the behavior across excited states as the strength of disorder varies.
Gaussian States Minimize the Output Entropy of One-Mode Quantum Gaussian Channels
De Palma, Giacomo; Trevisan, Dario; Giovannetti, Vittorio
2017-04-01
We prove the long-standing conjecture stating that Gaussian thermal input states minimize the output von Neumann entropy of one-mode phase-covariant quantum Gaussian channels among all the input states with a given entropy. Phase-covariant quantum Gaussian channels model the attenuation and the noise that affect any electromagnetic signal in the quantum regime. Our result is crucial to prove the converse theorems for both the triple trade-off region and the capacity region for broadcast communication of the Gaussian quantum-limited amplifier. Our result extends to the quantum regime the entropy power inequality that plays a key role in classical information theory. Our proof exploits a completely new technique based on the recent determination of the p →q norms of the quantum-limited amplifier [De Palma et al., arXiv:1610.09967]. This technique can be applied to any quantum channel.
The entangled accelerating universe
Energy Technology Data Exchange (ETDEWEB)
Gonzalez-Diaz, Pedro F. [Colina de los Chopos, Instituto de Fisica Fundamental, Consejo Superior de Investigaciones Cientificas, Serrano 121, 28006 Madrid (Spain); Estacion Ecologica de Biocosmologia, Pedro de Alvarado, 14, 06411-Medellin (Spain)], E-mail: p.gonzalezdiaz@imaff.cfmac.csic.es; Robles-Perez, Salvador [Colina de los Chopos, Instituto de Fisica Fundamental, Consejo Superior de Investigaciones Cientificas, Serrano 121, 28006 Madrid (Spain); Estacion Ecologica de Biocosmologia, Pedro de Alvarado, 14, 06411-Medellin (Spain)
2009-08-31
Using the known result that the nucleation of baby universes in correlated pairs is equivalent to spacetime squeezing, we show in this Letter that there exists a T-duality symmetry between two-dimensional warp drives, which are physically expressible as localized de Sitter little universes, and two-dimensional Tolman-Hawking and Gidding-Strominger baby universes respectively correlated in pairs, so that the creation of warp drives is also equivalent to spacetime squeezing. Perhaps more importantly, it has been also seen that the nucleation of warp drives entails a violation of the Bell's inequalities, and hence the phenomena of quantum entanglement, complementarity and wave function collapse. These results are generalized to the case of any dynamically accelerating universe filled with dark or phantom energy whose creation is also physically equivalent to spacetime squeezing and to the violation of the Bell's inequalities, so that the universe we are living in should be governed by essential sharp quantum theory laws and must be a quantum entangled system.
Classical Maxwellian polarization entanglement
Carroll, John E
2015-01-01
An explanation of polarization entanglement is presented using Maxwells classical electromagnetic theory.Two key features are required to understand these classical origins.The first is that all waves diffract and weakly diffracting waves,with a principal direction of propagation in the laboratory frame, travel along that direction at speeds ever so slightly less than c.This allows nontrivial Lorentz transformations that can act on selected forward F waves or selected waves R traveling in the opposite direction to show that both can arise from a single zero momentum frame where all the waves are transverse to the original principal direction.Such F and R waves then both belong to a single relativistic entity where correlations between the two are unremarkable.The second feature requires the avoidance of using the Coulomb gauge.Waves, tending to plane waves in the limit of zero diffraction,can then be shown to be composed of two coupled sets of E and B fields that demonstrate the classical entanglement of F an...
Schlawin, Frank
2017-10-01
This tutorial outlines the theory of nonlinear spectroscopy with quantum light, and in particular with entangled photons. To this end, we briefly review molecular quantum electrodynamics, and discuss the approximations involved. Then we outline the perturbation theory underlying nonlinear spectroscopy. In contrast to the conventional semiclassical theory, our derivation starts from Glauber's photon counting formalism, and naturally includes the semiclassical theory as a special case. Finally, we review previous work, which we sort into work depending on the unusual features of quantum noise, and work relying upon quantum correlations in entangled photons. This work naturally draws from both quantum optics and chemical physics. Even though it is impossible to provide a comprehensive overview of both fields in one tutorial, this text aims to be self-contained. We refer to specialised reviews, where we cannot provide details. We do not attempt to provide an exhaustive review of all the literature, but rather focus on specific examples intended to elucidate the underlying physics, and merely cite the remaining publications.
Lou, Jie; Tanaka, Shu; Katsura, Hosho; Kawashima, Naoki
2011-12-01
We investigate the entanglement properties of the valence-bond-solid (VBS) state defined on two-dimensional lattices, which is the exact ground state of the Affleck-Kennedy-Lieb-Tasaki model. It is shown that the entanglement entropy obeys an area law and the nonuniversal prefactor of the leading term is strictly less than ln2. The analysis of entanglement spectra for various lattices reveals that the reduced density matrix associated with the VBS state is closely related to a thermal density matrix of a holographic spin chain, the spectrum of which is reminiscent of that of the spin-1/2 Heisenberg chain. This correspondence is further supported by comparing the entanglement entropy in the holographic spin chain with conformal field theory predictions.
Experimental entanglement distillation of mesoscopic quantum states
DEFF Research Database (Denmark)
Dong, Ruifang; Lassen, Mikael Østergaard; Heersink, Joel
2008-01-01
channel, the distribution of loss-intolerant entangled states is inevitably afflicted by decoherence, which causes a degradation of the transmitted entanglement. To combat the decoherence, entanglement distillation, a process of extracting a small set of highly entangled states from a large set of less...... entangled states, can be used(4-14). Here we report on the distillation of deterministically prepared light pulses entangled in continuous variables that have undergone non-Gaussian noise. The entangled light pulses(15-17) are sent through a lossy channel, where the transmission is varying in time similarly...
Indian Academy of Sciences (India)
lay in uncovering the microscopic meaning of entropy, in answering the ... mann's life and work. More on the subject can be found in the various 'entropy articles' in this special issue dedicated to him, as well as in others to which I refer at the end. Ludwig Eduard .... to suicide partly because of a fear that his ideas were not ...
Gravitational Entropy and Inflation
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Øystein Elgarøy
2013-09-01
Full Text Available The main topic of this paper is a description of the generation of entropy at the end of the inflationary era. As a generalization of the present standard model of the Universe dominated by pressureless dust and a Lorentz invariant vacuum energy (LIVE, we first present a flat Friedmann universe model, where the dust is replaced with an ideal gas. It is shown that the pressure of the gas is inversely proportional to the fifth power of the scale factor and that the entropy in a comoving volume does not change during the expansion. We then review different measures of gravitational entropy related to the Weyl curvature conjecture and calculate the time evolution of two proposed measures of gravitational entropy in a LIVE-dominated Bianchi type I universe, and a Lemaitre-Bondi-Tolman universe with LIVE. Finally, we elaborate upon a model of energy transition from vacuum energy to radiation energy, that of Bonanno and Reuter, and calculate the time evolution of the entropies of vacuum energy and radiation energy. We also calculate the evolution of the maximal entropy according to some recipes and demonstrate how a gap between the maximal entropy and the actual entropy opens up at the end of the inflationary era.
Santos, A. P.; Silva, R.; Alcaniz, J. S.; Anselmo, D. H. A. L.
2011-08-01
A deduction of generalized quantum entropies within the Tsallis and Kaniadakis frameworks is derived using a generalization of the ordinary multinomial coefficient. This generalization is based on the respective deformed multiplication and division. We show that the two above entropies are consistent with ones arbitrarily assumed at other contexts.
Graphical Classification of Entangled Qutrits
Directory of Open Access Journals (Sweden)
Kentaro Honda
2012-10-01
Full Text Available A multipartite quantum state is entangled if it is not separable. Quantum entanglement plays a fundamental role in many applications of quantum information theory, such as quantum teleportation. Stochastic local quantum operations and classical communication (SLOCC cannot essentially change quantum entanglement without destroying it. Therefore, entanglement can be classified by dividing quantum states into equivalence classes, where two states are equivalent if each can be converted into the other by SLOCC. Properties of this classification, especially in the case of non two-dimensional quantum systems, have not been well studied. Graphical representation is sometimes used to clarify the nature and structural features of entangled states. SLOCC equivalence of quantum bits (qubits has been described graphically via a connection between tripartite entangled qubit states and commutative Frobenius algebras (CFAs in monoidal categories. In this paper, we extend this method to qutrits, i.e., systems that have three basis states. We examine the correspondence between CFAs and tripartite entangled qutrits. Using the symmetry property, which is required by the definition of a CFA, we find that there are only three equivalence classes that correspond to CFAs. We represent qutrits graphically, using the connection to CFAs. We derive equations that characterize the three equivalence classes. Moreover, we show that any qutrit can be represented as a composite of three graphs that correspond to the three classes.
Accessible quantification of multiparticle entanglement
Cianciaruso, Marco; Bromley, Thomas R.; Adesso, Gerardo
2016-10-01
Entanglement is a key ingredient for quantum technologies and a fundamental signature of quantumness in a broad range of phenomena encompassing many-body physics, thermodynamics, cosmology and life sciences. For arbitrary multiparticle systems, entanglement quantification typically involves nontrivial optimisation problems, and it may require demanding tomographical techniques. Here, we develop an experimentally feasible approach to the evaluation of geometric measures of multiparticle entanglement. Our framework provides analytical results for particular classes of mixed states of N qubits, and computable lower bounds to global, partial, or genuine multiparticle entanglement of any general state. For global and partial entanglement, useful bounds are obtained with minimum effort, requiring local measurements in just three settings for any N. For genuine entanglement, a number of measurements scaling linearly with N are required. We demonstrate the power of our approach to estimate and quantify different types of multiparticle entanglement in a variety of N-qubit states useful for quantum information processing and recently engineered in laboratories with quantum optics and trapped ion setups.
Out-of-equilibrium correlated systems: Bipartite entanglement as a probe of thermalization
Poilblanc, Didier
2011-07-01
Thermalization plays a central role in out-of-equilibrium physics of ultracold atoms or electronic transport phenomena. On the other hand, entanglement concepts have proven to be extremely useful to investigate quantum phases of matter. Here, it is argued that bipartite entanglement measures provide key information on out-of-equilibrium states and might therefore offer stringent thermalization criteria. This is illustrated by considering a global quench in an (extended) XXZ spin-1/2 chain across its (zero-temperature) quantum critical point. A nonlocal bipartition of the chain preserving translation symmetry is proposed. The time evolution after the quench of the reduced density matrix of the half-system is computed and its associated (time-dependent) entanglement spectrum is analyzed. Generically, the corresponding entanglement entropy quickly reaches a “plateau” after a short transient regime. However, in the case of the integrable XXZ chain, the low-energy entanglement spectrum still reveals strong time fluctuations. In addition, its infinite-time average shows strong deviations from the spectrum of a Boltzmann thermal density matrix. In contrast, when the integrability of the model is broken (by small next-nearest-neighbor couplings), the entanglement spectra of the time average and thermal density matrices become remarkably similar.
Entangled light from white noise.
Plenio, M B; Huelga, S F
2002-05-13
An atom that couples to two distinct leaky optical cavities is driven by an external optical white noise field. We describe how entanglement between the light fields sustained by two optical cavities arises in such a situation. The entanglement is maximized for intermediate values of the cavity damping rates and the intensity of the white noise field, vanishing both for small and for large values of these parameters and thus exhibiting a stochastic-resonancelike behavior. This example illustrates the possibility of generating entanglement by exclusively incoherent means and sheds new light on the constructive role noise may play in certain tasks of interest for quantum information processing.
Nonsymmetric entropy I: basic concepts and results
Liu, Chengshi
2006-01-01
A new concept named nonsymmetric entropy which generalizes the concepts of Boltzman's entropy and shannon's entropy, was introduced. Maximal nonsymmetric entropy principle was proven. Some important distribution laws were derived naturally from maximal nonsymmetric entropy principle.
Conditional Kaniadakis Entropy: a Preliminary Discussion
Sparavigna, Amelia Carolina
2015-01-01
Conditional entropies are fundamental for evaluating the mutual information of random variables. These entropies must be properly defined in the case of nonadditive entropies. Here, we propose the conditional entropy for one of them, the Kaniadakis entropy
Anomalies and entanglement renormalization
Bridgeman, Jacob C.; Williamson, Dominic J.
2017-09-01
We study 't Hooft anomalies of discrete groups in the framework of (1+1)-dimensional multiscale entanglement renormalization ansatz states on the lattice. Using matrix product operators, general topological restrictions on conformal data are derived. An ansatz class allowing for optimization of MERA with an anomalous symmetry is introduced. We utilize this class to numerically study a family of Hamiltonians with a symmetric critical line. Conformal data is obtained for all irreducible projective representations of each anomalous symmetry twist, corresponding to definite topological sectors. It is numerically demonstrated that this line is a protected gapless phase. Finally, we implement a duality transformation between a pair of critical lines using our subclass of MERA.
Three-dimensional Neumann-series approach to model light transport in nonuniform media.
Jha, Abhinav K; Kupinski, Matthew A; Barrett, Harrison H; Clarkson, Eric; Hartman, John H
2012-09-01
We present the implementation, validation, and performance of a three-dimensional (3D) Neumann-series approach to model photon propagation in nonuniform media using the radiative transport equation (RTE). The RTE is implemented for nonuniform scattering media in a spherical harmonic basis for a diffuse-optical-imaging setup. The method is parallelizable and implemented on a computing system consisting of NVIDIA Tesla C2050 graphics processing units (GPUs). The GPU implementation provides a speedup of up to two orders of magnitude over non-GPU implementation, which leads to good computational efficiency for the Neumann-series method. The results using the method are compared with the results obtained using the Monte Carlo simulations for various small-geometry phantoms, and good agreement is observed. We observe that the Neumann-series approach gives accurate results in many cases where the diffusion approximation is not accurate.
Standing in the gap: ref lections on translating the Jung-Neumann correspondence.
McCartney, Heather
2016-04-01
This paper considers the experience of translating the correspondence between C.G. Jung and Erich Neumann as part of the Philemon series. The translator explores the similarities between analytical work and the task of translation by means of the concepts of the dialectical third and the interactional field. The history and politics of the translation of analytic writing and their consequences for the lingua franca of analysis are discussed. Key themes within the correspondence are outlined, including Jung and Neumann's pre-war exploration of Judaism and the unconscious, the post-war difficulties around the publication of Neumann's Depth Psychology and a New Ethic set against the early years of the C.G. Jung Institute in Zurich, and the development of the correspondents' relationship over time. © 2016, The Society of Analytical Psychology.
Entropy coherent and entropy convex measures of risk
Laeven, R.J.A.; Stadje, M.
2013-01-01
We introduce two subclasses of convex measures of risk, referred to as entropy coherent and entropy convex measures of risk. Entropy coherent and entropy convex measures of risk are special cases of φ-coherent and φ-convex measures of risk. Contrary to the classical use of coherent and convex
Entropy of the Mixture of Sources and Entropy Dimension
Smieja, Marek; Tabor, Jacek
2011-01-01
We investigate the problem of the entropy of the mixture of sources. There is given an estimation of the entropy and entropy dimension of convex combination of measures. The proof is based on our alternative definition of the entropy based on measures instead of partitions.
Entropy Coherent and Entropy Convex Measures of Risk
Laeven, R.J.A.; Stadje, M.A.
2011-01-01
We introduce two subclasses of convex measures of risk, referred to as entropy coherent and entropy convex measures of risk. We prove that convex, entropy convex and entropy coherent measures of risk emerge as certainty equivalents under variational, homothetic and multiple priors preferences,
Measuring higher-dimensional entanglement
Datta, Chandan; Agrawal, Pankaj; Choudhary, Sujit K.
2017-04-01
We study local-realistic inequalities, Bell-type inequalities, for bipartite pure states of finite dimensional quantum systems—qudits. There are a number of proposed Bell-type inequalities for such systems. Our interest is in relating the value of the Bell-type inequality function with a measure of entanglement. Interestingly, we find that one of these inequalities, the Son-Lee-Kim inequality, can be used to measure entanglement of a pure bipartite qudit state and a class of mixed two-qudit states. Unlike the majority of earlier schemes in this direction, where the number of observables needed to characterize the entanglement increases with the dimension of the subsystems, this method needs only four observables. We also discuss the experimental feasibility of this scheme. It turns out that current experimental setups can be used to measure the entanglement using our scheme.
Continuous-Variable Entanglement Swapping
Directory of Open Access Journals (Sweden)
Kevin Marshall
2015-05-01
Full Text Available We present a very brief overview of entanglement swapping as it relates to continuous-variable quantum information. The technical background required is discussed and the natural link to quantum teleportation is established before discussing the nature of Gaussian entanglement swapping. The limitations of Gaussian swapping are introduced, along with the general applications of swapping in the context of to quantum communication and entanglement distribution. In light of this, we briefly summarize a collection of entanglement swapping schemes which incorporate a non-Gaussian ingredient and the benefits of such schemes are noted. Finally, we motivate the need to further study and develop such schemes by highlighting requirements of a continuous-variable repeater.
Entangled Bessel-Gaussian beams
CSIR Research Space (South Africa)
McLaren, M
2012-10-01
Full Text Available by performing a Bell-type experiment and showing a violation of the Clauser-Horne-Shimony-Holt inequality. In addition, we use quantum state tomography to indicate higher-dimensional entanglement in terms of BG modes....
Characterizing quantum correlations. Entanglement, uncertainty relations and exponential families
Energy Technology Data Exchange (ETDEWEB)
Niekamp, Soenke
2012-04-20
This thesis is concerned with different characterizations of multi-particle quantum correlations and with entropic uncertainty relations. The effect of statistical errors on the detection of entanglement is investigated. First, general results on the statistical significance of entanglement witnesses are obtained. Then, using an error model for experiments with polarization-entangled photons, it is demonstrated that Bell inequalities with lower violation can have higher significance. The question for the best observables to discriminate between a state and the equivalence class of another state is addressed. Two measures for the discrimination strength of an observable are defined, and optimal families of observables are constructed for several examples. A property of stabilizer bases is shown which is a natural generalization of mutual unbiasedness. For sets of several dichotomic, pairwise anticommuting observables, uncertainty relations using different entropies are constructed in a systematic way. Exponential families provide a classification of states according to their correlations. In this classification scheme, a state is considered as k-correlated if it can be written as thermal state of a k-body Hamiltonian. Witness operators for the detection of higher-order interactions are constructed, and an algorithm for the computation of the nearest k-correlated state is developed.
Entanglement distribution in quantum networks
Energy Technology Data Exchange (ETDEWEB)
Perseguers, Sebastien
2010-04-15
This Thesis contributes to the theory of entanglement distribution in quantum networks, analyzing the generation of long-distance entanglement in particular. We consider that neighboring stations share one partially entangled pair of qubits, which emphasizes the difficulty of creating remote entanglement in realistic settings. The task is then to design local quantum operations at the stations, such that the entanglement present in the links of the whole network gets concentrated between few parties only, regardless of their spatial arrangement. First, we study quantum networks with a two-dimensional lattice structure, where quantum connections between the stations (nodes) are described by non-maximally entangled pure states (links). We show that the generation of a perfectly entangled pair of qubits over an arbitrarily long distance is possible if the initial entanglement of the links is larger than a threshold. This critical value highly depends on the geometry of the lattice, in particular on the connectivity of the nodes, and is related to a classical percolation problem. We then develop a genuine quantum strategy based on multipartite entanglement, improving both the threshold and the success probability of the generation of long-distance entanglement. Second, we consider a mixed-state definition of the connections of the quantum networks. This formalism is well-adapted for a more realistic description of systems in which noise (random errors) inevitably occurs. New techniques are required to create remote entanglement in this setting, and we show how to locally extract and globally process some error syndromes in order to create useful long-distance quantum correlations. Finally, we turn to networks that have a complex topology, which is the case for most real-world communication networks such as the Internet for instance. Besides many other characteristics, these systems have in common the small-world feature, stating that any two nodes are separated by a
Directory of Open Access Journals (Sweden)
Leonid M. Martyushev
2015-06-01
Full Text Available The entropy production (inside the volume bounded by a photosphere of main-sequence stars, subgiants, giants, and supergiants is calculated based on B–V photometry data. A non-linear inverse relationship of thermodynamic fluxes and forces as well as an almost constant specific (per volume entropy production of main-sequence stars (for 95% of stars, this quantity lies within 0.5 to 2.2 of the corresponding solar magnitude is found. The obtained results are discussed from the perspective of known extreme principles related to entropy production.
Tensor Renormalization of Quantum Many-Body Systems Using Projected Entangled Simplex States
Directory of Open Access Journals (Sweden)
Z. Y. Xie
2014-02-01
Full Text Available We propose a new class of tensor-network states, which we name projected entangled simplex states (PESS, for studying the ground-state properties of quantum lattice models. These states extend the pair-correlation basis of projected entangled pair states to a simplex. PESS are exact representations of the simplex solid states, and they provide an efficient trial wave function that satisfies the area law of entanglement entropy. We introduce a simple update method for evaluating the PESS wave function based on imaginary-time evolution and the higher-order singular-value decomposition of tensors. By applying this method to the spin-1/2 antiferromagnetic Heisenberg model on the kagome lattice, we obtain accurate and systematic results for the ground-state energy, which approach the lowest upper bounds yet estimated for this quantity.
Lee, Khiy Wei; Murid, Ali H. M.; Sangawi, Ali W. K.
2017-08-01
We study a numerical approach for solving integral equation with adjoint generalized Neumann kernel related to conformal mapping. Previously, computation of conformal mapping of M + 1 connected regions require solving at least M + 1 integral equations with adjoint generalized Neumann kernel separately. We apply global simpler GMRES which solve nonsymmetric system with multiple right-hand sides to solve M + 1 integral equations simultaneously. We also apply fast multipole method for several matrix vector products in every iteration of global simpler GMRES. Numerical example is given to illustrate the effectiveness of the proposed method.
Introducing formalism in economics: The growth model of John von Neumann
Directory of Open Access Journals (Sweden)
Gloria-Palermo Sandye
2010-01-01
Full Text Available The objective is to interpret John von Neumann's growth model as a decisive step of the forthcoming formalist revolution of the 1950s in economics. This model gave rise to an impressive variety of comments about its classical or neoclassical underpinnings. We go beyond this traditional criterion and interpret rather this model as the manifestation of von Neumann's involvement in the formalist programme of mathematician David Hilbert. We discuss the impact of Kurt Gödel's discoveries on this programme. We show that the growth model reflects the pragmatic turn of the formalist programme after Gödel and proposes the extension of modern axiomatisation to economics.
Large time behavior of solutions to parabolic equations with Neumann boundary conditions
da Lio, Francesca
2008-03-01
In this paper we are interested in the large time behavior as t-->+[infinity] of the viscosity solutions of parabolic equations with nonlinear Neumann type boundary conditions in connection with ergodic boundary problems which have been recently studied by Barles and the author in [G. Barles, F. Da Lio, On the boundary ergodic problem for fully nonlinear equations in bounded domains with general nonlinear Neumann boundary conditions, Ann. Inst. H. Poincaré Anal. Non Linèaire 22 (5) (2005) 521-541].
Quantum Entanglement and Chemical Reactivity.
Molina-Espíritu, M; Esquivel, R O; López-Rosa, S; Dehesa, J S
2015-11-10
The water molecule and a hydrogenic abstraction reaction are used to explore in detail some quantum entanglement features of chemical interest. We illustrate that the energetic and quantum-information approaches are necessary for a full understanding of both the geometry of the quantum probability density of molecular systems and the evolution of a chemical reaction. The energy and entanglement hypersurfaces and contour maps of these two models show different phenomena. The energy ones reveal the well-known stable geometry of the models, whereas the entanglement ones grasp the chemical capability to transform from one state system to a new one. In the water molecule the chemical reactivity is witnessed through quantum entanglement as a local minimum indicating the bond cleavage in the dissociation process of the molecule. Finally, quantum entanglement is also useful as a chemical reactivity descriptor by detecting the transition state along the intrinsic reaction path in the hypersurface of the hydrogenic abstraction reaction corresponding to a maximally entangled state.
Paulinelli, H. G.; de Souza, S. M.; Rojas, Onofre
2013-07-01
In this paper we explore the entanglement in an orthogonal dimer-plaquette Ising-Heisenberg chain, assembled between plaquette edges, also known as orthogonal dimer plaquettes. The quantum entanglement properties involving an infinite chain structure are quite important, not only because the mathematical calculation is cumbersome but also because real materials are well represented by infinite chains. Using the local gauge symmetry of this model, we are able to map onto a simple spin-1 like Ising and spin-1/2 Heisenberg dimer model with single effective ion anisotropy. Thereafter this model can be solved using the decoration transformation and transfer matrix approach. First, we discuss the phase diagram at zero temperature of this model, where we find five ground states, one ferromagnetic, one antiferromagnetic, one triplet-triplet disordered and one triplet-singlet disordered phase, beside a dimer ferromagnetic-antiferromagnetic phase. In addition, we discuss the thermodynamic properties such as entropy, where we display the residual entropy. Furthermore, using the nearest site correlation function it is possible also to analyze the pairwise thermal entanglement for both orthogonal dimers. Additionally, we discuss the threshold temperature of the entangled region as a function of Hamiltonian parameters. We find a quite interesting thin reentrance threshold temperature for one of the dimers, and we also discuss the differences and similarities for both dimers.
Multipartite geometric entanglement in finite size XY model
Energy Technology Data Exchange (ETDEWEB)
Blasone, Massimo; Dell' Anno, Fabio; De Siena, Silvio; Giampaolo, Salvatore Marco; Illuminati, Fabrizio, E-mail: blasone@sa.infn.i [Dipartimento di Matematica e Informatica, Universita degli Studi di Salerno, Via Ponte don Melillo, I-84084 Fisciano (Italy)
2009-06-01
We investigate the behavior of the multipartite entanglement in the finite size XY model by means of the hierarchical geometric measure of entanglement. By selecting specific components of the hierarchy, we study both global entanglement and genuinely multipartite entanglement.
Entropy of international trades
Oh, Chang-Young; Lee, D.-S.
2017-05-01
The organization of international trades is highly complex under the collective efforts towards economic profits of participating countries given inhomogeneous resources for production. Considering the trade flux as the probability of exporting a product from a country to another, we evaluate the entropy of the world trades in the period 1950-2000. The trade entropy has increased with time, and we show that it is mainly due to the extension of trade partnership. For a given number of trade partners, the mean trade entropy is about 60% of the maximum possible entropy, independent of time, which can be regarded as a characteristic of the trade fluxes' heterogeneity and is shown to be derived from the scaling and functional behaviors of the universal trade-flux distribution. The correlation and time evolution of the individual countries' gross-domestic products and the number of trade partners show that most countries achieved their economic growth partly by extending their trade relationship.
Stabilities of generalized entropies
Energy Technology Data Exchange (ETDEWEB)
Abe, Sumiyoshi [Institute of Physics, University of Tsukuba, Ibaraki 305-8571 (Japan); Kaniadakis, G [Dipartimento di Fisica and Istituto Nazionale di Fisica della Materia (INFM), Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino (Italy); Scarfone, A M [Dipartimento di Fisica and Istituto Nazionale di Fisica della Materia (INFM), Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino (Italy)
2004-11-05
The generalized entropic measure, which is maximized by a given arbitrary distribution under the constraints on normalization of the distribution and the finite ordinary expectation value of a physical random quantity, is considered. To examine if it can be of physical relevance, its experimental robustness is discussed. In particular, Lesche's criterion is analysed, which states that an entropic measure is stable if its change under an arbitrary weak deformation of the distribution (representing fluctuations of experimental data) remains small. It is essential to note the difference between this criterion and thermodynamic stability. A general condition, under which the generalized entropy becomes stable, is derived. Examples known in the literature, including the entropy for the stretched-exponential distribution, the quantum-group entropy and the {kappa}-entropy are discussed.
Antibunching dynamics of plasmonically mediated entanglement generation
Dumitrescu, Eugene; Lawrie, Benjamin
2017-11-01
Dissipative entanglement-generation protocols embrace environmental interactions to generate long-lived entangled states. In this paper, we report on the antibunching dynamics for a pair of actively driven quantum emitters coupled to a shared dissipative plasmonic reservoir. We find that antibunching is a universal signature for entangled states generated by dissipative means and examine its use as an entanglement diagnostic. We discuss the experimental validation of plasmonically mediated entanglement generation by Hanbury Brown-Twiss interferometry with picosecond timing resolution determined by an effective two-qubit Rabi frequency, and we analyze the robustness of entanglement generation with respect to perturbations in local detunings, couplings, and driving fields.
Stabilities of generalized entropies
Abe, Sumiyoshi; Kaniadakis, G.; Scarfone, A. M.
2004-01-01
The generalized entropic measure, which is optimized by a given arbitrary distribution under the constraints on normalization of the distribution and the finite ordinary expectation value of a physical random quantity, is considered and its Lesche stability property (that is different from thermodynamic stability) is examined. A general condition, under which the generalized entropy becomes stable, is derived. Examples known in the literature, including the entropy for the stretched-exponenti...
Jha, Abhinav K; Kupinski, Matthew A; Masumura, Takahiro; Clarkson, Eric; Maslov, Alexey V; Barrett, Harrison H
2012-08-01
We present the implementation, validation, and performance of a Neumann-series approach for simulating light propagation at optical wavelengths in uniform media using the radiative transport equation (RTE). The RTE is solved for an anisotropic-scattering medium in a spherical harmonic basis for a diffuse-optical-imaging setup. The main objectives of this paper are threefold: to present the theory behind the Neumann-series form for the RTE, to design and develop the mathematical methods and the software to implement the Neumann series for a diffuse-optical-imaging setup, and, finally, to perform an exhaustive study of the accuracy, practical limitations, and computational efficiency of the Neumann-series method. Through our results, we demonstrate that the Neumann-series approach can be used to model light propagation in uniform media with small geometries at optical wavelengths.
Entropy Is Simple, Qualitatively
Lambert, Frank L.
2002-10-01
Qualitatively, entropy is simple. What it is, why it is useful in understanding the behavior of macro systems or of molecular systems is easy to state: Entropy increase from a macro viewpoint is a measure of the dispersal of energy from localized to spread out at a temperature T. The conventional q in qrev/T is the energy dispersed to or from a substance or a system. On a molecular basis, entropy increase means that a system changes from having fewer accessible microstates to having a larger number of accessible microstates. Fundamentally based on statistical and quantum mechanics, this approach is superior to the non-fundamental "disorder" as a descriptor of entropy change. The foregoing in no way denies the subtlety or the difficulty presented by entropy in thermodynamics—to first-year students or to professionals. However, as an aid to beginners in their quantitative study of thermodynamics, the qualitative conclusions in this article give students the advantage of a clear bird’s-eye view of why entropy increases in a wide variety of basic cases: a substance going from 0 K to T, phase change, gas expansion, mixing of ideal gases or liquids, colligative effects, and the Gibbs equation. See Letter re: this article.
Entropy, matter, and cosmology.
Prigogine, I; Géhéniau, J
1986-09-01
The role of irreversible processes corresponding to creation of matter in general relativity is investigated. The use of Landau-Lifshitz pseudotensors together with conformal (Minkowski) coordinates suggests that this creation took place in the early universe at the stage of the variation of the conformal factor. The entropy production in this creation process is calculated. It is shown that these dissipative processes lead to the possibility of cosmological models that start from empty conditions and gradually build up matter and entropy. Gravitational entropy takes a simple meaning as associated to the entropy that is necessary to produce matter. This leads to an extension of the third law of thermodynamics, as now the zero point of entropy becomes the space-time structure out of which matter is generated. The theory can be put into a convenient form using a supplementary "C" field in Einstein's field equations. The role of the C field is to express the coupling between gravitation and matter leading to irreversible entropy production.
Entangled states in quantum mechanics
Ruža, Jānis
2010-01-01
In some circles of quantum physicists, a view is maintained that the nonseparability of quantum systems-i.e., the entanglement-is a characteristic feature of quantum mechanics. According to this view, the entanglement plays a crucial role in the solution of quantum measurement problem, the origin of the “classicality” from the quantum physics, the explanation of the EPR paradox by a nonlocal character of the quantum world. Besides, the entanglement is regarded as a cornerstone of such modern disciplines as quantum computation, quantum cryptography, quantum information, etc. At the same time, entangled states are well known and widely used in various physics areas. In particular, this notion is widely used in nuclear, atomic, molecular, solid state physics, in scattering and decay theories as well as in other disciplines, where one has to deal with many-body quantum systems. One of the methods, how to construct the basis states of a composite many-body quantum system, is the so-called genealogical decomposition method. Genealogical decomposition allows one to construct recurrently by particle number the basis states of a composite quantum system from the basis states of its forming subsystems. These coupled states have a structure typical for entangled states. If a composite system is stable, the internal structure of its forming basis states does not manifest itself in measurements. However, if a composite system is unstable and decays onto its forming subsystems, then the measurables are the quantum numbers, associated with these subsystems. In such a case, the entangled state has a dynamical origin, determined by the Hamiltonian of the corresponding decay process. Possible correlations between the quantum numbers of resulting subsystems are determined by the symmetries-conservation laws of corresponding dynamical variables, and not by the quantum entanglement feature.
On the Conditional Rényi Entropy
S. Fehr (Serge); S. Berens (Stefan)
2014-01-01
htmlabstractThe Rényi entropy of general order unifies the well-known Shannon entropy with several other entropy notions, like the min-entropy or the collision entropy. In contrast to the Shannon entropy, there seems to be no commonly accepted definition for the conditional Rényi entropy: several
Dirichlet-Neumann bracketing for boundary-value problems on graphs
Directory of Open Access Journals (Sweden)
Sonja Currie
2005-08-01
Full Text Available We consider the spectral structure of second order boundary-value problems on graphs. A variational formulation for boundary-value problems on graphs is given. As a consequence we can formulate an analogue of Dirichlet-Neumann bracketing for boundary-value problems on graphs. This in turn gives rise to eigenvalue and eigenfunction asymptotic approximations.
Sahli, B.; Bencheikh, L.
2010-11-01
The question of non-uniqueness in boundary integral equation formulations of exterior Neumann boundary-value problem in elasticity can be resolved by seeking the solution in the form of a single-layer potential. We present an analysis of the appropriate choice of the multipole coefficients which is optimal in the sense of minimizing the condition number of the boundary integral operator.
Solvability of some Neumann-type boundary value problems for biharmonic equations
Directory of Open Access Journals (Sweden)
Valery Karachik
2017-09-01
Full Text Available We study some boundary-value problems for inhomogeneous biharmonic equation with periodic boundary conditions. These problems are generalization to periodic data of the Neumann-type boundary-value problems considered before by the authors. We obtain existence and uniqueness of solutions for the problems under consideration.
Nonlinear parabolic problems with Neumann-type boundary conditions and L^1-data
Directory of Open Access Journals (Sweden)
Abderrahmane El Hachimi
2007-11-01
$$ \\frac{\\partial u}{\\partial t}-\\triangle_{p}u+\\alpha(u=f \\quad \\text{in } ]0,\\ T[\\times\\Omega, $$ with Neumann-type boundary conditions and initial data in $L^1$. Our approach is based essentially on the time discretization technique by Euler forward scheme.
Existence of infinitely many nodal solutions for a superlinear Neumann boundary value problem
Directory of Open Access Journals (Sweden)
Aixia Qian
2005-11-01
Full Text Available We study the existence of a class of nonlinear elliptic equation with Neumann boundary condition, and obtain infinitely many nodal solutions. The study of such a problem is based on the variational methods and critical point theory. We prove the conclusion by using the symmetric mountain-pass theorem under the Cerami condition.
Pairs of sign-changing solutions for sublinear elliptic equations with Neumann boundary conditions
Directory of Open Access Journals (Sweden)
Chengyue Li
2014-04-01
Full Text Available We consider the Neumann problem for a sublinear elliptic equation in a convex bounded domain of $\\mathbb{R}^{N}$. Using an variant of Clark Theorem, we obtain the existence and multiplicity of its pairs of sign-changing solutions.
Directory of Open Access Journals (Sweden)
Zhe Hu
2016-07-01
Full Text Available This article concerns the existence of positive solutions for a nonlinear Neumann problem involving the m-Laplacian. The equation does not have a variational structure. We use a blow-up argument and a Liouville-type theorem to obtain a priori estimates and obtain the existence of positive solutions by the Krasnoselskii fixed point theorem.
Nonlinear Fredholm alternative for the p-Laplacian under nonhomogeneous Neumann boundary condition
Directory of Open Access Journals (Sweden)
Gustavo Ferron Madeira
2016-08-01
Full Text Available The nonlinear Fredholm alternative for the p-Laplacian in higher dimensions is established when nonhomogeneous terms appear in the equation and in the Neumann boundary condition. Further, the geometry of the associated energy functional is described and compared with the Dirichlet counterpart. The proofs require only variational methods.
On stability of difference schemes for hyperbolic multipoint NBVP with Neumann conditions
Yildirim, Ozgur; Uzun, Meltem
2016-08-01
In this work, a multipoint nonlocal boundary value problem (NBVP) for hyperbolic equations with Neumann conditions is considered. Third and fourth order of accuracy stable difference schemes for solving this problem are presented. Efficiency of these schemes are tested via MATLAB implementation.
Paulo Freire and the Politics of Education: A Response to Neumann
Roberts, Peter
2016-01-01
Jacob Neumann provides a thoughtful reading of "Paulo Freire in the 21st century: Education, dialogue, and transformation" [v48 n6 p634-644 2016]. His comments on the importance of contextualising Freire's work and the value of openness in engaging Freirean ideas are insightful and helpful. His use of the term "apolitical" is,…
Magnetic bottles for the Neumann problem: The case of dimension 3
Indian Academy of Sciences (India)
http://www.ias.ac.in/article/fulltext/pmsc/112/01/0071-0084. Keywords. Spectral theory; Schrödinger operators; magnetic fields; superconductivity. Abstract. The main object of this paper is to analyze the recent results obtained on the Neumann realization of the Schrödinger operator in the case of dimension 3 by Lu and Pan.
EEG entropy measures in anesthesia
Directory of Open Access Journals (Sweden)
Zhenhu eLiang
2015-02-01
Full Text Available Objective: Entropy algorithms have been widely used in analyzing EEG signals during anesthesia. However, a systematic comparison of these entropy algorithms in assessing anesthesia drugs’ effect is lacking. In this study, we compare the capability of twelve entropy indices for monitoring depth of anesthesia (DoA and detecting the burst suppression pattern (BSP, in anesthesia induced by GA-BAergic agents.Methods: Twelve indices were investigated, namely Response Entropy (RE and State entropy (SE, three wavelet entropy (WE measures (Shannon WE (SWE, Tsallis WE (TWE and Renyi WE (RWE, Hilbert-Huang spectral entropy (HHSE, approximate entropy (ApEn, sample entropy (SampEn, Fuzzy entropy, and three permutation entropy (PE measures (Shannon PE (SPE, Tsallis PE (TPE and Renyi PE (RPE. Two EEG data sets from sevoflurane-induced and isoflu-rane-induced anesthesia respectively were selected to assess the capability of each entropy index in DoA monitoring and BSP detection. To validate the effectiveness of these entropy algorithms, phar-macokinetic / pharmacodynamic (PK/PD modeling and prediction probability analysis were applied. The multifractal detrended fluctuation analysis (MDFA as a non-entropy measure was compared.Results: All the entropy and MDFA indices could track the changes in EEG pattern during different anesthesia states. Three PE measures outperformed the other entropy indices, with less baseline vari-ability, higher coefficient of determination and prediction probability, and RPE performed best; ApEn and SampEn discriminated BSP best. Additionally, these entropy measures showed an ad-vantage in computation efficiency compared with MDFA.Conclusion: Each entropy index has its advantages and disadvantages in estimating DoA. Overall, it is suggested that the RPE index was a superior measure.Significance: Investigating the advantages and disadvantages of these entropy indices could help improve current clinical indices for monitoring DoA.
Majorization theory approach to the Gaussian channel minimum entropy conjecture.
García-Patrón, Raúl; Navarrete-Benlloch, Carlos; Lloyd, Seth; Shapiro, Jeffrey H; Cerf, Nicolas J
2012-03-16
A long-standing open problem in quantum information theory is to find the classical capacity of an optical communication link, modeled as a Gaussian bosonic channel. It has been conjectured that this capacity is achieved by a random coding of coherent states using an isotropic Gaussian distribution in phase space. We show that proving a Gaussian minimum entropy conjecture for a quantum-limited amplifier is actually sufficient to confirm this capacity conjecture, and we provide a strong argument towards this proof by exploiting a connection between quantum entanglement and majorization theory.
Entanglement spectrum and entangled modes of random XX spin chains
Pouranvari, Mohammad; Yang, Kun
2013-08-01
In this paper, we study the ground-state entanglement properties of finite XX spin-1/2 chains with random couplings using the Jordan-Wigner transformation. We divide the system into two parts and study the reduced density matrices (RDMs) of its subsystems. Due to the free-fermion nature of the problem, the RDMs take the form of that of a free-fermion thermal ensemble. Finding the spectrum of the corresponding entanglement Hamiltonian and corresponding eigenvectors and comparing them with the real-space renormalization-group (RSRG) treatment, we establish the validity of the RSRG approach for entanglement in the limit of strong disorder but also find its limitations when disorder is weak. In the latter case, our paper provides a way to visualize the ``effective spins'' that form long-distance singlet pairs.
Protecting single-photon entanglement with practical entanglement source
Zhou, Lan; Ou-Yang, Yang; Wang, Lei; Sheng, Yu-Bo
2017-06-01
Single-photon entanglement (SPE) is important for quantum communication and quantum information processing. However, SPE is sensitive to photon loss. In this paper, we discuss a linear optical amplification protocol for protecting SPE. Different from the previous protocols, we exploit the practical spontaneous parametric down-conversion (SPDC) source to realize the amplification, for the ideal entanglement source is unavailable in current quantum technology. Moreover, we prove that the amplification using the entanglement generated from SPDC source as auxiliary is better than the amplification assisted with single photons. The reason is that the vacuum state from SPDC source will not affect the amplification, so that it can be eliminated automatically. This protocol may be useful in future long-distance quantum communications.
Robust entangled qutrit states in atmospheric turbulence
CSIR Research Space (South Africa)
Brunner, T
2013-06-01
Full Text Available The entangled quantum state of a photon pair propagating through atmospheric turbulence suffers decay of entanglement due to the scintillation it experiences. Here we investigate the robustness against this decay for different qutrit states. We use...
Sequential Path Entanglement for Quantum Metrology
Jin, Xian-Min; Peng, Cheng-Zhi; Deng, Youjin; Barbieri, Marco; Nunn, Joshua; Walmsley, Ian A.
2013-01-01
Path entanglement is a key resource for quantum metrology. Using path-entangled states, the standard quantum limit can be beaten, and the Heisenberg limit can be achieved. However, the preparation and detection of such states scales unfavourably with the number of photons. Here we introduce sequential path entanglement, in which photons are distributed across distinct time bins with arbitrary separation, as a resource for quantum metrology. We demonstrate a scheme for converting polarization Greenberger-Horne-Zeilinger entanglement into sequential path entanglement. We observe the same enhanced phase resolution expected for conventional path entanglement, independent of the delay between consecutive photons. Sequential path entanglement can be prepared comparably easily from polarization entanglement, can be detected without using photon-number-resolving detectors, and enables novel applications.
HMSRP Hawaiian Monk Seal Entanglement data
National Oceanic and Atmospheric Administration, Department of Commerce — The data set contains records of all entanglements of Hawaiian monk seals in marine debris. The data set comprises records of seals entangled by derelict fishing...
Evolution and Survival of Quantum Entanglement
2015-05-06
independently for tasks of quantum information. These include quantum computing, quantum cryptography , quantum teleportation and other forms of entanglement...Evolution and Survival of Quantum Entanglement Theoretical foundations for methods to preserve quantum entanglement are explored and explained...Research Triangle Park, NC 27709-2211 quantum entanglement, decoherence, qubit, revival, survival, Jaynes-Cummings, Rabi, rotating wave approximation
Farokhi, Saeed; Taghavi, Ray; Keshmiri, Shawn
2015-11-01
Stealth technology is developed for military aircraft to minimize their signatures. The primary attention was focused on radar signature, followed by the thermal and noise signatures of the vehicle. For radar evasion, advanced configuration designs, extensive use of carbon composites and radar-absorbing material, are developed. On thermal signature, mainly in the infra-red (IR) bandwidth, the solution was found in blended rectangular nozzles of high aspect ratio that are shielded from ground detectors. For noise, quiet and calm jets are integrated into vehicles with low-turbulence configuration design. However, these technologies are totally incapable of detecting new generation of revolutionary aircraft. These shall use all electric, distributed, propulsion system that are thermally transparent. In addition, composite skin and non-emitting sensors onboard the aircraft will lead to low signature. However, based on the second-law of thermodynamics, there is no air vehicle that can escape from leaving an entropy trail. Entropy is thus the only inevitable signature of any system, that once measured, can detect the source. By characterizing the entropy field based on its statistical properties, the source may be recognized, akin to face recognition technology. Direct measurement of entropy is cumbersome, however as a derived property, it can be easily measured. The measurement accuracy depends on the probe design and the sensors onboard. One novel air data sensor suite is introduced with promising potential to capture the entropy trail.
Entropy, color, and color rendering.
Price, Luke L A
2012-12-01
The Shannon entropy [Bell Syst. Tech J.27, 379 (1948)] of spectral distributions is applied to the problem of color rendering. With this novel approach, calculations for visual white entropy, spectral entropy, and color rendering are proposed, indices that are unreliant on the subjectivity inherent in reference spectra and color samples. The indices are tested against real lamp spectra, showing a simple and robust system for color rendering assessment. The discussion considers potential roles for white entropy in several areas of color theory and psychophysics and nonextensive entropy generalizations of the entropy indices in mathematical color spaces.
Entanglement in non-Hermitian quantum theory
Indian Academy of Sciences (India)
quantum theory. Furthermore, we will show how to create entanglement between two. PT qubits using non-Hermitian Hamiltonians and discuss the entangling capability of such interaction Hamiltonians that are non-Hermitian in nature. Keywords. Entanglement; non-Hermitian Hamiltonians; PT symmetry. PACS Nos 03.65.
Use of entanglement in quantum optics
Horne, Michael A.; Bernstein, Herbert J.; Greenberger, Daniel M.; Zeilinger, Anton
1992-01-01
Several recent demonstrations of two-particle interferometry are reviewed and shown to be examples of either color entanglement or beam entanglement. A device, called a number filter, is described and shown to be of value in preparing beam entanglements. Finally, we note that all three concepts (color and beam entaglement, and number filtering) may be extended to three or more particles.
Lithography system using quantum entangled photons
Williams, Colin (Inventor); Dowling, Jonathan (Inventor); della Rossa, Giovanni (Inventor)
2002-01-01
A system of etching using quantum entangled particles to get shorter interference fringes. An interferometer is used to obtain an interference fringe. N entangled photons are input to the interferometer. This reduces the distance between interference fringes by n, where again n is the number of entangled photons.
Polygamy of Entanglement in Multipartite Quantum Systems
Kim, Jeong San
2009-01-01
We show that bipartite entanglement distribution (or entanglement of assistance) in multipartite quantum systems is by nature polygamous. We first provide an analytic upper bound for the concurrence of assistance in bipartite quantum systems, and derive a polygamy inequality of multipartite entanglement in arbitrary dimensional quantum systems.
Quantum entanglement and quantum computational algorithms
Indian Academy of Sciences (India)
Abstract. The existence of entangled quantum states gives extra power to quantum computers over their classical counterparts. Quantum entanglement shows up qualitatively at the level of two qubits. We demonstrate that the one- and the two-bit Deutsch-Jozsa algorithm does not require entanglement and can be mapped ...
Measuring coherence with entanglement concurrence
Qi, Xianfei; Gao, Ting; Yan, Fengli
2017-07-01
Quantum coherence is a fundamental manifestation of the quantum superposition principle. Recently, Baumgratz et al (2014 Phys. Rev. Lett. 113 140401) presented a rigorous framework to quantify coherence from the view of theory of physical resource. Here we propose a new valid quantum coherence measure which is a convex roof measure, for a quantum system of arbitrary dimension, essentially using the generalized Gell-Mann matrices. Rigorous proof shows that the proposed coherence measure, coherence concurrence, fulfills all the requirements dictated by the resource theory of quantum coherence measures. Moreover, strong links between the resource frameworks of coherence concurrence and entanglement concurrence is derived, which shows that any degree of coherence with respect to some reference basis can be converted to entanglement via incoherent operations. Our work provides a clear quantitative and operational connection between coherence and entanglement based on two kinds of concurrence. This new coherence measure, coherence concurrence, may also be beneficial to the study of quantum coherence.
Quantum entanglement and temperature fluctuations.
Ourabah, Kamel; Tribeche, Mouloud
2017-04-01
In this paper, we consider entanglement in a system out of equilibrium, adopting the viewpoint given by the formalism of superstatistics. Such an approach yields a good effective description for a system in a slowly fluctuating environment within a weak interaction between the system and the environment. For this purpose, we introduce an alternative version of the formalism within a quantum mechanical picture and use it to study entanglement in the Heisenberg XY model, subject to temperature fluctuations. We consider both isotropic and anisotropic cases and explore the effect of different temperature fluctuations (χ^{2}, log-normal, and F distributions). Our results suggest that particular fluctuations may enhance entanglement and prevent it from vanishing at higher temperatures than those predicted for the same system at thermal equilibrium.
Entanglement renormalization for disordered systems
Goldsborough, Andrew M.; Evenbly, Glen
2017-10-01
We propose a tensor network method for investigating strongly disordered systems that is based on an adaptation of entanglement renormalization [G. Vidal, Phys. Rev. Lett. 99, 220405 (2007), 10.1103/PhysRevLett.99.220405]. This method makes use of the strong disorder renormalization group to determine the order in which lattice sites are coarse-grained, which sets the overall structure of the corresponding tensor network ansatz, before optimization using variational energy minimization. Benchmark results from the disordered X X Z model demonstrates that this approach accurately captures ground-state entanglement in disordered systems, even at long distances. This approach leads to a new class of efficiently contractible tensor network ansatz for one-dimensional systems, which may be understood as a generalization of the multiscale entanglement renormalization ansatz for disordered systems.
Structural entanglements in protein complexes
Zhao, Yani; Chwastyk, Mateusz; Cieplak, Marek
2017-06-01
We consider multi-chain protein native structures and propose a criterion that determines whether two chains in the system are entangled or not. The criterion is based on the behavior observed by pulling at both termini of each chain simultaneously in the two chains. We have identified about 900 entangled systems in the Protein Data Bank and provided a more detailed analysis for several of them. We argue that entanglement enhances the thermodynamic stability of the system but it may have other functions: burying the hydrophobic residues at the interface and increasing the DNA or RNA binding area. We also study the folding and stretching properties of the knotted dimeric proteins MJ0366, YibK, and bacteriophytochrome. These proteins have been studied theoretically in their monomeric versions so far. The dimers are seen to separate on stretching through the tensile mechanism and the characteristic unraveling force depends on the pulling direction.
Directory of Open Access Journals (Sweden)
Jian Li
2015-09-01
Full Text Available A novel quantum secure direct communication protocol based on four-particle genuine entangled state and quantum dense coding is proposed. In this protocol, the four-particle genuine entangled state is used to detect eavesdroppers, and quantum dense coding is used to encode the message. Finally, the security of the proposed protocol is discussed. During the security analysis, the method of entropy theory is introduced, and two detection strategies are compared quantitatively by comparing the relationship between the maximal information that the eavesdroppers (Eve can obtain, and the probability of being detected. Through the analysis we can state that our scheme is feasible and secure.
Directory of Open Access Journals (Sweden)
Angel Garrido
2011-07-01
Full Text Available Our paper analyzes some aspects of Uncertainty Measures. We need to obtain new ways to model adequate conditions or restrictions, constructed from vague pieces of information. The classical entropy measure originates from scientific fields; more specifically, from Statistical Physics and Thermodynamics. With time it was adapted by Claude Shannon, creating the current expanding Information Theory. However, the Hungarian mathematician, Alfred Rényi, proves that different and valid entropy measures exist in accordance with the purpose and/or need of application. Accordingly, it is essential to clarify the different types of measures and their mutual relationships. For these reasons, we attempt here to obtain an adequate revision of such fuzzy entropy measures from a mathematical point of view.
Bosonic behavior of entangled fermions
DEFF Research Database (Denmark)
C. Tichy, Malte; Alexander Bouvrie, Peter; Mølmer, Klaus
2012-01-01
Two bound, entangled fermions form a composite boson, which can be treated as an elementary boson as long as the Pauli principle does not affect the behavior of many such composite bosons. The departure of ideal bosonic behavior is quantified by the normalization ratio of multi-composite-boson st......Two bound, entangled fermions form a composite boson, which can be treated as an elementary boson as long as the Pauli principle does not affect the behavior of many such composite bosons. The departure of ideal bosonic behavior is quantified by the normalization ratio of multi...
Entropy in Pynchon's "Entropy" and Lefebvre's The Production of Space
Snart, Jason
2001-01-01
In his paper, "Entropy in Pynchon's 'Entropy' and Lefebvre's The Production of Space," Jason Snart examines Thomas Pynchon's short story "Entropy" for the ways in which it deals with the kinds of disorder(s) associated with entropy as a thermodynamic and informational concept. Those concepts are installed as a framework within which to consider cultural studies work like Henri Lefebfre's thought in his The Production of Space and Ludwig von Bertalanffy's general systems theory and themodynami...
EEG entropy measures in anesthesia.
Liang, Zhenhu; Wang, Yinghua; Sun, Xue; Li, Duan; Voss, Logan J; Sleigh, Jamie W; Hagihira, Satoshi; Li, Xiaoli
2015-01-01
► Twelve entropy indices were systematically compared in monitoring depth of anesthesia and detecting burst suppression.► Renyi permutation entropy performed best in tracking EEG changes associated with different anesthesia states.► Approximate Entropy and Sample Entropy performed best in detecting burst suppression. Entropy algorithms have been widely used in analyzing EEG signals during anesthesia. However, a systematic comparison of these entropy algorithms in assessing anesthesia drugs' effect is lacking. In this study, we compare the capability of 12 entropy indices for monitoring depth of anesthesia (DoA) and detecting the burst suppression pattern (BSP), in anesthesia induced by GABAergic agents. Twelve indices were investigated, namely Response Entropy (RE) and State entropy (SE), three wavelet entropy (WE) measures [Shannon WE (SWE), Tsallis WE (TWE), and Renyi WE (RWE)], Hilbert-Huang spectral entropy (HHSE), approximate entropy (ApEn), sample entropy (SampEn), Fuzzy entropy, and three permutation entropy (PE) measures [Shannon PE (SPE), Tsallis PE (TPE) and Renyi PE (RPE)]. Two EEG data sets from sevoflurane-induced and isoflurane-induced anesthesia respectively were selected to assess the capability of each entropy index in DoA monitoring and BSP detection. To validate the effectiveness of these entropy algorithms, pharmacokinetic/pharmacodynamic (PK/PD) modeling and prediction probability (Pk) analysis were applied. The multifractal detrended fluctuation analysis (MDFA) as a non-entropy measure was compared. All the entropy and MDFA indices could track the changes in EEG pattern during different anesthesia states. Three PE measures outperformed the other entropy indices, with less baseline variability, higher coefficient of determination (R (2)) and prediction probability, and RPE performed best; ApEn and SampEn discriminated BSP best. Additionally, these entropy measures showed an advantage in computation efficiency compared with MDFA. Each
EEG entropy measures in anesthesia
Liang, Zhenhu; Wang, Yinghua; Sun, Xue; Li, Duan; Voss, Logan J.; Sleigh, Jamie W.; Hagihira, Satoshi; Li, Xiaoli
2015-01-01
Highlights: ► Twelve entropy indices were systematically compared in monitoring depth of anesthesia and detecting burst suppression.► Renyi permutation entropy performed best in tracking EEG changes associated with different anesthesia states.► Approximate Entropy and Sample Entropy performed best in detecting burst suppression. Objective: Entropy algorithms have been widely used in analyzing EEG signals during anesthesia. However, a systematic comparison of these entropy algorithms in assessing anesthesia drugs' effect is lacking. In this study, we compare the capability of 12 entropy indices for monitoring depth of anesthesia (DoA) and detecting the burst suppression pattern (BSP), in anesthesia induced by GABAergic agents. Methods: Twelve indices were investigated, namely Response Entropy (RE) and State entropy (SE), three wavelet entropy (WE) measures [Shannon WE (SWE), Tsallis WE (TWE), and Renyi WE (RWE)], Hilbert-Huang spectral entropy (HHSE), approximate entropy (ApEn), sample entropy (SampEn), Fuzzy entropy, and three permutation entropy (PE) measures [Shannon PE (SPE), Tsallis PE (TPE) and Renyi PE (RPE)]. Two EEG data sets from sevoflurane-induced and isoflurane-induced anesthesia respectively were selected to assess the capability of each entropy index in DoA monitoring and BSP detection. To validate the effectiveness of these entropy algorithms, pharmacokinetic/pharmacodynamic (PK/PD) modeling and prediction probability (Pk) analysis were applied. The multifractal detrended fluctuation analysis (MDFA) as a non-entropy measure was compared. Results: All the entropy and MDFA indices could track the changes in EEG pattern during different anesthesia states. Three PE measures outperformed the other entropy indices, with less baseline variability, higher coefficient of determination (R2) and prediction probability, and RPE performed best; ApEn and SampEn discriminated BSP best. Additionally, these entropy measures showed an advantage in computation
Benchmarks and statistics of entanglement dynamics
Energy Technology Data Exchange (ETDEWEB)
Tiersch, Markus
2009-09-04
In the present thesis we investigate how the quantum entanglement of multicomponent systems evolves under realistic conditions. More specifically, we focus on open quantum systems coupled to the (uncontrolled) degrees of freedom of an environment. We identify key quantities that describe the entanglement dynamics, and provide efficient tools for its calculation. For quantum systems of high dimension, entanglement dynamics can be characterized with high precision. In the first part of this work, we derive evolution equations for entanglement. These formulas determine the entanglement after a given time in terms of a product of two distinct quantities: the initial amount of entanglement and a factor that merely contains the parameters that characterize the dynamics. The latter is given by the entanglement evolution of an initially maximally entangled state. A maximally entangled state thus benchmarks the dynamics, and hence allows for the immediate calculation or - under more general conditions - estimation of the change in entanglement. Thereafter, a statistical analysis supports that the derived (in-)equalities describe the entanglement dynamics of the majority of weakly mixed and thus experimentally highly relevant states with high precision. The second part of this work approaches entanglement dynamics from a topological perspective. This allows for a quantitative description with a minimum amount of assumptions about Hilbert space (sub-)structure and environment coupling. In particular, we investigate the limit of increasing system size and density of states, i.e. the macroscopic limit. In this limit, a universal behaviour of entanglement emerges following a ''reference trajectory'', similar to the central role of the entanglement dynamics of a maximally entangled state found in the first part of the present work. (orig.)
Directory of Open Access Journals (Sweden)
F. TopsÃƒÂ¸e
2001-09-01
Full Text Available Abstract: In its modern formulation, the Maximum Entropy Principle was promoted by E.T. Jaynes, starting in the mid-fifties. The principle dictates that one should look for a distribution, consistent with available information, which maximizes the entropy. However, this principle focuses only on distributions and it appears advantageous to bring information theoretical thinking more prominently into play by also focusing on the "observer" and on coding. This view was brought forward by the second named author in the late seventies and is the view we will follow-up on here. It leads to the consideration of a certain game, the Code Length Game and, via standard game theoretical thinking, to a principle of Game Theoretical Equilibrium. This principle is more basic than the Maximum Entropy Principle in the sense that the search for one type of optimal strategies in the Code Length Game translates directly into the search for distributions with maximum entropy. In the present paper we offer a self-contained and comprehensive treatment of fundamentals of both principles mentioned, based on a study of the Code Length Game. Though new concepts and results are presented, the reading should be instructional and accessible to a rather wide audience, at least if certain mathematical details are left aside at a rst reading. The most frequently studied instance of entropy maximization pertains to the Mean Energy Model which involves a moment constraint related to a given function, here taken to represent "energy". This type of application is very well known from the literature with hundreds of applications pertaining to several different elds and will also here serve as important illustration of the theory. But our approach reaches further, especially regarding the study of continuity properties of the entropy function, and this leads to new results which allow a discussion of models with so-called entropy loss. These results have tempted us to speculate over
Entropy, materials, and posterity
Cloud, P.
1977-01-01
Materials and energy are the interdependent feedstocks of economic systems, and thermodynamics is their moderator. It costs energy to transform the dispersed minerals of Earth's crust into ordered materials and structures. And it costs materials to collect and focus the energy to perform work - be it from solar, fossil fuel, nuclear, or other sources. The greater the dispersal of minerals sought, the more energy is required to collect them into ordered states. But available energy can be used once only. And the ordered materials of industrial economies become disordered with time. They may be partially reordered and recycled, but only at further costs in energy. Available energy everywhere degrades to bound states and order to disorder - for though entropy may be juggled it always increases. Yet industry is utterly dependent on low entropy states of matter and energy, while decreasing grades of ore require ever higher inputs of energy to convert them to metals, with ever increasing growth both of entropy and environmental hazard. Except as we may prize a thing for its intrinsic qualities - beauty, leisure, love, or gold - low-entropy is the only thing of real value. It is worth whatever the market will bear, and it becomes more valuable as entropy increases. It would be foolish of suppliers to sell it more cheaply or in larger amounts than their own enjoyment of life requires, whatever form it may take. For this reason, and because of physical constraints on the availability of all low-entropy states, the recent energy crises is only the first of a sequence of crises to be expected in energy and materials as long as current trends continue. The apportioning of low-entropy states in a modern industrial society is achieved more or less according to the theory of competitive markets. But the rational powers of this theory suffer as the world grows increasingly polarized into rich, over-industrialized nations with diminishing resource bases and poor, supplier nations
Harremoeës, P.; Topsøe, F.
2001-09-01
In its modern formulation, the Maximum Entropy Principle was promoted by E.T. Jaynes, starting in the mid-fifties. The principle dictates that one should look for a distribution, consistent with available information, which maximizes the entropy. However, this principle focuses only on distributions and it appears advantageous to bring information theoretical thinking more prominently into play by also focusing on the "observer" and on coding. This view was brought forward by the second named author in the late seventies and is the view we will follow-up on here. It leads to the consideration of a certain game, the Code Length Game and, via standard game theoretical thinking, to a principle of Game Theoretical Equilibrium. This principle is more basic than the Maximum Entropy Principle in the sense that the search for one type of optimal strategies in the Code Length Game translates directly into the search for distributions with maximum entropy. In the present paper we offer a self-contained and comprehensive treatment of fundamentals of both principles mentioned, based on a study of the Code Length Game. Though new concepts and results are presented, the reading should be instructional and accessible to a rather wide audience, at least if certain mathematical details are left aside at a rst reading. The most frequently studied instance of entropy maximization pertains to the Mean Energy Model which involves a moment constraint related to a given function, here taken to represent "energy". This type of application is very well known from the literature with hundreds of applications pertaining to several different elds and will also here serve as important illustration of the theory. But our approach reaches further, especially regarding the study of continuity properties of the entropy function, and this leads to new results which allow a discussion of models with so-called entropy loss. These results have tempted us to speculate over the development of natural
DEFF Research Database (Denmark)
Yuri, Shtarkov; Justesen, Jørn
1997-01-01
The concept of entropy for an image on a discrete two dimensional grid is introduced. This concept is used as an information theoretic bound on the coding rate for the image. It is proved that this quantity exists as a limit for arbitrary sets satisfying certain conditions.......The concept of entropy for an image on a discrete two dimensional grid is introduced. This concept is used as an information theoretic bound on the coding rate for the image. It is proved that this quantity exists as a limit for arbitrary sets satisfying certain conditions....
Entanglement enhances cooling in microscopic quantum refrigerators.
Brunner, Nicolas; Huber, Marcus; Linden, Noah; Popescu, Sandu; Silva, Ralph; Skrzypczyk, Paul
2014-03-01
Small self-contained quantum thermal machines function without external source of work or control but using only incoherent interactions with thermal baths. Here we investigate the role of entanglement in a small self-contained quantum refrigerator. We first show that entanglement is detrimental as far as efficiency is concerned-fridges operating at efficiencies close to the Carnot limit do not feature any entanglement. Moving away from the Carnot regime, we show that entanglement can enhance cooling and energy transport. Hence, a truly quantum refrigerator can outperform a classical one. Furthermore, the amount of entanglement alone quantifies the enhancement in cooling.
Classical-driving-assisted entanglement dynamics control
Energy Technology Data Exchange (ETDEWEB)
Zhang, Ying-Jie, E-mail: yingjiezhang@qfnu.edu.cn [Shandong Provincial Key Laboratory of Laser Polarization and Information Technology, Department of Physics, Qufu Normal University, Qufu 273165 (China); Han, Wei [Shandong Provincial Key Laboratory of Laser Polarization and Information Technology, Department of Physics, Qufu Normal University, Qufu 273165 (China); Xia, Yun-Jie, E-mail: yjxia@qfnu.edu.cn [Shandong Provincial Key Laboratory of Laser Polarization and Information Technology, Department of Physics, Qufu Normal University, Qufu 273165 (China); Fan, Heng, E-mail: hfan@iphy.ac.cn [Beijing National Laboratory of Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190 (China); Collaborative Innovation Center of Quantum Matter, Beijing, 100190 (China)
2017-04-15
We propose a scheme of controlling entanglement dynamics of a quantum system by applying the external classical driving field for two atoms separately located in a single-mode photon cavity. It is shown that, with a judicious choice of the classical-driving strength and the atom–photon detuning, the effective atom–photon interaction Hamiltonian can be switched from Jaynes–Cummings model to anti-Jaynes–Cummings model. By tuning the controllable atom–photon interaction induced by the classical field, we illustrate that the evolution trajectory of the Bell-like entanglement states can be manipulated from entanglement-sudden-death to no-entanglement-sudden-death, from no-entanglement-invariant to entanglement-invariant. Furthermore, the robustness of the initial Bell-like entanglement can be improved by the classical driving field in the leaky cavities. This classical-driving-assisted architecture can be easily extensible to multi-atom quantum system for scalability.
Multipartite quantum entanglement evolution in photosynthetic complexes.
Zhu, Jing; Kais, Sabre; Aspuru-Guzik, Alán; Rodriques, Sam; Brock, Ben; Love, Peter J
2012-08-21
We investigate the evolution of entanglement in the Fenna-Matthew-Olson (FMO) complex based on simulations using the scaled hierarchical equations of motion approach. We examine the role of entanglement in the FMO complex by direct computation of the convex roof. We use monogamy to give a lower bound for entanglement and obtain an upper bound from the evaluation of the convex roof. Examination of bipartite measures for all possible bipartitions provides a complete picture of the multipartite entanglement. Our results support the hypothesis that entanglement is maximum primary along the two distinct electronic energy transfer pathways. In addition, we note that the structure of multipartite entanglement is quite simple, suggesting that there are constraints on the mixed state entanglement beyond those due to monogamy.
Temporal Multimode Storage of Entangled Photon Pairs.
Tiranov, Alexey; Strassmann, Peter C; Lavoie, Jonathan; Brunner, Nicolas; Huber, Marcus; Verma, Varun B; Nam, Sae Woo; Mirin, Richard P; Lita, Adriana E; Marsili, Francesco; Afzelius, Mikael; Bussières, Félix; Gisin, Nicolas
2016-12-09
Multiplexed quantum memories capable of storing and processing entangled photons are essential for the development of quantum networks. In this context, we demonstrate and certify the simultaneous storage and retrieval of two entangled photons inside a solid-state quantum memory and measure a temporal multimode capacity of ten modes. This is achieved by producing two polarization-entangled pairs from parametric down-conversion and mapping one photon of each pair onto a rare-earth-ion-doped (REID) crystal using the atomic frequency comb (AFC) protocol. We develop a concept of indirect entanglement witnesses, which can be used as Schmidt number witnesses, and we use it to experimentally certify the presence of more than one entangled pair retrieved from the quantum memory. Our work puts forward REID-AFC as a platform compatible with temporal multiplexing of several entangled photon pairs along with a new entanglement certification method, useful for the characterization of multiplexed quantum memories.
Evolution and symmetry of multipartite entanglement.
Gour, Gilad
2010-11-05
We discover a simple factorization law describing how multipartite entanglement of a composite quantum system evolves when one of the subsystems undergoes an arbitrary physical process. This multipartite entanglement decay is determined uniquely by a single factor we call the entanglement resilience factor. Since the entanglement resilience factor is a function of the quantum channel alone, we find that multipartite entanglement evolves in exactly the same way as bipartite (two qudits) entanglement. For the two qubits case, our factorization law reduces to the main result of [T. Konrad, Nature Phys. 4, 99 (2008)10.1038/nphys885]. In addition, for a permutation P, we provide an operational definition of P asymmetry of entanglement, and find the conditions when a permuted version of a state can be achieved by local means.
Entropy is a Mathematical Formula
Garai, Jozsef
2003-01-01
The microscopic explanation of entropy has been challenged from both experimental and theoretical point of view. The expression of entropy is derived from the first law of thermodynamics indicating that entropy or the second law of thermodynamics is not an independent law.
Entangling light in high dimensions
Pors, Jan Bardeus
2011-01-01
Quantum entanglement is a fundamental trait of quantum mechanics that causes the information about the properties of two (or more) objects to be inextricably linked. When a measurement on one of the objects is performed, the state of the other object is immediately altered, even when these objects
Bessel-Gaussian entanglement; presentation
CSIR Research Space (South Africa)
Mclaren, M
2013-07-01
Full Text Available mode Hologram Page 9 Violation of Bell’s inequality demonstrates entanglement © CSIR 2013 www.csir.co.za P ro b ab il it y Classical Quantum mechanical M. McLaren et al.,2012, Opt. Express, 20, 23589 Page 10 Comparison...
Genetic algorithm optimization of entanglement
Navarro-Munoz, Jorge C.; Rosu, H. C.; Lopez-Sandoval, R.
2006-01-01
We present an application of a genetic algorithmic computational method to the optimization of the concurrence measure of entanglement for the cases of one dimensional chains, as well as square and triangular lattices in a simple tight-binding approach in which the hopping of electrons is much stronger than the phonon dissipation
Remote entanglement of transmon qubits
Hatridge, M.; Sliwa, K.; Narla, A.; Shankar, S.; Leghtas, Z.; Mirrahimi, M.; Girvin, S. M.; Schoelkopf, R. J.; Devoret, M. H.
2014-03-01
An open challenge in quantum information processing with superconducting circuits is to entangle distant (non-nearest neighbor) qubits. This can be accomplished by entangling the qubits with flying microwave oscillators (traveling pulses), and then performing joint operations on a pair of these oscillators. Remarkably, such a process is embedded in the act of phase-preserving amplification, which transforms two input modes (termed signal and idler) into a two-mode squeezed output state. For an ideal system, this process generates heralded, perfectly entangled states between remote qubits with a fifty percent success rate. For an imperfect system, the loss of information from the flying states degrades the purity of the entanglement. We show data on such a protocol involving two transmon qubits imbedded in superconducting cavities connected to the signal and idler inputs of a Josephson Parametric Converter (JPC) operated as a nearly-quantum limited phase-preserving amplifier. Strategies for optimizing performance will also be discussed. Work supported by: IARPA, ARO, and NSF.
Entanglement enhanced multiplayer quantum games
Du, Jiangfeng; Li, Hui; Xu, Xiaodong; Zhou, Xianyi; Han, Rongdian
2002-09-01
We investigate the 3-player quantum Prisoner's Dilemma with a certain strategic space, a particular Nash equilibrium that can remove the original dilemma is found. Based on this equilibrium, we show that the game is enhanced by the entanglement of its initial state.
Senegalese Immigrant Entrepreneurial Entanglements and ...
African Journals Online (AJOL)
Senegalese entrepreneurship in South Africa is a typical example of how entrepreneurial entanglements are beginning to pose huge challenges to the theorization and understanding of modern African forms of business. This group of immigrant entrepreneurs finds it difficult to separate the use of charms and magic in the ...
Sato, Humitaka
2010-06-01
Charles Darwin's calculation of a life of Earth had ignited Kelvin's insight on a life of Sun, which had eventually inherited to the physical study of stellar structure and energy source. Nuclear energy had secured a longevity of the universe and the goal of the cosmic evolution has been secured by the entropy of black holes.
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 6; Issue 9. Entropy à la Boltzmann. Jayanta K Bhattacharjee. General Article Volume 6 Issue 9 September 2001 pp 19-34. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/006/09/0019-0034. Author Affiliations.
Rescaling Temperature and Entropy
Olmsted, John, III
2010-01-01
Temperature and entropy traditionally are expressed in units of kelvin and joule/kelvin. These units obscure some important aspects of the natures of these thermodynamic quantities. Defining a rescaled temperature using the Boltzmann constant, T' = k[subscript B]T, expresses temperature in energy units, thereby emphasizing the close relationship…
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 6; Issue 9. Entropy in Biology. Jayant B Udgaonkar. General Article Volume 6 Issue 9 September 2001 pp 61-66. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/006/09/0061-0066. Author Affiliations.
Zucker, M. H.
This paper is a critical analysis and reassessment of entropic functioning as it applies to the question of whether the ultimate fate of the universe will be determined in the future to be "open" (expanding forever to expire in a big chill), "closed" (collapsing to a big crunch), or "flat" (balanced forever between the two). The second law of thermodynamics declares that entropy can only increase and that this principle extends, inevitably, to the universe as a whole. This paper takes the position that this extension is an unwarranted projection based neither on experience nonfact - an extrapolation that ignores the powerful effect of a gravitational force acting within a closed system. Since it was originally presented by Clausius, the thermodynamic concept of entropy has been redefined in terms of "order" and "disorder" - order being equated with a low degree of entropy and disorder with a high degree. This revised terminology more subjective than precise, has generated considerable confusion in cosmology in several critical instances. For example - the chaotic fireball of the big bang, interpreted by Stephen Hawking as a state of disorder (high entropy), is infinitely hot and, thermally, represents zero entropy (order). Hawking, apparently focusing on the disorderly "chaotic" aspect, equated it with a high degree of entropy - overlooking the fact that the universe is a thermodynamic system and that the key factor in evaluating the big-bang phenomenon is the infinitely high temperature at the early universe, which can only be equated with zero entropy. This analysis resolves this confusion and reestablishes entropy as a cosmological function integrally linked to temperature. The paper goes on to show that, while all subsystems contained within the universe require external sources of energization to have their temperatures raised, this requirement does not apply to the universe as a whole. The universe is the only system that, by itself can raise its own
Projective Power Entropy and Maximum Tsallis Entropy Distributions
Directory of Open Access Journals (Sweden)
Shinto Eguchi
2011-09-01
Full Text Available We discuss a one-parameter family of generalized cross entropy between two distributions with the power index, called the projective power entropy. The cross entropy is essentially reduced to the Tsallis entropy if two distributions are taken to be equal. Statistical and probabilistic properties associated with the projective power entropy are extensively investigated including a characterization problem of which conditions uniquely determine the projective power entropy up to the power index. A close relation of the entropy with the Lebesgue space Lp and the dual Lq is explored, in which the escort distribution associates with an interesting property. When we consider maximum Tsallis entropy distributions under the constraints of the mean vector and variance matrix, the model becomes a multivariate q-Gaussian model with elliptical contours, including a Gaussian and t-distribution model. We discuss the statistical estimation by minimization of the empirical loss associated with the projective power entropy. It is shown that the minimum loss estimator for the mean vector and variance matrix under the maximum entropy model are the sample mean vector and the sample variance matrix. The escort distribution of the maximum entropy distribution plays the key role for the derivation.
Injectivity of the Dirichlet-to-Neumann Functional and the Schwarzian Derivative
Directory of Open Access Journals (Sweden)
Fernando A.F.C. Silva
2010-12-01
Full Text Available In this article, we show the relation between the Schwartz kernels of the Dirichlet-to-Neumann operators associated to the metrics g0 and h = F* (e²φ g0 on the circular annulus A R, and the Schwarzian Derivative of the argument function f of the restriction of the diffeomorphism F to the boundary of A R.Neste artigo mostramos a relação entre os núcleos de Schwartz dos operadores Dirichlet-to-Neumann associados à métrica g0 e h = F* (e²φ g0, no anel circular A R, e a Derivada Schwarziana da função argumento f, da restrição do difeomorfismo F à fronteira de A R.
Contact angles on a soft solid: from Young's law to Neumann's law.
Marchand, Antonin; Das, Siddhartha; Snoeijer, Jacco H; Andreotti, Bruno
2012-12-07
The contact angle that a liquid drop makes on a soft substrate does not obey the classical Young's relation, since the solid is deformed elastically by the action of the capillary forces. The finite elasticity of the solid also renders the contact angles differently from those predicted by Neumann's law, which applies when the drop is floating on another liquid. Here, we derive an elastocapillary model for contact angles on a soft solid by coupling a mean-field model for the molecular interactions to elasticity. We demonstrate that the limit of a vanishing elastic modulus yields Neumann's law or a variation thereof, depending on the force transmission in the solid surface layer. The change in contact angle from the rigid limit to the soft limit appears when the length scale defined by the ratio of surface tension to elastic modulus γ/E reaches the range of molecular interactions.
Boundary integral equation Neumann-to-Dirichlet map method for gratings in conical diffraction.
Wu, Yumao; Lu, Ya Yan
2011-06-01
Boundary integral equation methods for diffraction gratings are particularly suitable for gratings with complicated material interfaces but are difficult to implement due to the quasi-periodic Green's function and the singular integrals at the corners. In this paper, the boundary integral equation Neumann-to-Dirichlet map method for in-plane diffraction problems of gratings [Y. Wu and Y. Y. Lu, J. Opt. Soc. Am. A26, 2444 (2009)] is extended to conical diffraction problems. The method uses boundary integral equations to calculate the so-called Neumann-to-Dirichlet maps for homogeneous subdomains of the grating, so that the quasi-periodic Green's functions can be avoided. Since wave field components are coupled on material interfaces with the involvement of tangential derivatives, a least squares polynomial approximation technique is developed to evaluate tangential derivatives along these interfaces for conical diffraction problems. Numerical examples indicate that the method performs equally well for dielectric or metallic gratings.
A High-Order Direct Solver for Helmholtz Equations with Neumann Boundary Conditions
Sun, Xian-He; Zhuang, Yu
1997-01-01
In this study, a compact finite-difference discretization is first developed for Helmholtz equations on rectangular domains. Special treatments are then introduced for Neumann and Neumann-Dirichlet boundary conditions to achieve accuracy and separability. Finally, a Fast Fourier Transform (FFT) based technique is used to yield a fast direct solver. Analytical and experimental results show this newly proposed solver is comparable to the conventional second-order elliptic solver when accuracy is not a primary concern, and is significantly faster than that of the conventional solver if a highly accurate solution is required. In addition, this newly proposed fourth order Helmholtz solver is parallel in nature. It is readily available for parallel and distributed computers. The compact scheme introduced in this study is likely extendible for sixth-order accurate algorithms and for more general elliptic equations.
Neumann Series on the Recursive Moments of Copula-Dependent Aggregate Discounted Claims
Directory of Open Access Journals (Sweden)
Siti Norafidah Mohd Ramli
2014-05-01
Full Text Available We study the recursive moments of aggregate discounted claims, where the dependence between the inter-claim time and the subsequent claim size is considered. Using the general expression for the m-th order moment proposed by Léveillé and Garrido (Scand. Actuar. J. 2001, 2, 98–110, which takes the form of the Volterra integral equation (VIE, we used the method of successive approximation to derive the Neumann series of the recursive moments. We then compute the first two moments of aggregate discounted claims, i.e., its mean and variance, based on the Neumann series expression, where the dependence structure is captured by a Farlie–Gumbel–Morgenstern (FGM copula, a Gaussian copula and a Gumbel copula with exponential marginal distributions. Insurance premium calculations with their figures are also illustrated.
Entropy, neutro-entropy and anti-entropy for neutrosophic information
Patrascu, Vasile
2017-01-01
This approach presents a multi-valued representation of the neutrosophic information. It highlights the link between the bifuzzy information and neutrosophic one. The constructed deca-valued structure shows the neutrosophic information complexity. This deca-valued structure led to construction of two new concepts for the neutrosophic information: neutro-entropy and anti-entropy. These two concepts are added to the two existing: entropy and non-entropy. Thus, we obtained the following triad: e...
Universal entanglement and boundary geometry in conformal field theory
Energy Technology Data Exchange (ETDEWEB)
Herzog, Christopher P.; Huang, Kuo-Wei; Jensen, Kristan [C.N. Yang Institute for Theoretical Physics, Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794 (United States)
2016-01-27
Employing a conformal map to hyperbolic space cross a circle, we compute the universal contribution to the vacuum entanglement entropy (EE) across a sphere in even-dimensional conformal field theory. Previous attempts to derive the EE in this way were hindered by a lack of knowledge of the appropriate boundary terms in the trace anomaly. In this paper we show that the universal part of the EE can be treated as a purely boundary effect. As a byproduct of our computation, we derive an explicit form for the A-type anomaly contribution to the Wess-Zumino term for the trace anomaly, now including boundary terms. In d=4 and 6, these boundary terms generalize earlier bulk actions derived in the literature.
Displacement-enhanced entanglement distillation of single-mode-squeezed entangled states
DEFF Research Database (Denmark)
Tipsmark, Anders; Neergaard-Nielsen, Jonas Schou; Andersen, Ulrik Lund
2013-01-01
It has been shown that entanglement distillation of Gaussian entangled states by means of local photon subtraction can be improved by local Gaussian transformations. Here we show that a similar effect can be expected for the distillation of an asymmetric Gaussian entangled state that is produced...... by a single squeezed beam. We show that for low initial entanglement, our largely simplified protocol generates more entanglement than previous proposed protocols. Furthermore, we show that the distillation scheme also works efficiently on decohered entangled states as well as with a practical photon...
Structure and Reversibility of 2D von Neumann Cellular Automata Over Triangular Lattice
Uguz, Selman; Redjepov, Shovkat; Acar, Ecem; Akin, Hasan
2017-06-01
Even though the fundamental main structure of cellular automata (CA) is a discrete special model, the global behaviors at many iterative times and on big scales could be a close, nearly a continuous, model system. CA theory is a very rich and useful phenomena of dynamical model that focuses on the local information being relayed to the neighboring cells to produce CA global behaviors. The mathematical points of the basic model imply the computable values of the mathematical structure of CA. After modeling the CA structure, an important problem is to be able to move forwards and backwards on CA to understand their behaviors in more elegant ways. A possible case is when CA is to be a reversible one. In this paper, we investigate the structure and the reversibility of two-dimensional (2D) finite, linear, triangular von Neumann CA with null boundary case. It is considered on ternary field ℤ3 (i.e. 3-state). We obtain their transition rule matrices for each special case. For given special triangular information (transition) rule matrices, we prove which triangular linear 2D von Neumann CAs are reversible or not. It is known that the reversibility cases of 2D CA are generally a much challenged problem. In the present study, the reversibility problem of 2D triangular, linear von Neumann CA with null boundary is resolved completely over ternary field. As far as we know, there is no structure and reversibility study of von Neumann 2D linear CA on triangular lattice in the literature. Due to the main CA structures being sufficiently simple to investigate in mathematical ways, and also very complex to obtain in chaotic systems, it is believed that the present construction can be applied to many areas related to these CA using any other transition rules.
A Neumann problem for a system depending on the unknown boundary values of the solution
Directory of Open Access Journals (Sweden)
Pablo Amster
2013-01-01
Full Text Available A semilinear system of second order ODEs under Neumann conditions is studied. The system has the particularity that its nonlinear term depends on the (unknown Dirichlet values $y(0$ and $y(1$ of the solution. Asymptotic and non-asymptotic sufficient conditions of Landesman-Lazer type for existence of solutions are given. We generalize our previous results for a scalar equation, and a well known result by Nirenberg for a nonlinearity independent of $y(0$ and $y(1$.
Dirichlet and Neumann Problems for String Equation, Poncelet Problem and Pell-Abel Equation
Directory of Open Access Journals (Sweden)
Vladimir P. Burskii
2006-04-01
Full Text Available We consider conditions for uniqueness of the solution of the Dirichlet or the Neumann problem for 2-dimensional wave equation inside of bi-quadratic algebraic curve. We show that the solution is non-trivial if and only if corresponding Poncelet problem for two conics associated with the curve has periodic trajectory and if and only if corresponding Pell-Abel equation has a solution.
Multiple solutions for nonhomogeneous Neumann differential inclusion problems by the p(x-Laplacian
Directory of Open Access Journals (Sweden)
Bin Ge
2011-03-01
Full Text Available In this paper we study Neumann-type $p(x$-Laplacian equation with nonsmooth potential. Firstly, applying a version of the non-smooth three-critical-points theorem we obtain the existence of three solutions of the problem in $W^{1,p(x}(\\Omega$. Finally, we obtain the existence of at least two nontrivial solutions, when $\\alpha^->p^+$.
DEFF Research Database (Denmark)
Gimperlein, Heiko; Grubb, Gerd
2014-01-01
The purpose of this article is to establish upper and lower estimates for the integral kernel of the semigroup exp(−t P) associated to a classical, strongly elliptic pseudodifferential operator P of positive order on a closed manifold. The Poissonian bounds generalize those obtained for perturbat...... for perturbations of fractional powers of the Laplacian. In the selfadjoint case, extensions to t∈C+ are studied. In particular, our results apply to the Dirichlet-to-Neumann semigroup....
Oil lenses on the air-water surface and the validity of Neumann's rule.
Nikolov, Alex; Wasan, Darsh
2017-06-01
Many studies have focused on the mechanisms of oil spreading over the air-water surface, oil lens formation, and lens dynamics: Franklin et al.(1774), Rayleigh (1890), Neumann and Wangerin (1894), Hardy (1912), Lyons (1930), Langmuir (1933), Miller (1941), Zisman (1941), Pujado and Scriven (1972), Seeto et al. (1983), and Takamura et al. (2012). Despite all of these studies, the phenomenon of the oil lens's air-water surface equilibrium is still under discussion. Here, we highlight an accurate method to study the oil lens's three-phase-contact angle by reflected light interferometry, using both common (CRLI) and differential reflected light interferometry (DRLI) to verify Neumann's rule (the vectorial sum of the three tensions is zero). For non-spreading oils, the validity of Neumann's rule is confirmed for small lenses when the role of the oil film tension around the lens's meniscus is taken into consideration. Neumann's rule was also validated when the monolayer surface pressure isotherm was taken into consideration for oil spreading on the air-water surface. The periodic monolayer surface pressure oscillation of the oil phase monolayer created by the air-evaporating biphilic oil was monitored with time. The monolayer's surface pressure periodic oscillation was attributed to the instability of the aqueous film covering the oil drop phase. The knowledge gained from this study will benefit the fundamental understanding of the oil lens's air-water surface equilibrium and oil spill mechanisms, thereby promoting better methods for the prevention and clean-up of oil spills. Copyright © 2016. Published by Elsevier B.V.
Directory of Open Access Journals (Sweden)
Allaberen Ashyralyev
2014-04-01
Full Text Available We study initial-boundary value problems for fractional parabolic equations with the Dirichlet-Neumann conditions. We obtain a stable difference schemes for this problem, and obtain theorems on coercive stability estimates for the solution of the first order of accuracy difference scheme. A procedure of modified Gauss elimination method is applied for the solution of the first and second order of accuracy difference schemes of one-dimensional fractional parabolic differential equations.
Entropy evolution of moving mirrors and the information loss problem
Chen, Pisin; Yeom, Dong-han
2017-07-01
We investigate the entanglement entropy and the information flow of two-dimensional moving mirrors. Here we point out that various mirror trajectories can help to mimic different candidate resolutions to the information loss paradox following the semiclassical quantum field theory: (i) a suddenly stopping mirror corresponds to the assertion that all information is attached to the last burst, (ii) a slowly stopping mirror corresponds to the assertion that thermal Hawking radiation carries information, and (iii) a long propagating mirror corresponds to the remnant scenario. Based on such analogy, we find that the last burst of a black hole cannot contain enough information, while slowly emitting radiation can restore unitarity. For all cases, there is an apparent inconsistency between the picture based on quantum entanglements and that based on the semiclassical quantum field theory. Based on the quantum entanglement theory, a stopping mirror will generate a firewall-like violent emission which is in conflict with notions based on the semiclassical quantum field theory.
Energy Technology Data Exchange (ETDEWEB)
Mejri, Youssef, E-mail: josef-bizert@hotmail.fr [Aix Marseille Universite, Toulon Universite, CNRS, CPT, Marseille (France); Dép. des Mathématiques, Faculté des Sciences de Bizerte, 7021 Jarzouna (Tunisia); Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l’Ingénieur, ENIT BP 37, Le Belvedere, 1002 Tunis (Tunisia)
2016-06-15
In this article, we study the boundary inverse problem of determining the aligned magnetic field appearing in the magnetic Schrödinger equation in a periodic quantum cylindrical waveguide, by knowledge of the Dirichlet-to-Neumann map. We prove a Hölder stability estimate with respect to the Dirichlet-to-Neumann map, by means of the geometrical optics solutions of the magnetic Schrödinger equation.
Charyyar Ashyralyyev; Gulzipa Akyuz; Mutlu Dedeturk
2017-01-01
In this work, we consider an inverse elliptic problem with Bitsadze-Samarskii type multipoint nonlocal and Neumann boundary conditions. We construct the first and second order of accuracy difference schemes (ADSs) for problem considered. We stablish stability and coercive stability estimates for solutions of these difference schemes. Also, we give numerical results for overdetermined elliptic problem with multipoint Bitsadze-Samarskii type nonlocal and Neumann boundary...
Franz Neumann e o nazismo como a destruição do estado
Directory of Open Access Journals (Sweden)
Diogo Ramos
2012-12-01
Full Text Available http://dx.doi.org/10.5007/1677-2954.2012v11n3p299Apresentamos no presente artigo a tese de Franz Neumann segundo a qual não haveria propriamente um Estado na Alemanha nacional socialista. Apesar de hoje relativamente pouco conhecido, Neumann foi um importante teórico do direito da chamada Escola de Frankfurt e membro ativo da promotoria dos julgamentos de Nuremberg; sua principal obra, Behemoth: estrutura e prática do nacional socialismo, publicada já em 1942, é o primeiro tratado sistemático sobre o tema, muito influente sobre diversos estudos posteriores, e de uma riqueza de intuições ainda hoje relevante. Neumann desenvolve sua tese da inexistência de um Estado nacional socialista a partir de seus estudos sobre o desenvolvimento do império da lei e da soberania na modernidade, características fundamentais do chamado Rechtsstaat, e que lhe permite concluir ser (ou parecer ser o regime nazi algo muito mais próximo do Beemote hobbesiano do que de seu Leviatã. Por isso, apresentamos na primeira parte deste trabalho sua discussão sobre o Estado e o direito modernos, para só na segunda parte discutir propriamente sua compreensão do nazismo.
Strain hardening of polymer glasses: entanglements, energetics, and plasticity.
Hoy, Robert S; Robbins, Mark O
2008-03-01
Simulations are used to examine the microscopic origins of strain hardening in polymer glasses. While stress-strain curves for a wide range of temperature can be fit to the functional form predicted by entropic network models, many other results are fundamentally inconsistent with the physical picture underlying these models. Stresses are too large to be entropic and have the wrong trend with temperature. The most dramatic hardening at large strains reflects increases in energy as chains are pulled taut between entanglements rather than a change in entropy. A weak entropic stress is only observed in shape recovery of deformed samples when heated above the glass transition. While short chains do not form an entangled network, they exhibit partial shape recovery, orientation, and strain hardening. Stresses for all chain lengths collapse when plotted against a microscopic measure of chain stretching rather than the macroscopic stretch. The thermal contribution to the stress is directly proportional to the rate of plasticity as measured by breaking and reforming of interchain bonds. These observations suggest that the correct microscopic theory of strain hardening should be based on glassy state physics rather than rubber elasticity.
Holographic torus entanglement and its renormalization group flow
Bueno, Pablo; Witczak-Krempa, William
2017-03-01
We study the universal contributions to the entanglement entropy (EE) of 2 +1 -dimensional and 3 +1 -dimensional holographic conformal field theories (CFTs) on topologically nontrivial manifolds, focusing on tori. The holographic bulk corresponds to anti-de Sitter-soliton geometries. We characterize the properties of these regulator-independent EE terms as a function of both the size of the cylindrical entangling region, and the shape of the torus. In 2 +1 dimensions, in the simple limit where the torus becomes a thin one-dimensional ring, the EE reduces to a shape-independent constant 2 γ . This is twice the EE obtained by bipartitioning an infinite cylinder into equal halves. We study the renormalization group flow of γ by defining a renormalized EE that (1) is applicable to general QFTs, (2) resolves the failure of the area law subtraction, and (3) is inspired by the F-theorem. We find that the renormalized γ decreases monotonically at small coupling when the holographic CFT is deformed by a relevant operator for all allowed scaling dimensions. We also discuss the question of nonuniqueness of such renormalized EEs both in 2 +1 dimensions and 3 +1 dimensions.
Energy Technology Data Exchange (ETDEWEB)
Weinberg, A.M.
1982-10-01
Utopians who use entropy to warn of a vast deterioration of energy and mineral resources seek a self-fulfilling prophesy when they work to deny society access to new energy sources, particularly nuclear power. While theoretically correct, entropy is not the relevant factor for the rest of this century. The more extreme entropists call for a return to an eotechnic society based on decentralized, renewable energy technologies, which rests on the assumptions of a loss in Gibbs Free Energy, a mineral depletion that will lead to OPEC-like manipulation, and a current technology that is destroying the environment. The author challenges these assumptions and calls for an exorcism of public fears over reactor accidents. He foresees a resurgence in public confidence in nuclear power by 1990 that will resolve Western dependence on foreign oil. (DCK)
Entanglement dynamics in quantum information theory
Energy Technology Data Exchange (ETDEWEB)
Cubitt, T.S.
2007-03-29
This thesis contributes to the theory of entanglement dynamics, that is, the behaviour of entanglement in systems that are evolving with time. Progressively more complex multipartite systems are considered, starting with low-dimensional tripartite systems, whose entanglement dynamics can nonetheless display surprising properties, progressing through larger networks of interacting particles, and finishing with infinitely large lattice models. Firstly, what is perhaps the most basic question in entanglement dynamics is considered: what resources are necessary in order to create entanglement between distant particles? The answer is surprising: sending separable states between the parties is sufficient; entanglement can be created without it being carried by a ''messenger'' particle. The analogous result also holds in the continuous-time case: two particles interacting indirectly via a common ancilla particle can be entangled without the ancilla ever itself becoming entangled. The latter result appears to discount any notion of entanglement flow. However, for pure states, this intuitive idea can be recovered, and even made quantitative. A ''bottleneck'' inequality is derived that relates the entanglement rate of the end particles in a tripartite chain to the entanglement of the middle one. In particular, no entanglement can be created if the middle particle is not entangled. However, although this result can be applied to general interaction networks, it does not capture the full entanglement dynamics of these more complex systems. This is remedied by the derivation of entanglement rate equations, loosely analogous to the rate equations describing a chemical reaction. A complete set of rate equations for a system reflects the full structure of its interaction network, and can be used to prove a lower bound on the scaling with chain length of the time required to entangle the ends of a chain. Finally, in contrast with these more
Entropy for Mechanically Vibrating Systems
Tufano, Dante
The research contained within this thesis deals with the subject of entropy as defined for and applied to mechanically vibrating systems. This work begins with an overview of entropy as it is understood in the fields of classical thermodynamics, information theory, statistical mechanics, and statistical vibroacoustics. Khinchin's definition of entropy, which is the primary definition used for the work contained in this thesis, is introduced in the context of vibroacoustic systems. The main goal of this research is to to establish a mathematical framework for the application of Khinchin's entropy in the field of statistical vibroacoustics by examining the entropy context of mechanically vibrating systems. The introduction of this thesis provides an overview of statistical energy analysis (SEA), a modeling approach to vibroacoustics that motivates this work on entropy. The objective of this thesis is given, and followed by a discussion of the intellectual merit of this work as well as a literature review of relevant material. Following the introduction, an entropy analysis of systems of coupled oscillators is performed utilizing Khinchin's definition of entropy. This analysis develops upon the mathematical theory relating to mixing entropy, which is generated by the coupling of vibroacoustic systems. The mixing entropy is shown to provide insight into the qualitative behavior of such systems. Additionally, it is shown that the entropy inequality property of Khinchin's entropy can be reduced to an equality using the mixing entropy concept. This equality can be interpreted as a facet of the second law of thermodynamics for vibroacoustic systems. Following this analysis, an investigation of continuous systems is performed using Khinchin's entropy. It is shown that entropy analyses using Khinchin's entropy are valid for continuous systems that can be decomposed into a finite number of modes. The results are shown to be analogous to those obtained for simple oscillators
Preimage entropy dimension of topological dynamical systems
Liu, Lei; Zhou, Xiaomin; Zhou, Xiaoyao
2014-01-01
We propose a new definition of preimage entropy dimension for continuous maps on compact metric spaces, investigate fundamental properties of the preimage entropy dimension, and compare the preimage entropy dimension with the topological entropy dimension. The defined preimage entropy dimension holds various basic properties of topological entropy dimension, for example, the preimage entropy dimension of a subsystem is bounded by that of the original system and topologically conjugated system...
Experimental quantum computing without entanglement.
Lanyon, B P; Barbieri, M; Almeida, M P; White, A G
2008-11-14
Deterministic quantum computation with one pure qubit (DQC1) is an efficient model of computation that uses highly mixed states. Unlike pure-state models, its power is not derived from the generation of a large amount of entanglement. Instead it has been proposed that other nonclassical correlations are responsible for the computational speedup, and that these can be captured by the quantum discord. In this Letter we implement DQC1 in an all-optical architecture, and experimentally observe the generated correlations. We find no entanglement, but large amounts of quantum discord-except in three cases where an efficient classical simulation is always possible. Our results show that even fully separable, highly mixed, states can contain intrinsically quantum mechanical correlations and that these could offer a valuable resource for quantum information technologies.
Quantum steganography using prior entanglement
Energy Technology Data Exchange (ETDEWEB)
Mihara, Takashi, E-mail: mihara@toyo.jp
2015-06-05
Steganography is the hiding of secret information within innocent-looking information (e.g., text, audio, image, video, etc.). A quantum version of steganography is a method based on quantum physics. In this paper, we propose quantum steganography by combining quantum error-correcting codes with prior entanglement. In many steganographic techniques, embedding secret messages in error-correcting codes may cause damage to them if the embedded part is corrupted. However, our proposed steganography can separately create secret messages and the content of cover messages. The intrinsic form of the cover message does not have to be modified for embedding secret messages. - Highlights: • Our steganography combines quantum error-correcting codes with prior entanglement. • Our steganography can separately create secret messages and the content of cover messages. • Errors in cover messages do not have affect the recovery of secret messages. • We embed a secret message in the Steane code as an example of our steganography.
Entanglement rules for holographic Fermi surfaces
Directory of Open Access Journals (Sweden)
Dibakar Roychowdhury
2016-08-01
Full Text Available In this paper, based on the notion of Gauge/Gravity duality, we explore the laws of entanglement thermodynamics for most generic classes of Quantum Field Theories with hyperscaling violation. In our analysis, we note that for Quantum Field Theories with compressible quark like excitation, the first law of entanglement thermodynamics gets modified due to the presence of an additional term that could be identified as the entanglement chemical potential associated with hidden Fermi surfaces of the boundary theory. Most notably, we find that the so called entanglement chemical potential does not depend on the size of the entangling region and is purely determined by the quark d.o.f. encoded within the entangling region.
Efficient entanglement distillation without quantum memory
Abdelkhalek, Daniela; Syllwasschy, Mareike; Cerf, Nicolas J.; Fiurášek, Jaromír; Schnabel, Roman
2016-01-01
Entanglement distribution between distant parties is an essential component to most quantum communication protocols. Unfortunately, decoherence effects such as phase noise in optical fibres are known to demolish entanglement. Iterative (multistep) entanglement distillation protocols have long been proposed to overcome decoherence, but their probabilistic nature makes them inefficient since the success probability decays exponentially with the number of steps. Quantum memories have been contemplated to make entanglement distillation practical, but suitable quantum memories are not realised to date. Here, we present the theory for an efficient iterative entanglement distillation protocol without quantum memories and provide a proof-of-principle experimental demonstration. The scheme is applied to phase-diffused two-mode-squeezed states and proven to distil entanglement for up to three iteration steps. The data are indistinguishable from those that an efficient scheme using quantum memories would produce. Since our protocol includes the final measurement it is particularly promising for enhancing continuous-variable quantum key distribution. PMID:27241946
Enhanced output entanglement with reservoir engineering
Yan, Xiao-Bo
2017-11-01
We study the output entanglement in a three-mode optomechanical system via reservoir engineering by shifting the center frequency of filter function away from resonant frequency. We find the bandwidth of the filter function can suppress the entanglement in the vicinity of resonant frequency of the system, while the entanglement will become strong if the center frequency departs from the resonant frequency. We obtain the approximate analytical expressions of the output entanglement, from which we give the optimal center frequency at which the entanglement takes the maximum. Furthermore, we study the effects of time delay between the two output fields on the output entanglement, and obtain the optimal time delay for the case of large filter bandwidth.
Displaced photon-number entanglement tests
Kühn, B.; Vogel, W.; Sperling, J.
2017-09-01
Based on correlations of coherently displaced photon numbers, we derive entanglement criteria for the purpose of verifying non-Gaussian entanglement. Our construction method enables us to verify bipartite and multipartite entanglement of complex states of light. An important advantage of our technique is that the certified entanglement persists even in the presence of arbitrarily high, constant losses. We exploit experimental correlation schemes for the two-mode and multimode scenarios, which allow us to directly measure the desired observables. To detect entanglement of a given state, a genetic algorithm is applied to optimize over the infinite set of our constructed witnesses. In particular, we provide suitable witnesses for several distinct two-mode states. Moreover, a mixed non-Gaussian four-mode state is shown to be entangled in all possible nontrivial partitions.
Efficient entanglement distillation without quantum memory.
Abdelkhalek, Daniela; Syllwasschy, Mareike; Cerf, Nicolas J; Fiurášek, Jaromír; Schnabel, Roman
2016-05-31
Entanglement distribution between distant parties is an essential component to most quantum communication protocols. Unfortunately, decoherence effects such as phase noise in optical fibres are known to demolish entanglement. Iterative (multistep) entanglement distillation protocols have long been proposed to overcome decoherence, but their probabilistic nature makes them inefficient since the success probability decays exponentially with the number of steps. Quantum memories have been contemplated to make entanglement distillation practical, but suitable quantum memories are not realised to date. Here, we present the theory for an efficient iterative entanglement distillation protocol without quantum memories and provide a proof-of-principle experimental demonstration. The scheme is applied to phase-diffused two-mode-squeezed states and proven to distil entanglement for up to three iteration steps. The data are indistinguishable from those that an efficient scheme using quantum memories would produce. Since our protocol includes the final measurement it is particularly promising for enhancing continuous-variable quantum key distribution.
Tree-shifts: the entropy of tree-shifts of finite type
Ban, Jung-Chao; Chang, Chih-Hung
2017-07-01
This paper studies the entropy of tree-shifts of finite type with and without boundary conditions. We demonstrate that computing the entropy of a tree-shift of finite type is equivalent to solving a system of nonlinear recurrence equations. Furthermore, the entropy of the binary Markov tree-shifts over two symbols is either 0 or \\ln 2 . Meanwhile, the realization of a class of reals including multinacci numbers is elaborated, which indicates that tree-shifts are capable of rich phenomena. By considering the influence of three different types of boundary conditions, say, the periodic, Dirichlet, and Neumann boundary conditions, the necessary and sufficient conditions for the coincidence of entropy with and without boundary conditions are addressed. This work is partially supported by the Ministry of Science and Technology, ROC (Contract No MOST 105-2115-M-259 -006 -MY2 and 105-2115-M-390 -001 -MY2). The first author is partially supported by National Center for Theoretical Sciences.
Ambient heat capacities and entropies of ionic solids: a unique view using the Debye equation.
Glasser, Leslie
2013-06-03
Entropies of solids are obtained experimentally as integrals of measured heat capacities over the temperature range from zero to ambient. Correspondingly, the Debye phonon distribution equation for solids provides a theoretical connection between these two chemical thermodynamic measures. We examine how the widely applicable Debye equation illuminates the relation between the corresponding experimental measures using more than 250 ionic solids. Estimation of heat capacities for simple ionic solids by the Dulong-Petit heat capacity limit, by the Neumann-Kopp elemental sum, and by the ion sum method is examined in relation to the Debye equation. We note that, and explain why, the ambient temperature heat capacities and entropies of ionic solids are found to be approximately equal, and how deviations from equality may be related to the Debye temperature, ΘD, which characterizes the Debye equation. It is also demonstrated that Debye temperatures may be readily estimated from the experimental ratio of ambient heat capacity to entropy, C(p)/S(p), rather than requiring resort to elaborate theoretical or experimental procedures for their determination. Correspondingly, ambient mineral entropies and heat capacities are linearly correlated and may thus be readily estimated from one another.
Entropy in probability and statistics
Energy Technology Data Exchange (ETDEWEB)
Rolke, W.A.
1992-01-01
The author develops a theory of entropy, where entropy is defined as the Legendre-Fenchel transform of the logarithmic moment generating function of a probability measure on a Banach space. A variety of properties relating the probability measure and its entropy are proven. It is shown that the entropy of a large class of stochastic processes can be approximated by the entropies of the finite-dimensional distributions of the process. For several types of measures the author finds explicit formulas for the entropy, for example for stochastic processes with independent increments and for Gaussian processes. For the entropy of Markov chains, evaluated at the observations of the process, the author proves a central limit theorem. Theorems relating weak convergence of probability measures on a finite dimensional space and pointwise convergence of their entropies are developed and then used to give a new proof of Donsker's theorem. Finally the use of entropy in statistics is discussed. The author shows the connection between entropy and Kullback's minimum discrimination information. A central limit theorem yields a test for the independence of a sequence of observations.
Locality of entangled polymer dynamics
Tsang, Chi Hang Boyce; Jiang, Lingxiang; Granick, Steve
2014-03-01
A combination of sparse and full fluorescence labeling of entangled actin solutions (filaments about 15 μm long at 1 mg/ml concentration) allowed us to probe both filament-scale polymer dynamics and effectively monomer dynamics. On the filament scale, the reptation tube idea of classical polymer physics works well. However, on a local scale comparable to mesh size, local tube width fluctuation becomes important. For the first time, the dependence of longitudinal diffusion on local tube width was quantified.
Quantum Entanglement in Fermionic Lattices
Zanardi, P.
2001-01-01
The Fock space of a system of indistinguishable particles is isomorphic (in a non-unique way) to the state-space of a composite i.e., many-modes, quantum system. One can then discuss quantum entanglement for fermionic as well as bosonic systems. We exemplify the use of this notion -central in quantum information - by studying some e.g., Hubbard,lattice fermionic models relevant to condensed matter physics.
Increasing Entanglement between Gaussian States by Coherent Photon Subtraction
DEFF Research Database (Denmark)
Ourjoumtsev, Alexei; Dantan, Aurelien Romain; Tualle Brouri, Rosa
2007-01-01
We experimentally demonstrate that the entanglement between Gaussian entangled states can be increased by non-Gaussian operations. Coherent subtraction of single photons from Gaussian quadrature-entangled light pulses, created by a nondegenerate parametric amplifier, produces delocalized states...
Tzeng, Yu-Chin; Dai, Li; Chung, Ming-Chiang; Amico, Luigi; Kwek, Leong-Chuan
2016-05-24
We study the entanglement structure and the topological edge states of the ground state of the spin-1/2 XXZ model with bond alternation. We employ parity-density matrix renormalization group with periodic boundary conditions. The finite-size scaling of Rényi entropies S2 and S∞ are used to construct the phase diagram of the system. The phase diagram displays three possible phases: Haldane type (an example of symmetry protected topological ordered phases), Classical Dimer and Néel phases, the latter bounded by two continuous quantum phase transitions. The entanglement and non-locality in the ground state are studied and quantified by the entanglement convertibility. We found that, at small spatial scales, the ground state is not convertible within the topological Haldane dimer phase. The phenomenology we observe can be described in terms of correlations between edge states. We found that the entanglement spectrum also exhibits a distinctive response in the topological phase: the effective rank of the reduced density matrix displays a specifically large "susceptibility" in the topological phase. These findings support the idea that although the topological order in the ground state cannot be detected by local inspection, the ground state response at local scale can tell the topological phases apart from the non-topological phases.
Entanglement Teleportation Through 1D Heisenberg Chain
Hao, X; Zhu, S
2005-01-01
Information transmission of two qubits through two independent 1D Heisenberg chains as a quantum channel is analyzed. It is found that the entanglement of two spin-$\\frac 12$ quantum systems is decreased during teleportation via the thermal mixed state in 1D Heisenberg chain. The entanglement teleportation will be realized if the minimal entanglement of the thermal mixed state is provided in such quantum channel. High average fidelity of teleportation with values larger than 2/3 is obtained w...
Cool horizons for entangled black holes
Maldacena, Juan; Susskind, Leonard
2013-01-01
General relativity contains solutions in which two distant black holes are connected through the interior via a wormhole, or Einstein-Rosen bridge. These solutions can be interpreted as maximally entangled states of two black holes that form a complex EPR pair. We suggest that similar bridges might be present for more general entangled states. In the case of entangled black holes one can formulate versions of the AMPS(S) paradoxes and resolve them. This suggests possible resolutions of the fi...
Cosmological dark energy effects from entanglement
Energy Technology Data Exchange (ETDEWEB)
Capozziello, Salvatore, E-mail: capozziello@na.infn.it [Dipartimento di Fisica, Università di Napoli “Federico II”, Via Cinthia, 80126 Napoli (Italy); Istituto Nazionale di Fisica Nucleare (INFN), Sez. di Napoli, Via Cinthia, 80126 Napoli (Italy); Luongo, Orlando [Dipartimento di Fisica, Università di Napoli “Federico II”, Via Cinthia, 80126 Napoli (Italy); Istituto Nazionale di Fisica Nucleare (INFN), Sez. di Napoli, Via Cinthia, 80126 Napoli (Italy); Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de México (UNAM) (Mexico); Mancini, Stefano [Scuola di Scienze and Tecnologie, Università di Camerino, 62032 Camerino (Italy); Istituto Nazionale di Fisica Nucleare (INFN), Sez. di Perugia, Via Pascoli, 06123 Perugia (Italy)
2013-06-03
The thorny issue of relating information theory to cosmology is here addressed by assuming a possible connection between quantum entanglement measures and observable universe. In particular, we propose a cosmological toy model, where the equation of state of the cosmological fluid, which drives the today observed cosmic acceleration, can be inferred from quantum entanglement between different cosmological epochs. In such a way the dynamical dark energy results as byproduct of quantum entanglement.