Holographic Entanglement Entropy

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Rangamani, Mukund

2016-01-01

We review the developments in the past decade on holographic entanglement entropy, a subject that has garnered much attention owing to its potential to teach us about the emergence of spacetime in holography. We provide an introduction to the concept of entanglement entropy in quantum field theories, review the holographic proposals for computing the same, providing some justification for where these proposals arise from in the first two parts. The final part addresses recent developments linking entanglement and geometry. We provide an overview of the various arguments and technical developments that teach us how to use field theory entanglement to detect geometry. Our discussion is by design eclectic; we have chosen to focus on developments that appear to us most promising for further insights into the holographic map. This is a preliminary draft of a few chapters of a book which will appear sometime in the near future, to be published by Springer. The book in addition contains a discussion of application o...

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 evolution under double-trace deformation

Energy Technology Data Exchange (ETDEWEB)

Song, Yushu [College of Physical Science and Technology, Hebei University, Baoding (China)

2017-12-15

In this paper, we study the bulk entanglement entropy evolution in conical BTZ black bole background using the heat kernel method. This is motivated by exploring the new examples where the quantum correction of the entanglement entropy gives the leading contribution. We find that in the large black hole limit the bulk entanglement entropy decreases under the double-trace deformation which is consistent with the holographic c theorem and in the small black hole limit the bulk entanglement entropy increases under the deformation. We also discuss the minimal area correction. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

Entanglement entropy after selective measurements in quantum chains

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Najafi, Khadijeh [Department of Physics, Georgetown University,37th and O Sts. NW, Washington, DC 20057 (United States); Rajabpour, M.A. [Instituto de Física, Universidade Federal Fluminense,Av. Gal. Milton Tavares de Souza s/n, Gragoatá, 24210-346, Niterói, RJ (Brazil)

2016-12-22

We study bipartite post measurement entanglement entropy after selective measurements in quantum chains. We first study the quantity for the critical systems that can be described by conformal field theories. We find a connection between post measurement entanglement entropy and the Casimir energy of floating objects. Then we provide formulas for the post measurement entanglement entropy for open and finite temperature systems. We also comment on the Affleck-Ludwig boundary entropy in the context of the post measurement entanglement entropy. Finally, we also provide some formulas regarding modular hamiltonians and entanglement spectrum in the after measurement systems. After through discussion regarding CFT systems we also provide some predictions regarding massive field theories. We then discuss a generic method to calculate the post measurement entanglement entropy in the free fermion systems. Using the method we study the post measurement entanglement entropy in the XY spin chain. We check numerically the CFT and the massive field theory results in the transverse field Ising chain and the XX model. In particular, we study the post meaurement entanglement entropy in the infinite, periodic and open critical transverse field Ising chain and the critical XX model. The effect of the temperature and the gap is also discussed in these models.

Entanglement entropy after selective measurements in quantum chains

International Nuclear Information System (INIS)

Najafi, Khadijeh; Rajabpour, M.A.

2016-01-01

We study bipartite post measurement entanglement entropy after selective measurements in quantum chains. We first study the quantity for the critical systems that can be described by conformal field theories. We find a connection between post measurement entanglement entropy and the Casimir energy of floating objects. Then we provide formulas for the post measurement entanglement entropy for open and finite temperature systems. We also comment on the Affleck-Ludwig boundary entropy in the context of the post measurement entanglement entropy. Finally, we also provide some formulas regarding modular hamiltonians and entanglement spectrum in the after measurement systems. After through discussion regarding CFT systems we also provide some predictions regarding massive field theories. We then discuss a generic method to calculate the post measurement entanglement entropy in the free fermion systems. Using the method we study the post measurement entanglement entropy in the XY spin chain. We check numerically the CFT and the massive field theory results in the transverse field Ising chain and the XX model. In particular, we study the post meaurement entanglement entropy in the infinite, periodic and open critical transverse field Ising chain and the critical XX model. The effect of the temperature and the gap is also discussed in these models.

Holographic entanglement entropy and entanglement thermodynamics of 'black' non-susy D3 brane

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Bhattacharya, Aranya; Roy, Shibaji

2018-06-01

Like BPS D3 brane, the non-supersymmetric (non-susy) D3 brane of type IIB string theory is also known to have a decoupling limit and leads to a non-supersymmetric AdS/CFT correspondence. The throat geometry in this case represents a QFT which is neither conformal nor supersymmetric. The 'black' version of the non-susy D3 brane in the decoupling limit describes a QFT at finite temperature. Here we first compute the entanglement entropy for small subsystem of such QFT from the decoupled geometry of 'black' non-susy D3 brane using holographic technique. Then we study the entanglement thermodynamics for the weakly excited states of this QFT from the asymptotically AdS geometry of the decoupled 'black' non-susy D3 brane. We observe that for small subsystem this background indeed satisfies a first law like relation with a universal (entanglement) temperature inversely proportional to the size of the subsystem and an (entanglement) pressure normal to the entangling surface. Finally we show how the entanglement entropy makes a cross-over to the thermal entropy at high temperature.

Holographic entanglement entropy in Lovelock gravities

NARCIS (Netherlands)

de Boer, J.; Kulaxizi, M.; Parnachev, A.

2011-01-01

We study entanglement entropies of simply connected surfaces in field theories dual to Lovelock gravities. We consider Gauss-Bonnet and cubic Lovelock gravities in detail. In the conformal case the logarithmic terms in the entanglement entropy are governed by the conformal anomalies of the CFT; we

Entanglement interpretation of black hole entropy in string theory

International Nuclear Information System (INIS)

Brustein, Ram; Einhorn, Martin B.; Yarom, Amos

2006-01-01

We show that the entropy resulting from the counting of microstates of non extremal black holes using field theory duals of string theories can be interpreted as arising from entanglement. The conditions for making such an interpretation consistent are discussed. First, we interpret the entropy (and thermodynamics) of spacetimes with non degenerate, bifurcating Killing horizons as arising from entanglement. We use a path integral method to define the Hartle-Hawking vacuum state in such spacetimes and discuss explicitly its entangled nature and its relation to the geometry. If string theory on such spacetimes has a field theory dual, then, in the low-energy, weak coupling limit, the field theory state that is dual to the Hartle-Hawking state is a thermofield double state. This allows the comparison of the entanglement entropy with the entropy of the field theory dual, and thus, with the Bekenstein-Hawking entropy of the black hole. As an example, we discuss in detail the case of the five dimensional anti-de Sitter, black hole spacetime

Discussion of entanglement entropy in quantum gravity

International Nuclear Information System (INIS)

Ma, Chen-Te

2018-01-01

We study entanglement entropy in gravity theory with quantum effects. A simplest model is a two dimensional Einstein gravity theory. We use an n-sheet manifold to obtain an area term of entanglement entropy by summing over all background fields. Based on AdS/CFT correspondence, strongly coupled conformal field theory is expected to describe perturbative quantum gravity theory. An ultraviolet complete quantum gravity theory should not depend on a choice of an entangling surface. To analysis the problem explicitly, we analyze two dimensional conformal field theory. We find that a coefficient of a universal term of entanglement entropy is independent of a choice of an entangling surface in two dimensional conformal field theory for one interval to show a tentative evidence. Finally, we discuss that translational invariance in a quantum system at zero temperature, size goes to infinity and no mass scales, except for cut-off, possibly be a necessary condition in quantum gravity theory by ruing out a volume law of entanglement entropy. (copyright 2018 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

Holographic entanglement entropy and cyclic cosmology

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Frampton, Paul H.

2018-06-01

We discuss a cyclic cosmology in which the visible universe, or introverse, is all that is accessible to an observer while the extroverse represents the total spacetime originating from the time when the dark energy began to dominate. It is argued that entanglement entropy of the introverse is the more appropriate quantity to render infinitely cyclic, rather than the entropy of the total universe. Since vanishing entanglement entropy implies disconnected spacetimes, at the turnaround when the introverse entropy is zero the disconnected extroverse can be jettisoned with impunity.

Proof of the holographic formula for entanglement entropy

International Nuclear Information System (INIS)

Fursaev, Dmitri V.

2006-01-01

Entanglement entropy for a spatial partition of a quantum system is studied in theories which admit a dual description in terms of the anti-de Sitter (AdS) gravity one dimension higher. A general proof of the holographic formula which relates the entropy to the area of a codimension 2 minimal hypersurface embedded in the bulk AdS space is given. The entanglement entropy is determined by a partition function which is defined as a path integral over Riemannian AdS geometries with non-trivial boundary conditions. The topology of the Riemannian spaces puts restrictions on the choice of the minimal hypersurface for a given boundary conditions. The entanglement entropy is also considered in Randall-Sundrum braneworld models where its asymptotic expansion is derived when the curvature radius of the brane is much larger than the AdS radius. Special attention is paid to the geometrical structure of anomalous terms in the entropy in four dimensions. Modification of the holographic formula by the higher curvature terms in the bulk is briefly discussed

Hierarchical Polygamy Inequality for Entanglement of Tsallis q-Entropy

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Luo, Yu; Li, Yong-Ming

2018-05-01

In this paper, we study the polygamy inequality of quantum entanglement in terms of Tsallis q-entropy. We first give a lower bound of Tsallis q-entropy entanglement of assistance (TOA) in the 2 ⊗ d systems. The relation-ships between Tsallis q-entropy entanglement (TEE) and TOA are also given. Furthermore, we prove TOA follows a hierarchical polygamy inequality in a 2 ⊗ 2 ⊗ 2 N‑2 systems. Supported by the National Natural Science Foundation of China under Grant No. 11671244, the Higher School Doctoral Subject Foun- dation of Ministry of Education of China under Grant No. 20130202110001, and Fundamental Research Funds for the Central Universities under Grants Nos. 2016TS060 and 2016CBY003

Holographic entanglement entropy of surface defects

International Nuclear Information System (INIS)

Gentle, Simon A.; Gutperle, Michael; Marasinou, Chrysostomos

2016-01-01

We calculate the holographic entanglement entropy in type IIB supergravity solutions that are dual to half-BPS disorder-type surface defects in N=4 supersymmetric Yang-Mills theory. The entanglement entropy is calculated for a ball-shaped region bisected by a surface defect. Using the bubbling supergravity solutions we also compute the expectation value of the defect operator. Combining our result with the previously-calculated one-point function of the stress tensor in the presence of the defect, we adapt the calculation of Lewkowycz and Maldacena http://dx.doi.org/10.1007/JHEP05(2014)025 to obtain a second expression for the entanglement entropy. Our two expressions agree up to an additional term, whose possible origin and significance is discussed.

Holographic entanglement entropy of surface defects

Energy Technology Data Exchange (ETDEWEB)

Gentle, Simon A.; Gutperle, Michael; Marasinou, Chrysostomos [Department of Physics and Astronomy, University of California,Los Angeles, CA 90095 (United States)

2016-04-12

We calculate the holographic entanglement entropy in type IIB supergravity solutions that are dual to half-BPS disorder-type surface defects in N=4 supersymmetric Yang-Mills theory. The entanglement entropy is calculated for a ball-shaped region bisected by a surface defect. Using the bubbling supergravity solutions we also compute the expectation value of the defect operator. Combining our result with the previously-calculated one-point function of the stress tensor in the presence of the defect, we adapt the calculation of Lewkowycz and Maldacena http://dx.doi.org/10.1007/JHEP05(2014)025 to obtain a second expression for the entanglement entropy. Our two expressions agree up to an additional term, whose possible origin and significance is discussed.

Entanglement entropy from tensor network states for stabilizer codes

Science.gov (United States)

He, Huan; Zheng, Yunqin; Bernevig, B. Andrei; Regnault, Nicolas

2018-03-01

In this paper, we present the construction of tensor network states (TNS) for some of the degenerate ground states of three-dimensional (3D) stabilizer codes. We then use the TNS formalism to obtain the entanglement spectrum and entropy of these ground states for some special cuts. In particular, we work out examples of the 3D toric code, the X-cube model, and the Haah code. The latter two models belong to the category of "fracton" models proposed recently, while the first one belongs to the conventional topological phases. We mention the cases for which the entanglement entropy and spectrum can be calculated exactly: For these, the constructed TNS is a singular value decomposition (SVD) of the ground states with respect to particular entanglement cuts. Apart from the area law, the entanglement entropies also have constant and linear corrections for the fracton models, while the entanglement entropies for the toric code models only have constant corrections. For the cuts we consider, the entanglement spectra of these three models are completely flat. We also conjecture that the negative linear correction to the area law is a signature of extensive ground-state degeneracy. Moreover, the transfer matrices of these TNSs can be constructed. We show that the transfer matrices are projectors whose eigenvalues are either 1 or 0. The number of nonzero eigenvalues is tightly related to the ground-state degeneracy.

Entanglement entropy for 2D gauge theories with matters

Science.gov (United States)

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.

Entanglement entropy in causal set theory

Science.gov (United States)

Sorkin, Rafael D.; Yazdi, Yasaman K.

2018-04-01

Entanglement entropy is now widely accepted as having deep connections with quantum gravity. It is therefore desirable to understand it in the context of causal sets, especially since they provide in a natural manner the UV cutoff needed to render entanglement entropy finite. Formulating a notion of entanglement entropy in a causal set is not straightforward because the type of canonical hypersurface-data on which its definition typically relies is not available. Instead, we appeal to the more global expression given in Sorkin (2012 (arXiv:1205.2953)) which, for a Gaussian scalar field, expresses the entropy of a spacetime region in terms of the field’s correlation function within that region (its ‘Wightman function’ W(x, x') ). Carrying this formula over to the causal set, one obtains an entropy which is both finite and of a Lorentz invariant nature. We evaluate this global entropy-expression numerically for certain regions (primarily order-intervals or ‘causal diamonds’) within causal sets of 1  +  1 dimensions. For the causal-set counterpart of the entanglement entropy, we obtain, in the first instance, a result that follows a (spacetime) volume law instead of the expected (spatial) area law. We find, however, that one obtains an area law if one truncates the commutator function (‘Pauli–Jordan operator’) and the Wightman function by projecting out the eigenmodes of the Pauli–Jordan operator whose eigenvalues are too close to zero according to a geometrical criterion which we describe more fully below. In connection with these results and the questions they raise, we also study the ‘entropy of coarse-graining’ generated by thinning out the causal set, and we compare it with what one obtains by similarly thinning out a chain of harmonic oscillators, finding the same, ‘universal’ behaviour in both cases.

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.

Entanglement entropy in a holographic p-wave superconductor model

Energy Technology Data Exchange (ETDEWEB)

Li, Li-Fang, E-mail: lilf@itp.ac.cn [State Key Laboratory of Space Weather, Center for Space Science and Applied Research, Chinese Academy of Sciences, Beijing 100190 (China); Cai, Rong-Gen, E-mail: cairg@itp.ac.cn [State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190 (China); Li, Li, E-mail: liliphy@itp.ac.cn [State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190 (China); Shen, Chao, E-mail: sc@nssc.ac.cn [State Key Laboratory of Space Weather, Center for Space Science and Applied Research, Chinese Academy of Sciences, Beijing 100190 (China)

2015-05-15

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

Energy Technology Data Exchange (ETDEWEB)

Arzano, Michele [Rome Univ. (Italy). Dipt. di Fisica; INFN, Rome (Italy); Calcagni, Gianluca [CSIC, Madrid (Spain). Inst. de Estructura de la Materia

2017-12-15

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. (orig.)

Finite entanglement entropy and spectral dimension in quantum gravity

Science.gov (United States)

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.

Finite entanglement entropy and spectral dimension in quantum gravity

International Nuclear Information System (INIS)

Arzano, Michele; Calcagni, Gianluca

2017-01-01

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. (orig.)

Entanglement entropy for descendent local operators in 2D CFTs

International Nuclear Information System (INIS)

Chen, Bin; Guo, Wu-Zhong; He, Song; Wu, Jie-qiang

2015-01-01

We mainly study the Rényi entropy and entanglement entropy of the states locally excited by the descendent operators in two dimensional conformal field theories (CFTs). In rational CFTs, we prove that the increase of entanglement entropy and Rényi entropy for a class of descendent operators, which are generated by L"("−")L̄"("−") onto the primary operator, always coincide with the logarithmic of quantum dimension of the corresponding primary operator. That means the Rényi entropy and entanglement entropy for these descendent operators are the same as the ones of their corresponding primary operator. For 2D rational CFTs with a boundary, we confirm that the Rényi entropy always coincides with the logarithmic of quantum dimension of the primary operator during some periods of the evolution. Furthermore, we consider more general descendent operators generated by ∑d_{_n__i_}_{_n__j_}(∏_iL_−_n__i∏_jL̄_−_n__j) on the primary operator. For these operators, the entanglement entropy and Rényi entropy get additional corrections, as the mixing of holomorphic and anti-holomorphic Virasoro generators enhance the entanglement. Finally, we employ perturbative CFT techniques to evaluate the Rényi entropy of the excited operators in deformed CFT. The Rényi and entanglement entropies are increased, and get contributions not only from local excited operators but also from global deformation of the theory.

Modifications to holographic entanglement entropy in warped CFT

Energy Technology Data Exchange (ETDEWEB)

Song, Wei; Wen, Qiang; Xu, Jianfei [Yau Mathematical Sciences Center, Tsinghua University,Beijing 100084 (China)

2017-02-13

In https://www.doi.org/10.1103/PhysRevLett.117.011602 it was observed that asymptotic boundary conditions play an important role in the study of holographic entanglement beyond AdS/CFT. In particular, the Ryu-Takayanagi proposal must be modified for warped AdS{sub 3} (WAdS{sub 3}) with Dirichlet boundary conditions. In this paper, we consider AdS{sub 3} and WAdS{sub 3} with Dirichlet-Neumann boundary conditions. The conjectured holographic duals are warped conformal field theories (WCFTs), featuring a Virasoro-Kac-Moody algebra. We provide a holographic calculation of the entanglement entropy and Rényi entropy using AdS{sub 3}/WCFT and WAdS{sub 3}/WCFT dualities. Our bulk results are consistent with the WCFT results derived by Castro-Hofman-Iqbal using the Rindler method. Comparing with https://www.doi.org/10.1103/PhysRevLett.117.011602, we explicitly show that the holographic entanglement entropy is indeed affected by boundary conditions. Both results differ from the Ryu-Takayanagi proposal, indicating new relations between spacetime geometry and quantum entanglement for holographic dualities beyond AdS/CFT.

Information loss in effective field theory: Entanglement and thermal entropies

Science.gov (United States)

Boyanovsky, Daniel

2018-03-01

Integrating out high energy degrees of freedom to yield a low energy effective field theory leads to a loss of information with a concomitant increase in entropy. We obtain the effective field theory of a light scalar field interacting with heavy fields after tracing out the heavy degrees of freedom from the time evolved density matrix. The initial density matrix describes the light field in its ground state and the heavy fields in equilibrium at a common temperature T . For T =0 , we obtain the reduced density matrix in a perturbative expansion; it reveals an emergent mixed state as a consequence of the entanglement between light and heavy fields. We obtain the effective action that determines the time evolution of the reduced density matrix for the light field in a nonperturbative Dyson resummation of one-loop correlations of the heavy fields. The Von-Neumann entanglement entropy associated with the reduced density matrix is obtained for the nonresonant and resonant cases in the asymptotic long time limit. In the nonresonant case the reduced density matrix displays an incipient thermalization albeit with a wave-vector, time and coupling dependent effective temperature as a consequence of memory of initial conditions. The entanglement entropy is time independent and is the thermal entropy for this effective, nonequilibrium temperature. In the resonant case the light field fully thermalizes with the heavy fields, the reduced density matrix loses memory of the initial conditions and the entanglement entropy becomes the thermal entropy of the light field. We discuss the relation between the entanglement entropy ultraviolet divergences and renormalization.

Statistical properties of quantum entanglement and information entropy

International Nuclear Information System (INIS)

Abdel-Aty, M.M.A.

2007-03-01

Key words: entropy, entanglement, atom-field interaction, trapped ions, cold atoms, information entropy. Objects of research: Pure state entanglement, entropy squeezing mazer. The aim of the work: Study of the new entanglement features and new measures for both pure-state and mixed state of particle-field interaction. Also, the impact of the information entropy on the quantum information theory. Method of investigation: Methods of theoretical physics and applied mathematics (statistical physics, quantum optics) are used. Results obtained and their novelty are: All the results of the dissertation are new and many new features have been discovered. Particularly: the most general case of the pure state entanglement has been introduced. Although various special aspects of the quantum entropy have been investigated previously, the general features of the dynamics, when a multi-level system and a common environment are considered, have not been treated before and our work therefore, field a gap in the literature. Specifically: 1) A new entanglement measure due to quantum mutual entropy (mixed-state entanglement) we called it DEM, has been introduced, 2) A new treatment of the atomic information entropy in higher level systems has been presented. The problem has been completely solved in the case of three-level system, 3) A new solution of the interaction between the ultra cold atoms and cavity field has been discovered, 4) Some new models of the atom-field interaction have been adopted. Practical value: The subject carries out theoretic character. Application region: Results can be used in quantum computer developments. Also, the presented results can be used for further developments of the quantum information and quantum communications. (author)

Entropy-driven phase transitions of entanglement

Science.gov (United States)

Facchi, Paolo; Florio, Giuseppe; Parisi, Giorgio; Pascazio, Saverio; Yuasa, Kazuya

2013-05-01

We study the behavior of bipartite entanglement at fixed von Neumann entropy. We look at the distribution of the entanglement spectrum, that is, the eigenvalues of the reduced density matrix of a quantum system in a pure state. We report the presence of two continuous phase transitions, characterized by different entanglement spectra, which are deformations of classical eigenvalue distributions.

Revisiting entanglement entropy of lattice gauge theories

Energy Technology Data Exchange (ETDEWEB)

Hung, Ling-Yan [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Lu, Shanghai 200433 (China); Collaborative Innovation Center of Advanced Microstructures, Fudan University,220 Handan Lu, Shanghai 200433 (China); Wan, Yidun [Perimeter Institute for Theoretical Physics,31 Caroline Street, Waterloo, ON N2L 2Y5 (Canada)

2015-04-22

It is realized recently that the entanglement entropy in gauge theories is ambiguous because the Hilbert space cannot be expressed as a simple direct product of Hilbert spaces defined on the two regions; different ways of dividing the Hilbert spaces near the boundary leads to significantly different result, to the extreme that it could annihilate the otherwise finite topological entanglement entropy between two regions altogether. In this article, we first show that the topological entanglement entropy in the Kitaev model http://dx.doi.org/10.1016/S0003-4916(02)00018-0 which is not a true gauge theory, is free of ambiguity. Then, we give a physical interpretation, from the perspectives of what can be measured in an experiment, to the purported ambiguity of true gauge theories, where the topological entanglement arises as redundancy in counting the degrees of freedom along the boundary separating two regions. We generalize these discussions to non-Abelian gauge theories.

On the entanglement entropy for gauge theories

International Nuclear Information System (INIS)

Ghosh, Sudip; Soni, Ronak M; Trivedi, Sandip P.

2015-01-01

We propose a definition for the entanglement entropy of a gauge theory on a spatial lattice. Our definition applies to any subset of links in the lattice, and is valid for both Abelian and Non-Abelian gauge theories. For ℤ_N and U(1) theories, without matter, our definition agrees with a particular case of the definition given by Casini, Huerta and Rosabal. We also argue that in general, both for Abelian and Non-Abelian theories, our definition agrees with the entanglement entropy calculated using a definition of the replica trick. Our definition, however, does not agree with some standard ways to measure entanglement, like the number of Bell pairs which can be produced by entanglement distillation.

Probing renormalization group flows using entanglement entropy

International Nuclear Information System (INIS)

Liu, Hong; Mezei, Márk

2014-01-01

In this paper we continue the study of renormalized entanglement entropy introduced in http://dx.doi.org/10.1007/JHEP04(2013)162. In particular, we investigate its behavior near an IR fixed point using holographic duality. We develop techniques which, for any static holographic geometry, enable us to extract the large radius expansion of the entanglement entropy for a spherical region. We show that for both a sphere and a strip, the approach of the renormalized entanglement entropy to the IR fixed point value contains a contribution that depends on the whole RG trajectory. Such a contribution is dominant, when the leading irrelevant operator is sufficiently irrelevant. For a spherical region such terms can be anticipated from a geometric expansion, while for a strip whether these terms have geometric origins remains to be seen

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.

Entanglement Entropy for the charged BTZ black hole

International Nuclear Information System (INIS)

Larrañaga, A.

2011-01-01

Using the AdS/CFT correspondence we calculate the explicit form of the entanglement entropy for the charged BTZ (Banados-Teitelboim-Zanelli) black hole. The leading term in the large temperature expansion of the entropy function for this black hole reproduces its Bekenstein-Hawking entropy and the subleading term, representing the first corrections due to quantum entanglement, behaves as a logarithm of the BH entropy. It has also been obtained an inverse of area term in subleading order similar to the reported when considering Hawking radiation as quantum tunneling of particles through the event horizon

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 in superconductor phase transition with dark matter sector

Directory of Open Access Journals (Sweden)

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.

Holographic entanglement entropy for gravitational anomaly in four dimensions

Energy Technology Data Exchange (ETDEWEB)

Ali, Tibra [Perimeter Institute for Theoretical Physics, 31 Caroline Street N., Waterloo, ON N2L 2Y5 (Canada); Haque, S. Shajidul [Laboratory for Quantum Gravity & Strings, Department of Mathematics & Applied Mathematics,University of Cape Town, Mathematics Building, Rondebosch, Cape Town, 7700 (South Africa); Murugan, Jeff [Laboratory for Quantum Gravity & Strings, Department of Mathematics & Applied Mathematics,University of Cape Town, Mathematics Building, Rondebosch, Cape Town, 7700 (South Africa); School of Natural Sciences, Institute for Advanced Study,1 Einstein Dr., Princeton, NJ 08540 (United States)

2017-03-15

We compute the holographic entanglement entropy for the anomaly polynomial TrR{sup 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.

On the entanglement entropy of quantum fields in causal sets

Science.gov (United States)

Belenchia, Alessio; Benincasa, Dionigi M. T.; Letizia, Marco; Liberati, Stefano

2018-04-01

In order to understand the detailed mechanism by which a fundamental discreteness can provide a finite entanglement entropy, we consider the entanglement entropy of two classes of free massless scalar fields on causal sets that are well approximated by causal diamonds in Minkowski spacetime of dimensions 2, 3 and 4. The first class is defined from discretised versions of the continuum retarded Green functions, while the second uses the causal set’s retarded nonlocal d’Alembertians parametrised by a length scale l k . In both cases we provide numerical evidence that the area law is recovered when the double-cutoff prescription proposed in Sorkin and Yazdi (2016 Entanglement entropy in causal set theory (arXiv:1611.10281)) is imposed. We discuss in detail the need for this double cutoff by studying the effect of two cutoffs on the quantum field and, in particular, on the entanglement entropy, in isolation. In so doing, we get a novel interpretation for why these two cutoff are necessary, and the different roles they play in making the entanglement entropy on causal sets finite.

Triviality of entanglement entropy in the Galilean vacuum

Science.gov (United States)

Hason, Itamar

2018-05-01

We study the entanglement entropy of the vacuum in non-relativistic local theories with Galilean or Schrödinger symmetry. We clear some confusion in the literature on the free Schrödinger case. We find that with only positive U (1) charge particles (states) and a unique zero U (1) charge state (the vacuum) the entanglement entropy must vanish in that state.

Entanglement entropy of ABJM theory and entropy of topological black hole

Science.gov (United States)

Nian, Jun; Zhang, Xinyu

2017-07-01

In this paper we discuss the supersymmetric localization of the 4D N = 2 offshell gauged supergravity on the background of the AdS4 neutral topological black hole, which is the gravity dual of the ABJM theory defined on the boundary {S}^1× H^2 . We compute the large- N expansion of the supergravity partition function. The result gives the black hole entropy with the logarithmic correction, which matches the previous result of the entanglement entropy of the ABJM theory up to some stringy effects. Our result is consistent with the previous on-shell one-loop computation of the logarithmic correction to black hole entropy. It provides an explicit example of the identification of the entanglement entropy of the boundary conformal field theory with the bulk black hole entropy beyond the leading order given by the classical Bekenstein-Hawking formula, which consequently tests the AdS/CFT correspondence at the subleading order.

Entanglement entropy of non-unitary integrable quantum field theory

Directory of Open Access Journals (Sweden)

Davide Bianchini

2015-07-01

Full Text Available In this paper we study the simplest massive 1+1 dimensional integrable quantum field theory which can be described as a perturbation of a non-unitary minimal conformal field theory: the Lee–Yang model. We are particularly interested in the features of the bi-partite entanglement entropy for this model and on building blocks thereof, namely twist field form factors. Non-unitarity selects out a new type of twist field as the operator whose two-point function (appropriately normalized yields the entanglement entropy. We compute this two-point function both from a form factor expansion and by means of perturbed conformal field theory. We find good agreement with CFT predictions put forward in a recent work involving the present authors. In particular, our results are consistent with a scaling of the entanglement entropy given by ceff3log⁡ℓ where ceff is the effective central charge of the theory (a positive number related to the central charge and ℓ is the size of the region. Furthermore the form factor expansion of twist fields allows us to explore the large region limit of the entanglement entropy and find the next-to-leading order correction to saturation. We find that this correction is very different from its counterpart in unitary models. Whereas in the latter case, it had a form depending only on few parameters of the model (the particle spectrum, it appears to be much more model-dependent for non-unitary models.

Entanglement entropy and the colored Jones polynomial

Science.gov (United States)

Balasubramanian, Vijay; DeCross, Matthew; Fliss, Jackson; Kar, Arjun; Leigh, Robert G.; Parrikar, Onkar

2018-05-01

We study the multi-party entanglement structure of states in Chern-Simons theory created by performing the path integral on 3-manifolds with linked torus boundaries, called link complements. For gauge group SU(2), the wavefunctions of these states (in a particular basis) are the colored Jones polynomials of the corresponding links. We first review the case of U(1) Chern-Simons theory where these are stabilizer states, a fact we use to re-derive an explicit formula for the entanglement entropy across a general link bipartition. We then present the following results for SU(2) Chern-Simons theory: (i) The entanglement entropy for a bipartition of a link gives a lower bound on the genus of surfaces in the ambient S 3 separating the two sublinks. (ii) All torus links (namely, links which can be drawn on the surface of a torus) have a GHZ-like entanglement structure — i.e., partial traces leave a separable state. By contrast, through explicit computation, we test in many examples that hyperbolic links (namely, links whose complements admit hyperbolic structures) have W-like entanglement — i.e., partial traces leave a non-separable state. (iii) Finally, we consider hyperbolic links in the complexified SL(2,C) Chern-Simons theory, which is closely related to 3d Einstein gravity with a negative cosmological constant. In the limit of small Newton constant, we discuss how the entanglement structure is controlled by the Neumann-Zagier potential on the moduli space of hyperbolic structures on the link complement.

Deterministic dense coding and entanglement entropy

International Nuclear Information System (INIS)

Bourdon, P. S.; Gerjuoy, E.; McDonald, J. P.; Williams, H. T.

2008-01-01

We present an analytical study of the standard two-party deterministic dense-coding protocol, under which communication of perfectly distinguishable messages takes place via a qudit from a pair of nonmaximally entangled qudits in a pure state |ψ>. Our results include the following: (i) We prove that it is possible for a state |ψ> with lower entanglement entropy to support the sending of a greater number of perfectly distinguishable messages than one with higher entanglement entropy, confirming a result suggested via numerical analysis in Mozes et al. [Phys. Rev. A 71, 012311 (2005)]. (ii) By explicit construction of families of local unitary operators, we verify, for dimensions d=3 and d=4, a conjecture of Mozes et al. about the minimum entanglement entropy that supports the sending of d+j messages, 2≤j≤d-1; moreover, we show that the j=2 and j=d-1 cases of the conjecture are valid in all dimensions. (iii) Given that |ψ> allows the sending of K messages and has √(λ 0 ) as its largest Schmidt coefficient, we show that the inequality λ 0 ≤d/K, established by Wu et al. [Phys. Rev. A 73, 042311 (2006)], must actually take the form λ 0 < d/K if K=d+1, while our constructions of local unitaries show that equality can be realized if K=d+2 or K=2d-1

Entanglement Entropy of Reissner—Nordström Black Hole and Quantum Isolated Horizon

International Nuclear Information System (INIS)

Ma Meng-Sen; Zhang Li-Chun; Zhao Ren

2014-01-01

Based on the work of Ghosh and Pereze, who view the black hole entropy as the logarithm of the number of quantum states on the Quantum Isolated Horizon (QIH) § the entropy of Reissner—Nordström black hole is studied. According to the Unruh temperature, the statistical entropy of quantum fields under the background of Reissner—Nordström spacetime is calculated by means of quantum statistics. In the calculations we take the integral from the position of QIH to infinity, so the obtained entropy is the entanglement entropy outside the QIH. In Reissner—Nordström spacetime it is shown that if only the position of QIH is properly chosen the leading term of logarithm of the number of quantum states on the QIH is equal to the leading term of the entanglement entropy outside the black hole horizon, and both are the Bekenstein—Hawking entropy. The results reveal the relation between the entanglement entropy of black hole and the logarithm of the number of quantum states. (general)

Rényi entropy, stationarity, and entanglement of the conformal scalar

Energy Technology Data Exchange (ETDEWEB)

Lee, Jeongseog; Lewkowycz, Aitor [Department of Physics, Princeton University,Princeton, NJ 08544 (United States); Perlmutter, Eric [DAMTP, Centre for Mathematical Sciences, University of Cambridge,Cambridge, CB3 0WA (United Kingdom); Safdi, Benjamin R. [Department of Physics, Princeton University,Princeton, NJ 08544 (United States)

2015-03-16

We extend previous work on the perturbative expansion of the Rényi entropy, S{sub q}, around q=1 for a spherical entangling surface in a general CFT. Applied to conformal scalar fields in various spacetime dimensions, the results appear to conflict with the known conformal scalar Rényi entropies. On the other hand, the perturbative results agree with known Rényi entropies in a variety of other theories, including theories of free fermions and vector fields and theories with Einstein gravity duals. We propose a resolution stemming from a careful consideration of boundary conditions near the entangling surface. This is equivalent to a proper treatment of total-derivative terms in the definition of the modular Hamiltonian. As a corollary, we are able to resolve an outstanding puzzle in the literature regarding the Rényi entropy of N=4 super-Yang-Mills near q=1. A related puzzle regards the question of stationarity of the renormalized entanglement entropy (REE) across a circle for a (2+1)-dimensional massive scalar field. We point out that the boundary contributions to the modular Hamiltonian shed light on the previously-observed non-stationarity. Moreover, IR divergences appear in perturbation theory about the massless fixed point that inhibit our ability to reliably calculate the REE at small non-zero mass.

Rényi entropy, stationarity, and entanglement of the conformal scalar

Science.gov (United States)

Lee, Jeongseog; Lewkowycz, Aitor; Perlmutter, Eric; Safdi, Benjamin R.

2015-03-01

We extend previous work on the perturbative expansion of the Rényi entropy, S q , around q = 1 for a spherical entangling surface in a general CFT. Applied to conformal scalar fields in various spacetime dimensions, the results appear to conflict with the known conformal scalar Rényi entropies. On the other hand, the perturbative results agree with known Rényi entropies in a variety of other theories, including theories of free fermions and vector fields and theories with Einstein gravity duals. We propose a resolution stemming from a careful consideration of boundary conditions near the entangling surface. This is equivalent to a proper treatment of total-derivative terms in the definition of the modular Hamiltonian. As a corollary, we are able to resolve an outstanding puzzle in the literature regarding the Rényi entropy of super-Yang-Mills near q = 1. A related puzzle regards the question of stationarity of the renormalized entanglement entropy (REE) across a circle for a (2+1)-dimensional massive scalar field. We point out that the boundary contributions to the modular Hamiltonian shed light on the previously-observed non-stationarity. Moreover, IR divergences appear in perturbation theory about the massless fixed point that inhibit our ability to reliably calculate the REE at small non-zero mass.

Entanglement entropy of gapped phase and topological order in three dimensions

NARCIS (Netherlands)

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

Linearity of holographic entanglement entropy

Energy Technology Data Exchange (ETDEWEB)

Almheiri, Ahmed [Stanford Institute for Theoretical Physics, Department of Physics,Stanford University, Stanford, CA 94305 (United States); Dong, Xi [School of Natural Sciences, Institute for Advanced Study,Princeton, NJ 08540 (United States); Swingle, Brian [Stanford Institute for Theoretical Physics, Department of Physics,Stanford University, Stanford, CA 94305 (United States)

2017-02-14

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. We investigate this property by computing the entanglement entropy, via the replica trick, in states dual to superpositions of macroscopically distinct geometries and find it consistent with evaluating the expectation value of the area operator within such states. However, we find that this fails once the number of semi-classical states in the superposition grows exponentially in the central charge of the CFT. Moreover, in certain such scenarios we find that the choice of surface on which to evaluate the area operator depends on the density matrix of the entire CFT. This nonlinearity is enforced in the bulk via the homology prescription of Ryu-Takayanagi. We thus conclude that the homology constraint is not a linear property in the CFT. We also discuss the existence of ‘entropy operators’ in general systems with a large number of degrees of freedom.

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.

Logarithmic terms in entanglement entropies of 2D quantum critical points and Shannon entropies of spin chains.

Science.gov (United States)

Zaletel, Michael P; Bardarson, Jens H; Moore, Joel E

2011-07-08

Universal logarithmic terms in the entanglement entropy appear at quantum critical points (QCPs) in one dimension (1D) and have been predicted in 2D at QCPs described by 2D conformal field theories. The entanglement entropy in a strip geometry at such QCPs can be obtained via the "Shannon entropy" of a 1D spin chain with open boundary conditions. The Shannon entropy of the XXZ chain is found to have a logarithmic term that implies, for the QCP of the square-lattice quantum dimer model, a logarithm with universal coefficient ±0.25. However, the logarithm in the Shannon entropy of the transverse-field Ising model, which corresponds to entanglement in the 2D Ising conformal QCP, is found to have a singular dependence on the replica or Rényi index resulting from flows to different boundary conditions at the entanglement cut.

Relative entropy and the RG flow

Energy Technology Data Exchange (ETDEWEB)

Casini, Horacio; Testé, Eduardo; Torroba, Gonzalo [Centro Atómico Bariloche and CONICET,S.C. de Bariloche, Río Negro, R8402AGP (Argentina)

2017-03-16

We consider the relative entropy between vacuum states of two different theories: a conformal field theory (CFT), and the CFT perturbed by a relevant operator. By restricting both states to the null Cauchy surface in the causal domain of a sphere, we make the relative entropy equal to the difference of entanglement entropies. As a result, this difference has the positivity and monotonicity properties of relative entropy. From this it follows a simple alternative proof of the c-theorem in d=2 space-time dimensions and, for d>2, the proof that the coefficient of the area term in the entanglement entropy decreases along the renormalization group (RG) flow between fixed points. We comment on the regimes of convergence of relative entropy, depending on the space-time dimensions and the conformal dimension Δ of the perturbation that triggers the RG flow.

Entanglement entropy in random quantum spin-S chains

International Nuclear Information System (INIS)

Saguia, A.; Boechat, B.; Continentino, M. A.; Sarandy, M. S.

2007-01-01

We discuss the scaling of entanglement entropy in the random singlet phase (RSP) of disordered quantum magnetic chains of general spin S. Through an analysis of the general structure of the RSP, we show that the entanglement entropy scales logarithmically with the size of a block, and we provide a closed expression for this scaling. This result is applicable for arbitrary quantum spin chains in the RSP, being dependent only on the magnitude S of the spin. Remarkably, the logarithmic scaling holds for the disordered chain even if the pure chain with no disorder does not exhibit conformal invariance, as is the case for Heisenberg integer-spin chains. Our conclusions are supported by explicit evaluations of the entanglement entropy for random spin-1 and spin-3/2 chains using an asymptotically exact real-space renormalization group approach

Entanglement entropy for (3+1)-dimensional topological order with excitations

Science.gov (United States)

Wen, Xueda; He, Huan; Tiwari, Apoorv; Zheng, Yunqin; Ye, Peng

2018-02-01

Excitations in (3+1)-dimensional [(3+1)D] topologically ordered phases have very rich structures. (3+1)D topological phases support both pointlike and stringlike excitations, and in particular the loop (closed string) excitations may admit knotted and linked structures. In this work, we ask the following question: How do different types of topological excitations contribute to the entanglement entropy or, alternatively, can we use the entanglement entropy to detect the structure of excitations, and further obtain the information of the underlying topological order? We are mainly interested in (3+1)D topological order that can be realized in Dijkgraaf-Witten (DW) gauge theories, which are labeled by a finite group G and its group 4-cocycle ω ∈H4[G ;U(1 ) ] up to group automorphisms. We find that each topological excitation contributes a universal constant lndi to the entanglement entropy, where di is the quantum dimension that depends on both the structure of the excitation and the data (G ,ω ) . The entanglement entropy of the excitations of the linked/unlinked topology can capture different information of the DW theory (G ,ω ) . In particular, the entanglement entropy introduced by Hopf-link loop excitations can distinguish certain group 4-cocycles ω from the others.

Universal corrections to entanglement entropy of local quantum quenches

Energy Technology Data Exchange (ETDEWEB)

David, Justin R.; Khetrapal, Surbhi [Centre for High Energy Physics, Indian Institute of Science,C.V. Raman Avenue, Bangalore 560012 (India); Kumar, S. Prem [Department of Physics, Swansea University,Singleton Park, Swansea SA2 8PP (United Kingdom)

2016-08-22

We study the time evolution of single interval Rényi and entanglement entropies following local quantum quenches in two dimensional conformal field theories at finite temperature for which the locally excited states have a finite temporal width ϵ. We show that, for local quenches produced by the action of a conformal primary field, the time dependence of Rényi and entanglement entropies at order ϵ{sup 2} is universal. It is determined by the expectation value of the stress tensor in the replica geometry and proportional to the conformal dimension of the primary field generating the local excitation. We also show that in CFTs with a gravity dual, the ϵ{sup 2} correction to the holographic entanglement entropy following a local quench precisely agrees with the CFT prediction. We then consider CFTs admitting a higher spin symmetry and turn on a higher spin chemical potential μ. We calculate the time dependence of the order ϵ{sup 2} correction to the entanglement entropy for small μ, and show that the contribution at order μ{sup 2} is universal. We verify our arguments against exact results for minimal models and the free fermion theory.

Variation of entanglement entropy in scattering process

Energy Technology Data Exchange (ETDEWEB)

Seki, Shigenori, E-mail: sigenori@hanyang.ac.kr [Research Institute for Natural Science, Hanyang University, Seoul 133-791 (Korea, Republic of); Park, I.Y., E-mail: inyongpark05@gmail.com [Department of Applied Mathematics, Philander Smith College, Little Rock, AR 72223 (United States); Sin, Sang-Jin, E-mail: sjsin@hanyang.ac.kr [Department of Physics, Hanyang University, Seoul 133-791 (Korea, Republic of)

2015-04-09

In a scattering process, the final state is determined by an initial state and an S-matrix. We focus on two-particle scattering processes and consider the entanglement between these particles. For two types initial states, i.e., an unentangled state and an entangled one, we calculate perturbatively the change of entanglement entropy from the initial state to the final one. Then we show a few examples in a field theory and in quantum mechanics.

Studies on entanglement entropy for Hubbard model with hole-doping and external magnetic field

International Nuclear Information System (INIS)

Yao, K.L.; Li, Y.C.; Sun, X.Z.; Liu, Q.M.; Qin, Y.; Fu, H.H.; Gao, G.Y.

2005-01-01

By using the density matrix renormalization group (DMRG) method for the one-dimensional (1D) Hubbard model, we have studied the von Neumann entropy of a quantum system, which describes the entanglement of the system block and the rest of the chain. It is found that there is a close relation between the entanglement entropy and properties of the system. The hole-doping can alter the charge-charge and spin-spin interactions, resulting in charge polarization along the chain. By comparing the results before and after the doping, we find that doping favors increase of the von Neumann entropy and thus also favors the exchange of information along the chain. Furthermore, we calculated the spin and entropy distribution in external magnetic filed. It is confirmed that both the charge-charge and the spin-spin interactions affect the exchange of information along the chain, making the entanglement entropy redistribute

Holographic entanglement entropy for the most general higher derivative gravity

International Nuclear Information System (INIS)

Miao, Rong-Xin; Guo, Wu-zhong

2015-01-01

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.

Hyperspherical entanglement entropy

International Nuclear Information System (INIS)

Dowker, J S

2010-01-01

The coefficient of the log term in the entanglement entropy associated with hyperspherical surfaces in flat spacetime is shown to equal the conformal anomaly by conformally transforming Euclideanized spacetime to a sphere and using already existing formulae for the relevant heat-kernel coefficients after cyclic factoring. The result follows from the fact that the conformal anomaly on this lune has an extremum at the ordinary sphere limit. A proof is given. Agreement with a recent evaluation of the coefficient is found.

Hyperspherical entanglement entropy

Energy Technology Data Exchange (ETDEWEB)

Dowker, J S, E-mail: dowker@man.ac.u [Theory Group, School of Physics and Astronomy, University of Manchester, Manchester (United Kingdom)

2010-11-05

The coefficient of the log term in the entanglement entropy associated with hyperspherical surfaces in flat spacetime is shown to equal the conformal anomaly by conformally transforming Euclideanized spacetime to a sphere and using already existing formulae for the relevant heat-kernel coefficients after cyclic factoring. The result follows from the fact that the conformal anomaly on this lune has an extremum at the ordinary sphere limit. A proof is given. Agreement with a recent evaluation of the coefficient is found.

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.

Pedagogical introduction to the entropy of entanglement for Gaussian states

Science.gov (United States)

Demarie, Tommaso F.

2018-05-01

In quantum information theory, the entropy of entanglement is a standard measure of bipartite entanglement between two partitions of a composite system. For a particular class of continuous variable quantum states, the Gaussian states, the entropy of entanglement can be expressed elegantly in terms of symplectic eigenvalues, elements that characterise a Gaussian state and depend on the correlations of the canonical variables. We give a rigorous step-by-step derivation of this result and provide physical insights, together with an example that can be useful in practice for calculations.

Entanglement entropy in integrable field theories with line defects II. Non-topological defect

Science.gov (United States)

Jiang, Yunfeng

2017-08-01

This is the second part of two papers where we study the effect of integrable line defects on bipartite entanglement entropy in integrable field theories. In this paper, we consider non-topological line defects in Ising field theory. We derive an infinite series expression for the entanglement entropy and show that both the UV and IR limits of the bulk entanglement entropy are modified by the line defect. In the UV limit, we give an infinite series expression for the coefficient in front of the logarithmic divergence and the exact defect g-function. By tuning the defect to be purely transmissive and reflective, we recover correctly the entanglement entropy of the bulk and with integrable boundary respectively.

Entanglement generation and entropy growth due to intrinsic decoherence in the Jaynes-Cummings model

International Nuclear Information System (INIS)

Obada, A.-S.F.; Hessian, Hosny A.

2004-01-01

We study how intrinsic decoherence leads to growing entropy and a strong degradation of the maximal generated entanglement in the multiquanta Jaynes-Cummings model. We find an exact solution of the Milburn equation in multiquanta precesses and calculate the partial entropy of the particle (atom or trapped ion) and field subsystem as well as total entropy. As the total entropy is not conserved, and it is shown to increase as time develops, one cannot use the partial field or atomic entropy as a direct measure of particle-field entanglement. For a good entropy measure, we also calculate the negativity of the eigenvalues of the partially transposed density matrix. We find that, at least qualitatively, the difference of the total entropy to the sum of field and atom partial entropies can be also used as an entanglement measure. Our results show that the degree of entanglement is very sensitive to any change in the intrinsic decoherence parameter

Entanglement entropy of excited states

International Nuclear Information System (INIS)

Alba, Vincenzo; Fagotti, Maurizio; Calabrese, Pasquale

2009-01-01

We study the entanglement entropy of a block of contiguous spins in excited states of spin chains. We consider the XY model in a transverse field and the XXZ Heisenberg spin chain. For the latter, we developed a numerical application of the algebraic Bethe ansatz. We find two main classes of states with logarithmic and extensive behavior in the dimension of the block, characterized by the properties of excitations of the state. This behavior can be related to the locality properties of the Hamiltonian having a given state as the ground state. We also provide several details of the finite size scaling

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.

Studies on entanglement entropy for Hubbard model with hole-doping and external magnetic field [rapid communication

Science.gov (United States)

Yao, K. L.; Li, Y. C.; Sun, X. Z.; Liu, Q. M.; Qin, Y.; Fu, H. H.; Gao, G. Y.

2005-10-01

By using the density matrix renormalization group (DMRG) method for the one-dimensional (1D) Hubbard model, we have studied the von Neumann entropy of a quantum system, which describes the entanglement of the system block and the rest of the chain. It is found that there is a close relation between the entanglement entropy and properties of the system. The hole-doping can alter the charge charge and spin spin interactions, resulting in charge polarization along the chain. By comparing the results before and after the doping, we find that doping favors increase of the von Neumann entropy and thus also favors the exchange of information along the chain. Furthermore, we calculated the spin and entropy distribution in external magnetic filed. It is confirmed that both the charge charge and the spin spin interactions affect the exchange of information along the chain, making the entanglement entropy redistribute.

Holographic entanglement entropy and gravitational anomalies

NARCIS (Netherlands)

Castro, A.; Detournay, S.; Iqbal, N.; Perlmutter, E.

2014-01-01

We study entanglement entropy in two-dimensional conformal field theories with a gravitational anomaly. In theories with gravity duals, this anomaly is holographically represented by a gravitational Chern-Simons term in the bulk action. We show that the anomaly broadens the Ryu-Takayanagi minimal

Entanglement entropy from the holographic stress tensor

International Nuclear Information System (INIS)

Bhattacharyya, Arpan; Sinha, Aninda

2013-01-01

We consider entanglement entropy in the context of gauge/gravity duality for conformal field theories in even dimensions. The holographic prescription due to Ryu and Takayanagi (RT) leads to an equation describing how the entangling surface extends into the bulk geometry. We show that setting to zero, the time–time component of the Brown–York stress tensor evaluated on the co-dimension 1 entangling surface, leads to the same equation. By considering a spherical entangling surface as an example, we observe that the Euclidean action methods in AdS/CFT will lead to the RT area functional arising as a counterterm needed to regularize the stress tensor. We present arguments leading to a justification for the minimal area prescription. (paper)

Entanglement entropy in the quantum networks of a coupled quantum harmonic oscillator

International Nuclear Information System (INIS)

Jafarizadeh, M A; Nami, S; Eghbalifam, F

2015-01-01

We investigate the entanglement of the ground state in the quantum networks that their nodes are considered as quantum harmonic oscillators. To this aim, the Schmidt numbers and entanglement entropy between two arbitrary partitions of a network are calculated.In partitioning an arbitrary graph into two parts there are some nodes in each part which are not connected to the nodes of the other part. So, these nodes of each part can be in distinct subsets. Therefore, the graph is separated into four subsets. The nodes of the first and last subsets are those which are not connected to the nodes of the other part. In theorem 1, by using the generalized Schur complement method in these four subsets, we prove that all the graphs whose connections between the two alternative subsets are complete, have the same entropy. A large number of graphs satisfy this theorem. Then the entanglement entropy in the limit of the large coupling and large size of the system is investigated in these graphs. Also, the asymptotic behaviors of the Schmidt numbers and entanglement entropy in the limit of infinite coupling are shown.One important quantity about partitioning is the conductance of the graph. The conductance of the graph is considered in various graphs. In these graphs we compare the conductance of the graph and the entanglement entropy. (paper)

Von Neumann entropy in a Rashba-Dresselhaus nanodot; dynamical electronic spin-orbit entanglement

Science.gov (United States)

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

Field space entanglement entropy, zero modes and Lifshitz models

Science.gov (United States)

Huffel, Helmuth; Kelnhofer, Gerald

2017-12-01

The field space entanglement entropy of a quantum field theory is obtained by integrating out a subset of its fields. We study an interacting quantum field theory consisting of massless scalar fields on a closed compact manifold M. To this model we associate its Lifshitz dual model. The ground states of both models are invariant under constant shifts. We interpret this invariance as gauge symmetry and subject the models to proper gauge fixing. By applying the heat kernel regularization one can show that the field space entanglement entropies of the massless scalar field model and of its Lifshitz dual are agreeing.

Volume-law scaling for the entanglement entropy in spin-1/2 chains

International Nuclear Information System (INIS)

Vitagliano, G; Riera, A; Latorre, J I

2010-01-01

Entanglement entropy obeys area law scaling for typical physical quantum systems. This may naively be argued to follow from the locality of interactions. We show that this is not the case by constructing an explicit simple spin chain Hamiltonian with nearest-neighbor interactions that presents an entanglement volume scaling law. This non-translational model is contrived to have couplings that force the accumulation of singlet bonds across the half-chain. This configuration of the couplings is suggested by real-space renormalization group arguments. Computation of the entanglement entropy is performed by mapping the system to free fermions and diagonalizing numerically its correlation matrix. An analytical relationship between the entanglement entropy and the Frobenius norm of the correlation matrix is also established. Our result is complementary to the known relationship between non-translational invariant, nearest-neighbor interacting Hamiltonians and quantum Merlin-Arthur (QMA)-complete problems.

Entanglement entropy in scalar field theory on the fuzzy sphere

International Nuclear Information System (INIS)

Okuno, Shizuka; Suzuki, Mariko; Tsuchiya, Asato

2016-01-01

We study entanglement entropy on the fuzzy sphere. We calculate it in a scalar field theory on the fuzzy sphere, which is given by a matrix model. We use a method that is based on the replica method and applicable to interacting fields as well as free fields. For free fields, we obtain results consistent with the previous study, which serves as a test of the validity of the method. For interacting fields, we perform Monte Carlo simulations at strong coupling and see a novel behavior of entanglement entropy

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.

Field space entanglement entropy, zero modes and Lifshitz models

Directory of Open Access Journals (Sweden)

Helmuth Huffel

2017-12-01

Full Text Available The field space entanglement entropy of a quantum field theory is obtained by integrating out a subset of its fields. We study an interacting quantum field theory consisting of massless scalar fields on a closed compact manifold M. To this model we associate its Lifshitz dual model. The ground states of both models are invariant under constant shifts. We interpret this invariance as gauge symmetry and subject the models to proper gauge fixing. By applying the heat kernel regularization one can show that the field space entanglement entropies of the massless scalar field model and of its Lifshitz dual are agreeing.

Entanglement entropy production in gravitational collapse: covariant regularization and solvable models

Science.gov (United States)

Bianchi, Eugenio; De Lorenzo, Tommaso; Smerlak, Matteo

2015-06-01

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.

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.

Entanglement entropy in (3 + 1)-d free U(1) gauge theory

Science.gov (United States)

Soni, Ronak M.; Trivedi, Sandip P.

2017-02-01

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.

Entanglement entropy production in gravitational collapse: covariant regularization and solvable models

International Nuclear Information System (INIS)

Bianchi, Eugenio; Lorenzo, Tommaso De; Smerlak, Matteo

2015-01-01

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.

Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum.

Science.gov (United States)

Fradkin, Eduardo; Moore, Joel E

2006-08-04

The entanglement entropy of a pure quantum state of a bipartite system A union or logical sumB is defined as the von Neumann entropy of the reduced density matrix obtained by tracing over one of the two parts. In one dimension, the entanglement of critical ground states diverges logarithmically in the subsystem size, with a universal coefficient that for conformally invariant critical points is related to the central charge of the conformal field theory. We find that the entanglement entropy of a standard class of z=2 conformal quantum critical points in two spatial dimensions, in addition to a nonuniversal "area law" contribution linear in the size of the AB boundary, generically has a universal logarithmically divergent correction, which is completely determined by the geometry of the partition and by the central charge of the field theory that describes the critical wave function.

Entanglement entropy and higher spin holography in AdS{sub 3}

Energy Technology Data Exchange (ETDEWEB)

Boer, Jan de; Jottar, Juan I. [Institute for Theoretical Physics, University of Amsterdam,Science Park 904, Postbus 94485, 1090 GL Amsterdam (Netherlands)

2014-04-14

A holographic correspondence has been recently developed between higher spin theories in three-dimensional anti-de Sitter space (AdS{sub 3}) and two-dimensional Conformal Field Theories (CFTs) with extended symmetries. A class of such dualities involves SL(N,R)×SL(N,R) Chern-Simons gauge theories in the (2+1)-dimensional bulk spacetime, and CFTs with W{sub N} symmetry algebras on the (1+1)-dimensional boundary. The topological character of the bulk theory forces one to reconsider standard geometric notions such as black hole horizons and entropy, as well as the usual holographic dictionary. Motivated by this challenge, in this note we present a proposal to compute entanglement entropy in the W{sub N} CFTs via holographic methods. In particular, we introduce a functional constructed from Wilson lines in the bulk Chern-Simons theory that captures the entanglement entropy in the CFTs dual to standard AdS{sub 3} gravity, corresponding to SL(2,R)×SL(2,R) gauge group, and admits an immediate generalization to the higher spin case. We explicitly evaluate this functional for several known solutions of the bulk theory, including charged black holes dual to thermal CFT states carrying higher spin charge, and show that it reproduces expected features of entanglement entropy, study whether it obeys strong subadditivity, and moreover show that it reduces to the thermal entropy in the appropriate limit.

Linear growth of the entanglement entropy and the Kolmogorov-Sinai rate

Science.gov (United States)

Bianchi, Eugenio; Hackl, Lucas; Yokomizo, Nelson

2018-03-01

The rate of entropy production in a classical dynamical system is characterized by the Kolmogorov-Sinai entropy rate h KS given by the sum of all positive Lyapunov exponents of the system. We prove a quantum version of this result valid for bosonic systems with unstable quadratic Hamiltonian. The derivation takes into account the case of time-dependent Hamiltonians with Floquet instabilities. We show that the entanglement entropy S A of a Gaussian state grows linearly for large times in unstable systems, with a rate Λ A ≤ h KS determined by the Lyapunov exponents and the choice of the subsystem A. We apply our results to the analysis of entanglement production in unstable quadratic potentials and due to periodic quantum quenches in many-body quantum systems. Our results are relevant for quantum field theory, for which we present three applications: a scalar field in a symmetry-breaking potential, parametric resonance during post-inflationary reheating and cosmological perturbations during inflation. Finally, we conjecture that the same rate Λ A appears in the entanglement growth of chaotic quantum systems prepared in a semiclassical state.

Numerical calculation of the entanglement entropy for scalar field in dilaton spacetimes

Science.gov (United States)

Huang, Shifeng; Fang, Xiongjun; Jing, Jiliang

2018-06-01

Using coupled harmonic oscillators model, we numerical analyze the entanglement entropy of massless scalar field in Gafinkle-Horowitz-Strominger (GHS) dilaton spacetime and Gibbons-Maeda (GM) dilaton spacetime. By numerical fitting, we find that the entanglement entropy of the dilaton black holes receive contribution from dilaton charge and is proportional to the area of the event horizon. It is interesting to note that the results of numerical fitting are coincide with ones obtained by using brick wall method and Euclidean path integral approach.

Entropy correlation and entanglement for mixed states in an algebraic model

International Nuclear Information System (INIS)

Hou Xiwen; Chen Jinghua; Wan Mingfang; Ma Zhongqi

2009-01-01

As an alternative with potential connections to actual experiments, other than the systems more usually used in the field of entanglement, the dynamics of entropy correlation and entanglement between two anharmonic vibrations in a well-established algebraic model, with parameters extracted from fitting to highly excited spectral experimental results for molecules H 2 O and SO 2 , is studied in terms of the linear entropy and two negativities for various initial states that are respectively taken to be the mixed density matrices of thermal states and squeezed states on each mode. For a suitable parameter in initial states the entropies in two stretches can show positive correlation or anti-correlation. And the linear entropy of each mode is positively correlated with the negativities just for the mixed-squeezed states with small parameters in H 2 O while they do not display any correlation in other cases. For the mixed-squeezed states the negativities exhibit dominantly positive correlations with an effective mutual entropy. The differences in the linear entropy and the negativities between H 2 O and SO 2 are discussed as well. Those are useful for molecular quantum computing and quantum information processing

Entanglement entropy for a particle coupled with its surrounding

International Nuclear Information System (INIS)

Puttarprom, C.; Yoo-Kong, S.; Tanasittikosol, M.; Liewrian, W.

2014-01-01

We investigate the entanglement for a model of a particle moving in the lattice (many-body system). The interaction between the particle and the lattice is modelled using Hooke's law. The Feynman path integral approach is applied to compute the density matrix of the system. The complexity of the problem is reduced by considering two-body system (bipartite system). The spatial entanglement of ground state is studied using the linear entropy. We find that increasing the confining potential implies a large spatial separation between the two particles. Thus the interaction between the particles increases according to Hooke's law. This results in the increase in the spatial entanglement

Holographic entanglement entropy for hollow cones and banana shaped regions

Energy Technology Data Exchange (ETDEWEB)

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.

Extended First Law for Entanglement Entropy in Lovelock Gravity

Directory of Open Access Journals (Sweden)

David Kastor

2016-05-01

Full Text Available The first law for the holographic entanglement entropy of spheres in a boundary CFT (Conformal Field Theory with a bulk Lovelock dual is extended to include variations of the bulk Lovelock coupling constants. Such variations in the bulk correspond to perturbations within a family of boundary CFTs. The new contribution to the first law is found to be the product of the variation δ a of the “A”-type trace anomaly coefficient for even dimensional CFTs, or more generally its extension δ a * to include odd dimensional boundaries, times the ratio S / a * . Since a * is a measure of the number of degrees of freedom N per unit volume of the boundary CFT, this new term has the form μ δ N , where the chemical potential μ is given by the entanglement entropy per degree of freedom.

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.

Holographic entanglement entropy and the extended phase structure of STU black holes

International Nuclear Information System (INIS)

Caceres, Elena; Nguyen, Phuc H.; Pedraza, Juan F.

2015-01-01

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.

Holographic charged Rényi entropies

Science.gov (United States)

Belin, Alexandre; Hung, Ling-Yan; Maloney, Alexander; Matsuura, Shunji; Myers, Robert C.; Sierens, Todd

2013-12-01

We construct a new class of entanglement measures by extending the usual definition of Rényi entropy to include a chemical potential. These charged Rényi entropies measure the degree of entanglement in different charge sectors of the theory and are given by Euclidean path integrals with the insertion of a Wilson line encircling the entangling surface. We compute these entropies for a spherical entangling surface in CFT's with holographic duals, where they are related to entropies of charged black holes with hyperbolic horizons. We also compute charged Rényi entropies in free field theories.

Entanglement Entropy in Quantum Spin Chains with Finite Range Interaction

Science.gov (United States)

Its, A. R.; Mezzadri, F.; Mo, M. Y.

2008-11-01

We study the entropy of entanglement of the ground state in a wide family of one-dimensional quantum spin chains whose interaction is of finite range and translation invariant. Such systems can be thought of as generalizations of the XY model. The chain is divided in two parts: one containing the first consecutive L spins; the second the remaining ones. In this setting the entropy of entanglement is the von Neumann entropy of either part. At the core of our computation is the explicit evaluation of the leading order term as L → ∞ of the determinant of a block-Toeplitz matrix with symbol Φ(z) = left(begin{array}{cc} iλ & g(z) \\ g^{-1}(z) & i λ right), where g( z) is the square root of a rational function and g(1/ z) = g -1( z). The asymptotics of such determinant is computed in terms of multi-dimensional theta-functions associated to a hyperelliptic curve {mathcal{L}} of genus g ≥ 1, which enter into the solution of a Riemann-Hilbert problem. Phase transitions for these systems are characterized by the branch points of {mathcal{L}} approaching the unit circle. In these circumstances the entropy diverges logarithmically. We also recover, as particular cases, the formulae for the entropy discovered by Jin and Korepin [14] for the XX model and Its, Jin and Korepin [12, 13] for the XY model.

Quantum entanglement and special relativity

International Nuclear Information System (INIS)

Nishikawa, Yoshihisa

2008-01-01

Quantum entanglement was suggested by Einstein to indicate that quantum mechanics was incomplete. However, against Einstein's expectation, the phenomenon due to quantum entanglement has been verified by experiments. Recently, in quantum information theory, it has been also treated as a resource for quantum teleportation and so on. In around 2000, it is recognized that quantum correlations between two particles of one pair state in an entangled spin-state are affected by the non-trivial effect due to the successive Lorentz transformation. This relativistic effect is called the Wigner rotation. The Wigner rotation has to been taken into account when we observe spin-correlation of moving particles in a different coordinate frame. In this paper, first, we explain quantum entanglement and its modification due to the Wigner rotation. After that, we introduce an extended model instead of one pair state model. In the extended model, quantum entanglement state is prepared as a superposition state of various pair states. We have computed the von Neumann entropy and the Shannon entropy to see the global behavior of variation for the spin correlation due to the relativistic effect. We also discuss distinguishability between the two particles of the pair. (author)

Entanglement entropy of two disjoint intervals in c = 1 theories

International Nuclear Information System (INIS)

Alba, Vincenzo; Tagliacozzo, Luca; Calabrese, Pasquale

2011-01-01

We study the scaling of the Rényi entanglement entropy of two disjoint blocks of critical lattice models described by conformal field theories with central charge c = 1. We provide the analytic conformal field theory result for the second order Rényi entropy for a free boson compactified on an orbifold describing the scaling limit of the Ashkin–Teller (AT) model on the self-dual line. We have checked this prediction in cluster Monte Carlo simulations of the classical two-dimensional AT model. We have also performed extensive numerical simulations of the anisotropic Heisenberg quantum spin chain with tree tensor network techniques that allowed us to obtain the reduced density matrices of disjoint blocks of the spin chain and to check the correctness of the predictions for Rényi and entanglement entropies from conformal field theory. In order to match these predictions, we have extrapolated the numerical results by properly taking into account the corrections induced by the finite length of the blocks on the leading scaling behavior

Entanglement in random pure states: spectral density and average von Neumann entropy

Energy Technology Data Exchange (ETDEWEB)

Kumar, Santosh; Pandey, Akhilesh, E-mail: skumar.physics@gmail.com, E-mail: ap0700@mail.jnu.ac.in [School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110 067 (India)

2011-11-04

Quantum entanglement plays a crucial role in quantum information, quantum teleportation and quantum computation. The information about the entanglement content between subsystems of the composite system is encoded in the Schmidt eigenvalues. We derive here closed expressions for the spectral density of Schmidt eigenvalues for all three invariant classes of random matrix ensembles. We also obtain exact results for average von Neumann entropy. We find that maximum average entanglement is achieved if the system belongs to the symplectic invariant class. (paper)

Measuring the quality of a quantum reference frame: The relative entropy of frameness

International Nuclear Information System (INIS)

Gour, Gilad; Marvian, Iman; Spekkens, Robert W.

2009-01-01

In the absence of a reference frame for transformations associated with group G, any quantum state that is noninvariant under the action of G may serve as a token of the missing reference frame. We here present a measure of the quality of such a token: the relative entropy of frameness. This is defined as the relative entropy distance between the state of interest and the nearest G-invariant state. Unlike the relative entropy of entanglement, this quantity is straightforward to calculate, and we find it to be precisely equal to the G-asymmetry, a measure of frameness introduced by Vaccaro et al. It is shown to provide an upper bound on the mutual information between the group element encoded into the token and the group element that may be extracted from it by measurement. In this sense, it quantifies the extent to which the token successfully simulates a full reference frame. We also show that despite a suggestive analogy from entanglement theory, the regularized relative entropy of frameness is zero and therefore does not quantify the rate of interconversion between the token and some standard form of quantum reference frame. Finally, we show how these investigations yield an approach to bounding the relative entropy of entanglement.

Entanglement negativity and entropy in non-equilibrium conformal field theory

Directory of Open Access Journals (Sweden)

Marianne Hoogeveen

2015-09-01

Full Text Available We study the dynamics of the entanglement in one-dimensional critical quantum systems after a local quench in which two independently thermalized semi-infinite halves are joined to form a homogeneous infinite system and left to evolve unitarily. We show that under certain conditions a nonequilibrium steady state (NESS is reached instantaneously as soon as the entanglement interval is within the light cone emanating from the contact point. In this steady state, the exact expressions for the entanglement entropy and the logarithmic negativity are in agreement with the steady state density matrix being a boosted thermal state, as expected. We derive various general identities: relating the negativity after the quench with unequal left and right initial temperatures with that where the left and right temperatures are equal; and relating these with the negativity in equilibrium thermal states. In certain regimes the resulting expressions can be analytically evaluated. Immediately after the interval intersects the light cone, we find logarithmic growth. For a very long interval, we find that the negativity approaches a plateau after sufficiently long times, different from its NESS value. The NESS value is reached instantly as soon as the entire interval is contained in the light cone. This provides a theoretical framework explaining recently obtained numerical results.

Entanglement negativity and entropy in non-equilibrium conformal field theory

International Nuclear Information System (INIS)

Hoogeveen, Marianne; Doyon, Benjamin

2015-01-01

We study the dynamics of the entanglement in one-dimensional critical quantum systems after a local quench in which two independently thermalized semi-infinite halves are joined to form a homogeneous infinite system and left to evolve unitarily. We show that under certain conditions a nonequilibrium steady state (NESS) is reached instantaneously as soon as the entanglement interval is within the light cone emanating from the contact point. In this steady state, the exact expressions for the entanglement entropy and the logarithmic negativity are in agreement with the steady state density matrix being a boosted thermal state, as expected. We derive various general identities: relating the negativity after the quench with unequal left and right initial temperatures with that where the left and right temperatures are equal; and relating these with the negativity in equilibrium thermal states. In certain regimes the resulting expressions can be analytically evaluated. Immediately after the interval intersects the light cone, we find logarithmic growth. For a very long interval, we find that the negativity approaches a plateau after sufficiently long times, different from its NESS value. The NESS value is reached instantly as soon as the entire interval is contained in the light cone. This provides a theoretical framework explaining recently obtained numerical results

On holographic entanglement entropy with second order excitations

Science.gov (United States)

He, Song; Sun, Jia-Rui; Zhang, Hai-Qing

2018-03-01

We study the low-energy corrections to the holographic entanglement entropy (HEE) in the boundary CFT by perturbing the bulk geometry up to second order excitations. Focusing on the case that the boundary subsystem is a strip, we show that the area of the bulk minimal surface can be expanded in terms of the conserved charges, such as mass, angular momentum and electric charge of the AdS black brane. We also calculate the variation of the energy in the subsystem and verify the validity of the first law-like relation of thermodynamics at second order. Moreover, the HEE is naturally bounded at second order perturbations if the cosmic censorship conjecture for the dual black hole still holds.

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.

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.

Effect of the time-dependent coupling on a superconducting qubit-field system under decoherence: Entanglement and Wehrl entropy

Energy Technology Data Exchange (ETDEWEB)

Abdel-Khalek, S., E-mail: sayedquantum@yahoo.co.uk [Mathematics Department, Faculty of Science, Sohag University, 82524 Sohag (Egypt); The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, Miramare-Trieste (Italy); Berrada, K. [The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, Miramare-Trieste (Italy); Al Imam Mohammad Ibn Saud Islamic University (IMSIU), College of Science, Department of Physics, Riyadh (Saudi Arabia); Eleuch, H. [Department of Physics, McGill University, 3600 rue University, Montreal, QC, H3A 2T8 (Canada); Department of Physics, Université de Montréal, 2900 boul. douard-Montpetit, Montreal, QC, H3T 1J4 (Canada)

2015-10-15

The dynamics of a superconducting (SC) qubit interacting with a field under decoherence with and without time-dependent coupling effect is analyzed. Quantum features like the collapse–revivals for the dynamics of population inversion, sudden birth and sudden death of entanglement, and statistical properties are investigated under the phase damping effect. Analytic results for certain parametric conditions are obtained. We analyze the influence of decoherence on the negativity and Wehrl entropy for different values of the physical parameters. We also explore an interesting relation between the SC-field entanglement and Wehrl entropy behavior during the time evolution. We show that the amount of SC-field entanglement can be enhanced as the field tends to be more classical. The studied model of SC-field system with the time-dependent coupling has high practical importance due to their experimental accessibility which may open new perspectives in different tasks of quantum formation processing.

Breakdown of the equal area law for holographic entanglement entropy

Science.gov (United States)

McCarthy, Fiona; Kubizňák, David; Mann, Robert B.

2017-11-01

We investigate a holographic version of Maxwell's equal area law analogous to that for the phase transition in the black hole temperature/black hole entropy plane of a charged AdS black hole. We consider proposed area laws for both the black hole temperature/holographic entanglement entropy plane and the black hole temperature/2- point correlation function plane. Despite recent claims to the contrary, we demonstrate numerically that neither proposal is valid. We argue that there is no physical reason to expect such a construction in these planes.

On holographic entanglement entropy with second order excitations

Directory of Open Access Journals (Sweden)

Song He

2018-03-01

Full Text Available We study the low-energy corrections to the holographic entanglement entropy (HEE in the boundary CFT by perturbing the bulk geometry up to second order excitations. Focusing on the case that the boundary subsystem is a strip, we show that the area of the bulk minimal surface can be expanded in terms of the conserved charges, such as mass, angular momentum and electric charge of the AdS black brane. We also calculate the variation of the energy in the subsystem and verify the validity of the first law-like relation of thermodynamics at second order. Moreover, the HEE is naturally bounded at second order perturbations if the cosmic censorship conjecture for the dual black hole still holds.

Entanglement entropy in quantum many-particle systems and their simulation via ansatz states

International Nuclear Information System (INIS)

Barthel, Thomas

2009-01-01

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

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

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 of two disjoint blocks in XY chains

International Nuclear Information System (INIS)

Fagotti, Maurizio; Calabrese, Pasquale

2010-01-01

We study the Rényi entanglement entropies of two disjoint intervals in XY chains. We exploit the exact solution of the model in terms of free Majorana fermions and we show how to construct the reduced density matrix in the spin variables by taking the Jordan–Wigner string between the two blocks properly into account. From this we can evaluate any Rényi entropy of finite integer order. We study in detail critical XX and Ising chains and we show that the asymptotic results for large blocks agree with recent conformal field theory predictions if corrections to the scaling are included in the analysis correctly. We also report results for the gapped phase and after a quantum quench

Entropy exchange and entanglement in the Jaynes-Cummings model

International Nuclear Information System (INIS)

Boukobza, E.; Tannor, D.J.

2005-01-01

The Jaynes-Cummings model (JCM) is the simplest fully quantum model that describes the interaction between light and matter. We extend a previous analysis by Phoenix and Knight [Ann. Phys. 186, 381 (1988)] of the JCM by considering mixed states of both the light and matter. We present examples of qualitatively different entropic correlations. In particular, we explore the regime of entropy exchange between light and matter, i.e., where the rate of change of the two are anticorrelated. This behavior contrasts with the case of pure light-matter states in which the rate of change of the two entropies are positively correlated and in fact identical. We give an analytical derivation of the anticorrelation phenomenon and discuss the regime of its validity. Finally, we show a strong correlation between the region of the Bloch sphere characterized by entropy exchange and that characterized by minimal entanglement as measured by the negative eigenvalues of the partially transposed density matrix

Exact results for corner contributions to the entanglement entropy and Rényi entropies of free bosons and fermions in 3d

Directory of Open Access Journals (Sweden)

Henriette Elvang

2015-10-01

Full Text Available In the presence of a sharp corner in the boundary of the entanglement region, the entanglement entropy (EE and Rényi entropies for 3d CFTs have a logarithmic term whose coefficient, the corner function, is scheme-independent. In the limit where the corner becomes smooth, the corner function vanishes quadratically with coefficient σ for the EE and σn for the Rényi entropies. For a free real scalar and a free Dirac fermion, we evaluate analytically the integral expressions of Casini, Huerta, and Leitao to derive exact results for σ and σn for all n=2,3,… . The results for σ agree with a recent universality conjecture of Bueno, Myers, and Witczak-Krempa that σ/CT=π2/24 in all 3d CFTs, where CT is the central charge. For the Rényi entropies, the ratios σn/CT do not indicate similar universality. However, in the limit n→∞, the asymptotic values satisfy a simple relationship and equal 1/(4π2 times the asymptotic values of the free energy of free scalars/fermions on the n-covered 3-sphere.

Entanglement of heavy quark impurities and generalized gravitational entropy

Science.gov (United States)

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.

Quantum Entanglement and Shannon Information Entropy for the Doubly Excited Resonance State in Positronium Negative Ion

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.

Entanglement property in matrix product spin systems

International Nuclear Information System (INIS)

Zhu Jingmin

2012-01-01

We study the entanglement property in matrix product spin-ring systems systemically by von Neumann entropy. We find that: (i) the Hilbert space dimension of one spin determines the upper limit of the maximal value of the entanglement entropy of one spin, while for multiparticle entanglement entropy, the upper limit of the maximal value depends on the dimension of the representation matrices. Based on the theory, we can realize the maximum of the entanglement entropy of any spin block by choosing the appropriate control parameter values. (ii) When the entanglement entropy of one spin takes its maximal value, the entanglement entropy of an asymptotically large spin block, i.e. the renormalization group fixed point, is not likely to take its maximal value, and so only the entanglement entropy S n of a spin block that varies with size n can fully characterize the spin-ring entanglement feature. Finally, we give the entanglement dynamics, i.e. the Hamiltonian of the matrix product system. (author)

Exact valence bond entanglement entropy and probability distribution in the XXX spin chain and the potts model.

Science.gov (United States)

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.

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.

Entanglement of Generalized Two-Mode Binomial States and Teleportation

International Nuclear Information System (INIS)

Wang Dongmei; Yu Youhong

2009-01-01

The entanglement of the generalized two-mode binomial states in the phase damping channel is studied by making use of the relative entropy of the entanglement. It is shown that the factors of q and p play the crucial roles in control the relative entropy of the entanglement. Furthermore, we propose a scheme of teleporting an unknown state via the generalized two-mode binomial states, and calculate the mean fidelity of the scheme. (general)

Quantification of entanglement entropies for doubly excited resonance states in two-electron atomic systems

International Nuclear Information System (INIS)

Ho, Yew Kam; Lin, Chien-Hao

2015-01-01

In this work, we study the quantum entanglement for doubly excited resonance states in two-electron atomic systems such as the H - and Ps - ions and the He atom by using highly correlated Hylleraas type functions The resonance states are determined by calculation of density of resonance states with the stabilization method. The spatial (electron-electron orbital) entanglement entropies (linear and von Neumann) for the low-lying doubly excited states are quantified using the Schmidt-Slater decomposition method. (paper)

Logarithmic black hole entropy corrections and holographic Renyi entropy

Energy Technology Data Exchange (ETDEWEB)

Mahapatra, Subhash [The Institute of Mathematical Sciences, Chennai (India); KU Leuven - KULAK, Department of Physics, Kortrijk (Belgium)

2018-01-15

The entanglement and Renyi entropies for spherical entangling surfaces in CFTs with gravity duals can be explicitly calculated by mapping these entropies first to the thermal entropy on hyperbolic space and then, using the AdS/CFT correspondence, to the Wald entropy of topological black holes. Here we extend this idea by taking into account corrections to the Wald entropy. Using the method based on horizon symmetries and the asymptotic Cardy formula, we calculate corrections to the Wald entropy and find that these corrections are proportional to the logarithm of the area of the horizon. With the corrected expression for the entropy of the black hole, we then find corrections to the Renyi entropies. We calculate these corrections for both Einstein and Gauss-Bonnet gravity duals. Corrections with logarithmic dependence on the area of the entangling surface naturally occur at the order G{sub D}{sup 0}. The entropic c-function and the inequalities of the Renyi entropy are also satisfied even with the correction terms. (orig.)

Logarithmic black hole entropy corrections and holographic Renyi entropy

International Nuclear Information System (INIS)

Mahapatra, Subhash

2018-01-01

The entanglement and Renyi entropies for spherical entangling surfaces in CFTs with gravity duals can be explicitly calculated by mapping these entropies first to the thermal entropy on hyperbolic space and then, using the AdS/CFT correspondence, to the Wald entropy of topological black holes. Here we extend this idea by taking into account corrections to the Wald entropy. Using the method based on horizon symmetries and the asymptotic Cardy formula, we calculate corrections to the Wald entropy and find that these corrections are proportional to the logarithm of the area of the horizon. With the corrected expression for the entropy of the black hole, we then find corrections to the Renyi entropies. We calculate these corrections for both Einstein and Gauss-Bonnet gravity duals. Corrections with logarithmic dependence on the area of the entangling surface naturally occur at the order G D 0 . The entropic c-function and the inequalities of the Renyi entropy are also satisfied even with the correction terms. (orig.)

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.

The relation between majorization theory and quantum information from entanglement monotones perspective

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.

Logarithmic black hole entropy corrections and holographic Rényi entropy

Science.gov (United States)

Mahapatra, Subhash

2018-01-01

The entanglement and Rényi entropies for spherical entangling surfaces in CFTs with gravity duals can be explicitly calculated by mapping these entropies first to the thermal entropy on hyperbolic space and then, using the AdS/CFT correspondence, to the Wald entropy of topological black holes. Here we extend this idea by taking into account corrections to the Wald entropy. Using the method based on horizon symmetries and the asymptotic Cardy formula, we calculate corrections to the Wald entropy and find that these corrections are proportional to the logarithm of the area of the horizon. With the corrected expression for the entropy of the black hole, we then find corrections to the Rényi entropies. We calculate these corrections for both Einstein and Gauss-Bonnet gravity duals. Corrections with logarithmic dependence on the area of the entangling surface naturally occur at the order GD^0. The entropic c-function and the inequalities of the Rényi entropy are also satisfied even with the correction terms.

Entanglement entropy in quantum spin chains with broken reflection symmetry

International Nuclear Information System (INIS)

Kadar, Zoltan; Zimboras, Zoltan

2010-01-01

We investigate the entanglement entropy of a block of L sites in quasifree translation-invariant spin chains concentrating on the effect of reflection-symmetry breaking. The Majorana two-point functions corresponding to the Jordan-Wigner transformed fermionic modes are determined in the most general case; from these, it follows that reflection symmetry in the ground state can only be broken if the model is quantum critical. The large L asymptotics of the entropy are calculated analytically for general gauge-invariant models, which have, until now, been done only for the reflection-symmetric sector. Analytical results are also derived for certain nongauge-invariant models (e.g., for the Ising model with Dzyaloshinskii-Moriya interaction). We also study numerically finite chains of length N with a nonreflection-symmetric Hamiltonian and report that the reflection symmetry of the entropy of the first L spins is violated but the reflection-symmetric Calabrese-Cardy formula is recovered asymptotically. Furthermore, for noncritical reflection-symmetry-breaking Hamiltonians, we find an anomaly in the behavior of the saturation entropy as we approach the critical line. The paper also provides a concise but extensive review of the block-entropy asymptotics in translation-invariant quasifree spin chains with an analysis of the nearest-neighbor case and the enumeration of the yet unsolved parts of the quasifree landscape.

Vacuum state of the Dirac field in de Sitter space and entanglement entropy

Energy Technology Data Exchange (ETDEWEB)

Kanno, Sugumi [Department of Theoretical Physics and History of Science,University of the Basque Country,48080 Bilbao (Spain); IKERBASQUE, Basque Foundation for Science,Maria Diaz de Haro 3, 48013, Bilbao (Spain); Sasaki, Misao [Center for Gravitational Physics,Yukawa Institute for Theoretical Physics, Kyoto University,Kyoto 606-8502 (Japan); Tanaka, Takahiro [Department of Physics, Kyoto University,Kyoto 606-8502 (Japan); Center for Gravitational Physics,Yukawa Institute for Theoretical Physics, Kyoto University,Kyoto 606-8502 (Japan)

2017-03-13

We compute the entanglement entropy of a free massive Dirac field between two causally disconnected open charts in de Sitter space. We first derive the Bunch-Davies vacuum mode functions of the Dirac field. We find there exists no supercurvature mode for the Dirac field. We then give the Bogoliubov transformation between the Bunch-Davies vacuum and the open chart vacua that makes the reduced density matrix diagonal. We find that the Dirac field becomes more entangled than a scalar field as m{sup 2}/H{sup 2} becomes small, and the difference is maximal in the massless limit.

Characterizing entanglement with global and marginal entropic measures

International Nuclear Information System (INIS)

Adesso, Gerardo; Illuminati, Fabrizio; De Siena, Silvio

2003-01-01

We qualify the entanglement of arbitrary mixed states of bipartite quantum systems by comparing global and marginal mixednesses quantified by different entropic measures. For systems of two qubits we discriminate the class of maximally entangled states with fixed marginal mixednesses, and determine an analytical upper bound relating the entanglement of formation to the marginal linear entropies. This result partially generalizes to mixed states the quantification of entanglement with marginal mixednesses holding for pure states. We identify a class of entangled states that, for fixed marginals, are globally more mixed than product states when measured by the linear entropy. Such states cannot be discriminated by the majorization criterion

New Aspects of Field Entropy Squeezing as an Indicator for Mixed State Entanglement in an Effective Two-Level System with Stark Shift

Institute of Scientific and Technical Information of China (English)

S.Abdel-Khalek; M.M.A.Ahmed; A-S F.Obada

2011-01-01

We present an effective two-level system in interaction through two-photon processes with a single mode quantized electromagnetic field,initially prepared in a coherent state.Field entropy squeezing as an indicator of the entanglement in a mixed state system is suggested.The temporal evolution of the negativity,Wehrl entropy,Wehrl phase distribution and field entropy squeezing are investigated.The results highlight the important roles played by both the Stark shift parameters and the mixed state setting in the dynamics of the Wehrl entropy,Wehrl phase distribution and field entropy squeezing.%We present an effective two-level system in interaction through two-photon processes with a single mode quantized electromagnetic Reid, initially prepared in a coherent state. Field entropy squeezing as an indicator of the entanglement in a mixed state system is suggested. The temporal evolution of the negativity, Wehrl entropy, Wehrl phase distribution and field entropy squeezing are investigated. The results highlight the important roles played by both the Stark shift parameters and the mixed state setting in the dynamics of the Wehrl entropy, Wehrl phase distribution and field entropy squeezing.

Entanglement entropy and complexity for one-dimensional holographic superconductors

Science.gov (United States)

Kord Zangeneh, Mahdi; Ong, Yen Chin; Wang, Bin

2017-08-01

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.

Entangled spins and ghost-spins

Directory of Open Access Journals (Sweden)

Dileep P. Jatkar

2017-09-01

Full Text Available We study patterns of quantum entanglement in systems of spins and ghost-spins regarding them as simple quantum mechanical toy models for theories containing negative norm states. We define a single ghost-spin as in [20] as a 2-state spin variable with an indefinite inner product in the state space. We find that whenever the spin sector is disentangled from the ghost-spin sector (both of which could be entangled within themselves, the reduced density matrix obtained by tracing over all the ghost-spins gives rise to positive entanglement entropy for positive norm states, while negative norm states have an entanglement entropy with a negative real part and a constant imaginary part. However when the spins are entangled with the ghost-spins, there are new entanglement patterns in general. For systems where the number of ghost-spins is even, it is possible to find subsectors of the Hilbert space where positive norm states always lead to positive entanglement entropy after tracing over the ghost-spins. With an odd number of ghost-spins however, we find that there always exist positive norm states with negative real part for entanglement entropy after tracing over the ghost-spins.

Entanglement Entropy of the N=4 SYM spin chain

International Nuclear Information System (INIS)

Georgiou, George; Zoakos, Dimitrios

2016-01-01

We present a detailed study of the Entanglement Entropy (EE) of excited states in all closed rank one subsectors of N=4 SYM, namely SU(2), SU(1|1) and SL(2). Exploiting the techniques of the Coordinate and the Algebraic Bethe Ansatz we obtain the EE for spin chains with up to seven magnons, at leading order in the coupling expansion but exact in the length of the spin chain and of the part of it that we cut. Focusing on the superconformal primary operator with two magnons in the BMN limit, we derive analytic and exact, in the coupling λ ′ , expressions for the Renyi and the EE. The interpolating functions for the Renyi and the EE monotonically increase as the coupling increases from the weak coupling λ ′ →0 regime to the strong coupling λ ′ →∞ regime. This results to a violation of a certain bound for the EE that is present at weak coupling and confirms the physical intuition that entanglement increases when the coupling increases.

Evolution of the field quantum entropy and entanglement in a system of multimode light field interacting resonantly with a two-level atom through N_j-degenerate N~Σ-photon process

Institute of Scientific and Technical Information of China (English)

2008-01-01

The time evolution of the field quantum entropy and entanglement in a system of multi-mode coherent light field resonantly interacting with a two-level atom by de-generating the multi-photon process is studied by utilizing the Von Neumann re-duced entropy theory,and the analytical expressions of the quantum entropy of the multimode field and the numerical calculation results for three-mode field inter-acting with the atom are obtained. Our attention focuses on the discussion of the influences of the initial average photon number,the atomic distribution angle and the phase angle of the atom dipole on the evolution of the quantum field entropy and entanglement. The results obtained from the numerical calculation indicate that: the stronger the quantum field is,the weaker the entanglement between the quan-tum field and the atom will be,and when the field is strong enough,the two sub-systems may be in a disentangled state all the time; the quantum field entropy is strongly dependent on the atomic distribution angle,namely,the quantum field and the two-level atom are always in the entangled state,and are nearly stable at maximum entanglement after a short time of vibration; the larger the atomic dis-tribution angle is,the shorter the time for the field quantum entropy to evolve its maximum value is; the phase angles of the atom dipole almost have no influences on the entanglement between the quantum field and the two-level atom. Entangled states or pure states based on these properties of the field quantum entropy can be prepared.

Problems in black-hole entropy interpretation

International Nuclear Information System (INIS)

Liberati, S.

1997-01-01

In this work some proposals for black-hole entropy interpretation are exposed and investigated. In particular, the author will firstly consider the so-called 'entanglement entropy' interpretation, in the framework of the brick wall model and the divergence problem arising in the one-loop calculations of various thermodynamical quantities, like entropy, internal energy and heat capacity. It is shown that the assumption of equality of entanglement entropy and Bekenstein-Hawking one appears to give inconsistent results. These will be a starting point for a different interpretation of black.hole entropy based on peculiar topological structures of manifolds with 'intrinsic' thermodynamical features. It is possible to show an exact relation between black-hole gravitational entropy and topology of these Euclidean space-times. the expression for the Euler characteristic, through the Gauss-Bonnet integral, and the one for entropy for gravitational instantons are proposed in a form which makes the relation between these self-evident. Using this relation he propose a generalization of the Bekenstein-Hawking entropy in which the former and Euler characteristic are related in the equation S = χA / 8. Finally, he try to expose some conclusions and hypotheses about possible further development of this research

First law of entanglement rates from holography

Science.gov (United States)

O'Bannon, Andy; Probst, Jonas; Rodgers, Ronnie; Uhlemann, Christoph F.

2017-09-01

For a perturbation of the state of a conformal field theory (CFT), the response of the entanglement entropy is governed by the so-called "first law" of entanglement entropy, in which the change in entanglement entropy is proportional to the change in energy. Whether such a first law holds for other types of perturbations, such as a change to the CFT Lagrangian, remains an open question. We use holography to study the evolution in time t of entanglement entropy for a CFT driven by a t -linear source for a conserved U (1 ) current or marginal scalar operator. We find that although the usual first law of entanglement entropy may be violated, a first law for the rates of change of entanglement entropy and energy still holds. More generally, we prove that this first law for rates holds in holography for any asymptotically (d +1 )-dimensional anti-de Sitter metric perturbation whose t dependence first appears at order zd in the Fefferman-Graham expansion about the boundary at z =0 .

Gauge field entanglement in Kitaev's honeycomb model

Science.gov (United States)

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.

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.

Dynamics of entanglement and uncertainty relation in coupled harmonic oscillator system: exact results

Science.gov (United States)

Park, DaeKil

2018-06-01

The dynamics of entanglement and uncertainty relation is explored by solving the time-dependent Schrödinger equation for coupled harmonic oscillator system analytically when the angular frequencies and coupling constant are arbitrarily time dependent. We derive the spectral and Schmidt decompositions for vacuum solution. Using the decompositions, we derive the analytical expressions for von Neumann and Rényi entropies. Making use of Wigner distribution function defined in phase space, we derive the time dependence of position-momentum uncertainty relations. To show the dynamics of entanglement and uncertainty relation graphically, we introduce two toy models and one realistic quenched model. While the dynamics can be conjectured by simple consideration in the toy models, the dynamics in the realistic quenched model is somewhat different from that in the toy models. In particular, the dynamics of entanglement exhibits similar pattern to dynamics of uncertainty parameter in the realistic quenched model.

On S-mixing entropy of quantum channels

Science.gov (United States)

Mukhamedov, Farrukh; Watanabe, Noboru

2018-06-01

In this paper, an S-mixing entropy of quantum channels is introduced as a generalization of Ohya's S-mixing entropy. We investigate several properties of the introduced entropy. Moreover, certain relations between the S-mixing entropy and the existing map and output entropies of quantum channels are investigated as well. These relations allowed us to find certain connections between separable states and the introduced entropy. Hence, there is a sufficient condition to detect entangled states. Moreover, several properties of the introduced entropy are investigated. Besides, entropies of qubit and phase-damping channels are calculated.

Renyi entropy and conformal defects

Energy Technology Data Exchange (ETDEWEB)

Bianchi, Lorenzo [Humboldt-Univ. Berlin (Germany). Inst. fuer Physik; Hamburg Univ. (Germany). II. Inst. fuer Theoretische Physik; Meineri, Marco [Scuola Normale Superiore, Pisa (Italy); Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada); Istituto Nazionale di Fisica Nucleare, Pisa (Italy); Myers, Robert C. [Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada); Smolkin, Michael [California Univ., Berkely, CA (United States). Center for Theoretical Physics and Department of Physics

2016-04-18

We propose a field theoretic framework for calculating the dependence of Renyi entropies on the shape of the entangling surface in a conformal field theory. Our approach rests on regarding the corresponding twist operator as a conformal defect and in particular, we define the displacement operator which implements small local deformations of the entangling surface. We identify a simple constraint between the coefficient defining the two-point function of the displacement operator and the conformal weight of the twist operator, which consolidates a number of distinct conjectures on the shape dependence of the Renyi entropy. As an example, using this approach, we examine a conjecture regarding the universal coefficient associated with a conical singularity in the entangling surface for CFTs in any number of spacetime dimensions. We also provide a general formula for the second order variation of the Renyi entropy arising from small deformations of a spherical entangling surface, extending Mezei's results for the entanglement entropy.

Renyi entropy and conformal defects

International Nuclear Information System (INIS)

Bianchi, Lorenzo; Myers, Robert C.; Smolkin, Michael

2016-01-01

We propose a field theoretic framework for calculating the dependence of Renyi entropies on the shape of the entangling surface in a conformal field theory. Our approach rests on regarding the corresponding twist operator as a conformal defect and in particular, we define the displacement operator which implements small local deformations of the entangling surface. We identify a simple constraint between the coefficient defining the two-point function of the displacement operator and the conformal weight of the twist operator, which consolidates a number of distinct conjectures on the shape dependence of the Renyi entropy. As an example, using this approach, we examine a conjecture regarding the universal coefficient associated with a conical singularity in the entangling surface for CFTs in any number of spacetime dimensions. We also provide a general formula for the second order variation of the Renyi entropy arising from small deformations of a spherical entangling surface, extending Mezei's results for the entanglement entropy.

Holographic entropy inequalities and gapped phases of matter

Energy Technology Data Exchange (ETDEWEB)

Bao, Ning [Institute for Quantum Information and Matter, California Institute of Technology,Pasadena, CA 91125 (United States); Walter Burke Institute for Theoretical Physics, California Institute of Technology,Pasadena, CA 91125 (United States); Cao, ChunJun [Walter Burke Institute for Theoretical Physics, California Institute of Technology,Pasadena, CA 91125 (United States); Walter, Michael [Stanford Institute for Theoretical Physics,Stanford University, Stanford, CA 94305 (United States); Wang, Zitao [Institute for Quantum Information and Matter, California Institute of Technology,Pasadena, CA 91125 (United States); Walter Burke Institute for Theoretical Physics, California Institute of Technology,Pasadena, CA 91125 (United States)

2015-09-29

We extend our studies of holographic entropy inequalities to gapped phases of matter. For any number of regions, we determine the linear entropy inequalities satisfied by systems in which the entanglement entropy satisfies an exact area law. In particular, we find that all holographic entropy inequalities are valid in such systems. In gapped systems with topological order, the “cyclic inequalities” derived recently for the holographic entanglement entropy generalize the Kitaev-Preskill formula for the topological entanglement entropy. Finally, we propose a candidate linear inequality for general 4-party quantum states.

Holographic entropy inequalities and gapped phases of matter

International Nuclear Information System (INIS)

Bao, Ning; Cao, ChunJun; Walter, Michael; Wang, Zitao

2015-01-01

We extend our studies of holographic entropy inequalities to gapped phases of matter. For any number of regions, we determine the linear entropy inequalities satisfied by systems in which the entanglement entropy satisfies an exact area law. In particular, we find that all holographic entropy inequalities are valid in such systems. In gapped systems with topological order, the “cyclic inequalities” derived recently for the holographic entanglement entropy generalize the Kitaev-Preskill formula for the topological entanglement entropy. Finally, we propose a candidate linear inequality for general 4-party quantum states.

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.

Characterizing quantum correlations. Entanglement, uncertainty relations and exponential families

International Nuclear Information System (INIS)

Niekamp, Soenke

2012-01-01

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.

Extremal entanglement and mixedness in continuous variable systems

International Nuclear Information System (INIS)

Adesso, Gerardo; Serafini, Alessio; Illuminati, Fabrizio

2004-01-01

We investigate the relationship between mixedness and entanglement for Gaussian states of continuous variable systems. We introduce generalized entropies based on Schatten p norms to quantify the mixedness of a state and derive their explicit expressions in terms of symplectic spectra. We compare the hierarchies of mixedness provided by such measures with the one provided by the purity (defined as tr ρ 2 for the state ρ) for generic n-mode states. We then review the analysis proving the existence of both maximally and minimally entangled states at given global and marginal purities, with the entanglement quantified by the logarithmic negativity. Based on these results, we extend such an analysis to generalized entropies, introducing and fully characterizing maximally and minimally entangled states for given global and local generalized entropies. We compare the different roles played by the purity and by the generalized p entropies in quantifying the entanglement and the mixedness of continuous variable systems. We introduce the concept of average logarithmic negativity, showing that it allows a reliable quantitative estimate of continuous variable entanglement by direct measurements of global and marginal generalized p entropies

Two intervals Rényi entanglement entropy of compact free boson on torus

International Nuclear Information System (INIS)

Liu, Feihu; Liu, Xiao

2016-01-01

We compute the N=2 Rényi entanglement entropy of two intervals at equal time in a circle, for the theory of a 2D compact complex free scalar at finite temperature. This is carried out by performing functional integral on a genus 3 ramified cover of the torus, wherein the quantum part of the integral is captured by the four point function of twist fields on the worldsheet torus, and the classical piece is given by summing over winding modes of the genus 3 surface onto the target space torus. The final result is given in terms of a product of theta functions and certain multi-dimensional theta functions. We demonstrate the T-duality invariance of the result. We also study its low temperature limit. In the case in which the size of the intervals and of their separation are much smaller than the whole system, our result is in exact agreement with the known result for two intervals on an infinite system at zero temperature http://dx.doi.org/10.1088/1742-5468/2009/11/P11001. In the case in which the separation between the two intervals is much smaller than the interval length, the leading thermal corrections take the same universal form as proposed in http://dx.doi.org/10.1103/PhysRevLett.112.171603, http://dx.doi.org/10.1103/PhysRevD.91.105013 for Rényi entanglement entropy of a single interval.

Rényi entropy and conformal defects

International Nuclear Information System (INIS)

Bianchi, Lorenzo; Meineri, Marco; Myers, Robert C.; Smolkin, Michael

2016-01-01

We propose a field theoretic framework for calculating the dependence of Rényi entropies on the shape of the entangling surface in a conformal field theory. Our approach rests on regarding the corresponding twist operator as a conformal defect and in particular, we define the displacement operator which implements small local deformations of the entangling surface. We identify a simple constraint between the coefficient defining the two-point function of the displacement operator and the conformal weight of the twist operator, which consolidates a number of distinct conjectures on the shape dependence of the Rényi entropy. As an example, using this approach, we examine a conjecture regarding the universal coefficient associated with a conical singularity in the entangling surface for CFTs in any number of spacetime dimensions. We also provide a general formula for the second order variation of the Rényi entropy arising from small deformations of a spherical entangling surface, extending Mezei’s results for the entanglement entropy.

Rényi entropy and conformal defects

Energy Technology Data Exchange (ETDEWEB)

Bianchi, Lorenzo [Institut für Physik, Humboldt-Universität zu Berlin,Zum Großen Windkanal 6, 12489 Berlin (Germany); II. Institut für Theoretische Physik, Universität Hamburg,Luruper Chaussee 149, 22761 Hamburg (Germany); Meineri, Marco [Scuola Normale Superiore and Istituto Nazionale di Fisica Nucleare - Sezione di Pisa,Piazza dei Cavalieri 7, I-56126 Pisa (Italy); Perimeter Institute for Theoretical Physics,31 Caroline Street North, Waterloo, ON N2L 2Y5 (Canada); Myers, Robert C. [Perimeter Institute for Theoretical Physics,31 Caroline Street North, Waterloo, ON N2L 2Y5 (Canada); Smolkin, Michael [Center for Theoretical Physics, Department of Physics, University of California,Berkeley, CA 94720 (United States)

2016-07-14

We propose a field theoretic framework for calculating the dependence of Rényi entropies on the shape of the entangling surface in a conformal field theory. Our approach rests on regarding the corresponding twist operator as a conformal defect and in particular, we define the displacement operator which implements small local deformations of the entangling surface. We identify a simple constraint between the coefficient defining the two-point function of the displacement operator and the conformal weight of the twist operator, which consolidates a number of distinct conjectures on the shape dependence of the Rényi entropy. As an example, using this approach, we examine a conjecture regarding the universal coefficient associated with a conical singularity in the entangling surface for CFTs in any number of spacetime dimensions. We also provide a general formula for the second order variation of the Rényi entropy arising from small deformations of a spherical entangling surface, extending Mezei’s results for the entanglement entropy.

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.

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.

Interuniversal entanglement in a cyclic multiverse

Science.gov (United States)

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.

Bounds on the entanglement entropy of droplet states in the XXZ spin chain

Science.gov (United States)

Beaud, V.; Warzel, S.

2018-01-01

We consider a class of one-dimensional quantum spin systems on the finite lattice Λ ⊂Z , related to the XXZ spin chain in its Ising phase. It includes in particular the so-called droplet Hamiltonian. The entanglement entropy of energetically low-lying states over a bipartition Λ = B ∪ Bc is investigated and proven to satisfy a logarithmic bound in terms of min{n, |B|, |Bc|}, where n denotes the maximal number of down spins in the considered state. Upon addition of any (positive) random potential, the bound becomes uniformly constant on average, thereby establishing an area law. The proof is based on spectral methods: a deterministic bound on the local (many-body integrated) density of states is derived from an energetically motivated Combes-Thomas estimate.

Entanglement from dissipation and holographic interpretation

Science.gov (United States)

Cantcheff, M. Botta; Gadelha, Alexandre L.; Marchioro, Dáfni F. Z.; Nedel, Daniel Luiz

2018-02-01

In this work we study a dissipative field theory where the dissipation process is manifestly related to dynamical entanglement and put it in the holographic context. Such endeavour is realized by further development of a canonical approach to study quantum dissipation, which consists of doubling the degrees of freedom of the original system by defining an auxiliary one. A time dependent entanglement entropy for the vacumm state is calculated and a geometrical interpretation of the auxiliary system and the entropy is given in the context of the AdS/CFT correspondence using the Ryu-Takayanagi formula. We show that the dissipative dynamics is controlled by the entanglement entropy and there are two distinct stages: in the early times the holographic interpretation requires some deviation from classical General Relativity; in the later times the quantum system is described as a wormhole, a solution of the Einstein's equations near to a maximally extended black hole with two asymptotically AdS boundaries. We focus our holographic analysis in this regime, and suggest a mechanism similar to teleportation protocol to exchange (quantum) information between the two CFTs on the boundaries (see Maldacena et al. in Fortschr Phys 65(5):1700034, arXiv:1704.05333 [hep-th], 2017).

Entanglement from dissipation and holographic interpretation

Energy Technology Data Exchange (ETDEWEB)

Cantcheff, M.B. [IFLP-CONICET CC 67, La Plata, Buenos Aires (Argentina); Gadelha, Alexandre L. [Universidade Federal da Bahia, Instituto de Fisica, Salvador, BA (Brazil); Marchioro, Dafni F.Z.; Nedel, Daniel Luiz [Universidade Federal da Integracao Latino-Americana, Instituto Latino-Americano de Ciencias da Vida e da Natureza, Foz do Iguacu, PR (Brazil)

2018-02-15

In this work we study a dissipative field theory where the dissipation process is manifestly related to dynamical entanglement and put it in the holographic context. Such endeavour is realized by further development of a canonical approach to study quantum dissipation, which consists of doubling the degrees of freedom of the original system by defining an auxiliary one. A time dependent entanglement entropy for the vacuum state is calculated and a geometrical interpretation of the auxiliary system and the entropy is given in the context of the AdS/CFT correspondence using the Ryu-Takayanagi formula. We show that the dissipative dynamics is controlled by the entanglement entropy and there are two distinct stages: in the early times the holographic interpretation requires some deviation from classical General Relativity; in the later times the quantum system is described as a wormhole, a solution of the Einstein's equations near to a maximally extended black hole with two asymptotically AdS boundaries. We focus our holographic analysis in this regime, and suggest a mechanism similar to teleportation protocol to exchange (quantum) information between the two CFTs on the boundaries (see Maldacena et al. in Fortschr Phys 65(5):1700034, arXiv:1704.05333 [hep-th], 2017). (orig.)

Higher Curvature Gravity from Entanglement in Conformal Field Theories

Science.gov (United States)

Haehl, Felix M.; Hijano, Eliot; Parrikar, Onkar; Rabideau, Charles

2018-05-01

By generalizing different recent works to the context of higher curvature gravity, we provide a unifying framework for three related results: (i) If an asymptotically anti-de Sitter (AdS) spacetime computes the entanglement entropies of ball-shaped regions in a conformal field theory using a generalized Ryu-Takayanagi formula up to second order in state deformations around the vacuum, then the spacetime satisfies the correct gravitational equations of motion up to second order around the AdS background. (ii) The holographic dual of entanglement entropy in higher curvature theories of gravity is given by the Wald entropy plus a particular correction term involving extrinsic curvatures. (iii) Conformal field theory relative entropy is dual to gravitational canonical energy (also in higher curvature theories of gravity). Especially for the second point, our novel derivation of this previously known statement does not involve the Euclidean replica trick.

Detecting quantum entanglement. Entanglement witnesses and uncertainty relations

International Nuclear Information System (INIS)

Guehne, O.

2004-01-01

This thesis deals with methods of the detection of entanglement. After recalling some facts and definitions concerning entanglement and separability, we investigate two methods of the detection of entanglement. In the first part of this thesis we consider so-called entanglement witnesses, mainly in view of the detection of multipartite entanglement. Entanglement witnesses are observables for which a negative expectation value indicates entanglement. We first present a simple method to construct these witnesses. Since witnesses are nonlocal observables, they are not easy to measure in a real experiment. However, as we will show, one can circumvent this problem by decomposing the witness into several local observables which can be measured separately. We calculate the local decompositions for several interesting witnesses for two, three and four qubits. Local decompositions can be optimized in the number of measurement settings which are needed for an experimental implementation. We present a method to prove that a given local decomposition is optimal and discuss with this the optimality of our decompositions. Then we present another method of designing witnesses which are by construction measurable with local measurements. Finally, we shortly report on experiments where some of the witnesses derived in this part have been used to detect three- and four-partite entanglement of polarized photons. The second part of this thesis deals with separability criteria which are written in terms of uncertainty relations. There are two different formulations of uncertainty relations since one can measure the uncertainty of an observable by its variance as well as by entropic quantities. We show that both formulations are useful tools for the derivation of separability criteria for finite-dimensional systems and investigate the resulting criteria. Our results in this part exhibit also some more fundamental properties of entanglement: We show how known separability criteria for

Comparison of the attempts of quantum discord and quantum entanglement to capture quantum correlations

International Nuclear Information System (INIS)

Qasimi, Asma Al-; James, Daniel F. V.

2011-01-01

Measurements of quantum systems disturb their states. To quantify this nonclassical characteristic, Zurek and Ollivier [Phys. Rev. Lett. 88, 017901 (2001)] introduced the quantum discord, a quantum correlation that can be nonzero even when entanglement in the system is zero. Discord has aroused great interest as a resource that is more robust against the effects of decoherence and offers the exponential speed-up of certain computational algorithms. Here, we study general two-level bipartite systems and give general results on the relationship between discord, entanglement, and linear entropy. We also identify the states for which discord takes a maximal value for a given entropy or entanglement, thus placing strong bounds on entanglement-discord and entropy-discord relations. We find out that although discord and entanglement are identical for pure states, they differ when generalized to mixed states as a result of the difference in the method of generalization.

Relating Out-of-Time-Order Correlations to Entanglement via Multiple-Quantum Coherences.

Science.gov (United States)

Gärttner, Martin; Hauke, Philipp; Rey, Ana Maria

2018-01-26

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.

Relating Out-of-Time-Order Correlations to Entanglement via Multiple-Quantum Coherences

Science.gov (United States)

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.

Holography and Entanglement in Flat Spacetime

International Nuclear Information System (INIS)

Li Wei; Takayanagi, Tadashi

2011-01-01

We propose a holographic correspondence of the flat spacetime based on the behavior of the entanglement entropy and the correlation functions. The holographic dual theory turns out to be highly nonlocal. We argue that after most part of the space is traced out, the reduced density matrix gives the maximal entropy and the correlation functions become trivial. We present a toy model for this holographic dual using a nonlocal scalar field theory that reproduces the same property of the entanglement entropy. Our conjecture is consistent with the entropy of Schwarzschild black holes in asymptotically flat spacetimes.

Entanglement Equilibrium and the Einstein Equation.

Science.gov (United States)

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.

Revivals and entanglement from initially entangled mixed states of a damped Jaynes-Cummings model

International Nuclear Information System (INIS)

Rendell, R.W.; Rajagopal, A.K.

2003-01-01

An exact density matrix of a phase-damped Jaynes-Cummings model (JCM) with entangled Bell-like initial states formed from a model two-state atom and sets of adjacent photon number states of a single-mode radiation field is presented. The entanglement of the initial states and the subsequent time evolution is assured by finding a positive lower bound on the concurrence of local 2x2 projections of the full 2x∞ JCM density matrix. It is found that the time evolution of the lower bound of the concurrence systematically captures the corresponding collapse and revival features in atomic inversion, relative entropies of atomic and radiation, mutual entropy, and quantum deficit. The atom and radiation subsystems exhibit alternating sets of collapses and revivals in a complementary fashion due to the initially mixed states of the atom and radiation employed here. This is in contrast with the result obtained when the initial state of the dissipationless system is a factored pure state of the atom and radiation, where the atomic and radiation entropies are necessarily the same. The magnitudes of the entanglement lower bound and the atomic and radiation revivals become larger as both the magnitude and phase of the Bell-like initial state contribution increase. The time evolution of the entropy difference of the total system and that of the radiation subsystem exhibit negative regions called 'supercorrelated' states which do not appear in the atomic subsystem. Entangled initial states are found to enhance this supercorrelated feature. Finally, the effect of phase damping is to randomize both the subsystems for asymptotically long times. It may be feasible to experimentally investigate the results presented here using the Rabi oscillation methods of microwave and optical cavity quantum electrodynamics since pure photon number states have recently been produced and observed

Entanglement dynamics after quantum quenches in generic integrable systems

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Vincenzo Alba, Pasquale Calabrese

2018-03-01

Full Text Available The time evolution of the entanglement entropy in non-equilibrium quantum systems provides crucial information about the structure of the time-dependent state. For quantum quench protocols, by combining a quasiparticle picture for the entanglement spreading with the exact knowledge of the stationary state provided by Bethe ansatz, it is possible to obtain an exact and analytic description of the evolution of the entanglement entropy. Here we discuss the application of these ideas to several integrable models. First we show that for non-interacting systems, both bosonic and fermionic, the exact time-dependence of the entanglement entropy can be derived by elementary techniques and without solving the dynamics. We then provide exact results for interacting spin chains that are carefully tested against numerical simulations. Finally, we apply this method to integrable one-dimensional Bose gases (Lieb-Liniger model both in the attractive and repulsive regimes. We highlight a peculiar behaviour of the entanglement entropy due to the absence of a maximum velocity of excitations.

On holographic defect entropy

International Nuclear Information System (INIS)

Estes, John; Jensen, Kristan; O’Bannon, Andy; Tsatis, Efstratios; Wrase, Timm

2014-01-01

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

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.

Entanglement hamiltonian and entanglement contour in inhomogeneous 1D critical systems

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Tonni, Erik; Rodríguez-Laguna, Javier; Sierra, Germán

2018-04-01

Inhomogeneous quantum critical systems in one spatial dimension have been studied by using conformal field theory in static curved backgrounds. Two interesting examples are the free fermion gas in the harmonic trap and the inhomogeneous XX spin chain called rainbow chain. For conformal field theories defined on static curved spacetimes characterised by a metric which is Weyl equivalent to the flat metric, with the Weyl factor depending only on the spatial coordinate, we study the entanglement hamiltonian and the entanglement spectrum of an interval adjacent to the boundary of a segment where the same boundary condition is imposed at the endpoints. A contour function for the entanglement entropies corresponding to this configuration is also considered, being closely related to the entanglement hamiltonian. The analytic expressions obtained by considering the curved spacetime which characterises the rainbow model have been checked against numerical data for the rainbow chain, finding an excellent agreement.

Entanglement in the XY spin chain

International Nuclear Information System (INIS)

Its, A R; Jin, B-Q; Korepin, V E

2005-01-01

We consider the entanglement in the ground state of the XY model of an infinite chain. Following Bennett, Bernstein, Popescu and Schumacher, we use the entropy of a sub-system as a measure of entanglement. Vidal, Latorre, Rico and Kitaev have conjectured that the von Neumann entropy of a large block of neighbouring spins approaches a constant as the size of the block increases. We evaluate this limiting entropy as a function of anisotropy and transverse magnetic field. We use the methods based on the integrable Fredholm operators and the Riemann-Hilbert approach. It is shown how the entropy becomes singular at the phase transition points

Gravitation from entanglement in holographic CFTs

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Faulkner, Thomas [Institute for Advanced Study,Princeton, NJ 08540 (United States); Guica, Monica [Department of Physics and Astronomy, University of Pennsylvania,209 S. 33rd St., Philadelphia, PA 19104-6396 (United States); Hartman, Thomas [Kavli Institute for Theoretical Physics, University of California,Santa Barbara, CA 93106-4030 (United States); Myers, Robert C. [Perimeter Institute for Theoretical Physics,31 Caroline Street N., Waterloo, Ontario N2L 2Y5 (Canada); Raamsdonk, Mark Van [Department of Physics and Astronomy, University of British Columbia,6224 Agricultural Road, Vancouver, B.C. V6T 1W9 (Canada)

2014-03-11

Entanglement entropy obeys a ‘first law’, an exact quantum generalization of the ordinary first law of thermodynamics. In any CFT with a semiclassical holographic dual, this first law has an interpretation in the dual gravitational theory as a constraint on the spacetimes dual to CFT states. For small perturbations around the CFT vacuum state, we show that the set of such constraints for all ball-shaped spatial regions in the CFT is exactly equivalent to the requirement that the dual geometry satisfy the gravitational equations of motion, linearized about pure AdS. For theories with entanglement entropy computed by the Ryu-Takayanagi formula S=A/(4G{sub N}), we obtain the linearized Einstein equations. For theories in which the vacuum entanglement entropy for a ball is computed by more general Wald functionals, we obtain the linearized equations for the associated higher-curvature theories. Using the first law, we also derive the holographic dictionary for the stress tensor, given the holographic formula for entanglement entropy. This method provides a simple alternative to holographic renormalization for computing the stress tensor expectation value in arbitrary higher derivative gravitational theories.

Emergent Geometry from Entropy and Causality

Science.gov (United States)

Engelhardt, Netta

In this thesis, we investigate the connections between the geometry of spacetime and aspects of quantum field theory such as entanglement entropy and causality. This work is motivated by the idea that spacetime geometry is an emergent phenomenon in quantum gravity, and that the physics responsible for this emergence is fundamental to quantum field theory. Part I of this thesis is focused on the interplay between spacetime and entropy, with a special emphasis on entropy due to entanglement. In general spacetimes, there exist locally-defined surfaces sensitive to the geometry that may act as local black hole boundaries or cosmological horizons; these surfaces, known as holographic screens, are argued to have a connection with the second law of thermodynamics. Holographic screens obey an area law, suggestive of an association with entropy; they are also distinguished surfaces from the perspective of the covariant entropy bound, a bound on the total entropy of a slice of the spacetime. This construction is shown to be quite general, and is formulated in both classical and perturbatively quantum theories of gravity. The remainder of Part I uses the Anti-de Sitter/ Conformal Field Theory (AdS/CFT) correspondence to both expand and constrain the connection between entanglement entropy and geometry. The AdS/CFT correspondence posits an equivalence between string theory in the "bulk" with AdS boundary conditions and certain quantum field theories. In the limit where the string theory is simply classical General Relativity, the Ryu-Takayanagi and more generally, the Hubeny-Rangamani-Takayanagi (HRT) formulae provide a way of relating the geometry of surfaces to entanglement entropy. A first-order bulk quantum correction to HRT was derived by Faulkner, Lewkowycz and Maldacena. This formula is generalized to include perturbative quantum corrections in the bulk at any (finite) order. Hurdles to spacetime emergence from entanglement entropy as described by HRT and its quantum

Universal distortion-free entanglement concentration

International Nuclear Information System (INIS)

Matsumoto, Keiji; Hayashi, Masahito

2007-01-01

We propose a new protocol of universal entanglement concentration, which converts many copies of an unknown pure state to an exact maximally entangled state. The yield of the protocol, which is outputted as a classical information, is probabilistic, and achieves the entropy rate with high probability, just as nonuniversal entanglement concentration protocols do

Multi-boundary entanglement in Chern-Simons theory and link invariants

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Balasubramanian, Vijay [David Rittenhouse Laboratory, University of Pennsylvania,209 S.33rd Street, Philadelphia, PA 19104 (United States); Theoretische Natuurkunde, Vrije Universiteit Brussel (VUB) andInternational Solvay Institutes,Pleinlaan 2, B-1050 Brussels (Belgium); Fliss, Jackson R.; Leigh, Robert G. [Department of Physics, University of Illinois,1110 W. Green Street, Urbana, IL 61801 (United States); Parrikar, Onkar [David Rittenhouse Laboratory, University of Pennsylvania,209 S.33rd Street, Philadelphia, PA 19104 (United States)

2017-04-11

We consider Chern-Simons theory for gauge group G at level k on 3-manifolds M{sub n} with boundary consisting of n topologically linked tori. The Euclidean path integral on M{sub n} defines a quantum state on the boundary, in the n-fold tensor product of the torus Hilbert space. We focus on the case where M{sub n} is the link-complement of some n-component link inside the three-sphere S{sup 3}. The entanglement entropies of the resulting states define framing-independent link invariants which are sensitive to the topology of the chosen link. For the Abelian theory at level k (G=U(1){sub k}) we give a general formula for the entanglement entropy associated to an arbitrary (m|n−m) partition of a generic n-component link into sub-links. The formula involves the number of solutions to certain Diophantine equations with coefficients related to the Gauss linking numbers (mod k) between the two sublinks. This formula connects simple concepts in quantum information theory, knot theory, and number theory, and shows that entanglement entropy between sublinks vanishes if and only if they have zero Gauss linking (mod k). For G=SU(2){sub k}, we study various two and three component links. We show that the 2-component Hopf link is maximally entangled, and hence analogous to a Bell pair, and that the Whitehead link, which has zero Gauss linking, nevertheless has entanglement entropy. Finally, we show that the Borromean rings have a “W-like' entanglement structure (i.e., tracing out one torus does not lead to a separable state), and give examples of other 3-component links which have “GHZ-like” entanglement (i.e., tracing out one torus does lead to a separable state).

Universal terms of entanglement entropy for 6d CFTs

International Nuclear Information System (INIS)

Miao, Rong-Xin

2015-01-01

We derive the universal terms of entanglement entropy for 6d CFTs by applying the holographic and the field theoretical approaches, respectively. Our formulas are conformal invariant and agree with the results of http://dx.doi.org/10.1007/JHEP04(2011)025 http://dx.doi.org/10.1007/JHEP12(2012)005. Remarkably, we find that the holographic and the field theoretical results match exactly for the C 2 and Ck 2 terms, where C and k denote the Weyl tensor and the extrinsic curvature, respectively. As for the k 4 terms, we meet the splitting problem of the conical metrics. The splitting problem in the bulk can be fixed by equations of motion. As for the splitting on the boundary, we assume the general forms and find that there indeed exists suitable splitting which can make the holographic and the field theoretical k 4 terms match. Since we have much more equations than the free parameters, the match for k 4 terms is non-trivial.

Squashed entanglement in infinite dimensions

International Nuclear Information System (INIS)

Shirokov, M. E.

2016-01-01

We analyse two possible definitions of the squashed entanglement in an infinite-dimensional bipartite system: direct translation of the finite-dimensional definition and its universal extension. It is shown that the both definitions produce the same lower semicontinuous entanglement measure possessing all basis properties of the squashed entanglement on the set of states having at least one finite marginal entropy. It is also shown that the second definition gives an adequate lower semicontinuous extension of this measure to all states of the infinite-dimensional bipartite system. A general condition relating continuity of the squashed entanglement to continuity of the quantum mutual information is proved and its corollaries are considered. Continuity bound for the squashed entanglement under the energy constraint on one subsystem is obtained by using the tight continuity bound for quantum conditional mutual information (proved in the Appendix by using Winter’s technique). It is shown that the same continuity bound is valid for the entanglement of formation. As a result the asymptotic continuity of the both entanglement measures under the energy constraint on one subsystem is proved.

The von Neumann entanglement entropy for Wigner-crystal states in one dimensional N-particle systems

International Nuclear Information System (INIS)

Kościk, Przemysław

2015-01-01

We study one-dimensional systems of N particles in a one-dimensional harmonic trap with an inverse power law interaction ∼|x| −d . Within the framework of the harmonic approximation we derive, in the strong interaction limit, the Schmidt decomposition of the one-particle reduced density matrix and investigate the nature of the degeneracy appearing in its spectrum. Furthermore, the ground-state asymptotic occupancies and their natural orbitals are derived in closed analytic form, which enables their easy determination for a wide range of values of N. A closed form asymptotic expression for the von Neumann entanglement entropy is also provided and its dependence on N is discussed for the systems with d=1 (charged particles) and with d=3 (dipolar particles). - Highlights: • We study confined systems of N particles with an inverse power law interaction. • We apply the harmonic approximation to the systems. • We derive closed form expressions for the asymptotic von Neumann entropy. • The asymptotic von Neumann entropy grows monotonically as N increases

Entanglement branching operator

Science.gov (United States)

Harada, Kenji

2018-01-01

We introduce an entanglement branching operator to split a composite entanglement flow in a tensor network which is a promising theoretical tool for many-body systems. We can optimize an entanglement branching operator by solving a minimization problem based on squeezing operators. The entanglement branching is a new useful operation to manipulate a tensor network. For example, finding a particular entanglement structure by an entanglement branching operator, we can improve a higher-order tensor renormalization group method to catch a proper renormalization flow in a tensor network space. This new method yields a new type of tensor network states. The second example is a many-body decomposition of a tensor by using an entanglement branching operator. We can use it for a perfect disentangling among tensors. Applying a many-body decomposition recursively, we conceptually derive projected entangled pair states from quantum states that satisfy the area law of entanglement entropy.

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.

Entanglement and discord of the superposition of Greenberger-Horne-Zeilinger states

International Nuclear Information System (INIS)

Parashar, Preeti; Rana, Swapan

2011-01-01

We calculate the analytic expression for geometric measure of entanglement for arbitrary superposition of two N-qubit canonical orthonormal Greenberger-Horne-Zeilinger (GHZ) states and the same for two W states. In the course of characterizing all kinds of nonclassical correlations, an explicit formula for quantum discord (via relative entropy) for the former class of states has been presented. Contrary to the GHZ state, the closest separable state to the W state is not classical. Therefore, in this case, the discord is different from the relative entropy of entanglement. We conjecture that the discord for the N-qubit W state is log 2 N.

Criticality and entanglement in random quantum systems

International Nuclear Information System (INIS)

Refael, G; Moore, J E

2009-01-01

We review studies of entanglement entropy in systems with quenched randomness, concentrating on universal behavior at strongly random quantum critical points. The disorder-averaged entanglement entropy provides insight into the quantum criticality of these systems and an understanding of their relationship to non-random ('pure') quantum criticality. The entanglement near many such critical points in one dimension shows a logarithmic divergence in subsystem size, similar to that in the pure case but with a different universal coefficient. Such universal coefficients are examples of universal critical amplitudes in a random system. Possible measurements are reviewed along with the one-particle entanglement scaling at certain Anderson localization transitions. We also comment briefly on higher dimensions and challenges for the future.

Entropy for gravitational Chern-Simons terms by squashed cone method

International Nuclear Information System (INIS)

Guo, Wu-Zhong; Miao, Rong-Xin

2016-01-01

In this paper we investigate the entropy of gravitational Chern-Simons terms for the horizon with non-vanishing extrinsic curvatures, or the holographic entanglement entropy for arbitrary entangling surface. In 3D there is no anomaly of entropy. But the original squashed cone method can not be used directly to get the correct result. For higher dimensions the anomaly of entropy would appear, still, we can not use the squashed cone method directly. That is becasuse the Chern-Simons action is not gauge invariant. To get a reasonable result we suggest two methods. One is by adding a boundary term to recover the gauge invariance. This boundary term can be derived from the variation of the Chern-Simons action. The other one is by using the Chern-Simons relation dΩ_4_n_−_1=tr(R"2"n). We notice that the entropy of tr(R"2"n) is a total derivative locally, i.e. S=ds_C_S. We propose to identify s_C_S with the entropy of gravitational Chern-Simons terms Ω_4_n_−_1. In the first method we could get the correct result for Wald entropy in arbitrary dimension. In the second approach, in addition to Wald entropy, we can also obtain the anomaly of entropy with non-zero extrinsic curvatures. Our results imply that the entropy of a topological invariant, such as the Pontryagin term tr(R"2"n) and the Euler density, is a topological invariant on the entangling surface.

Entanglement and thermodynamics after a quantum quench in integrable systems.

Science.gov (United States)

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.

Holographic entanglement in a noncommutative gauge theory

International Nuclear Information System (INIS)

Fischler, Willy; Kundu, Arnab; Kundu, Sandipan

2014-01-01

In this article we investigate aspects of entanglement entropy and mutual information in a large-N strongly coupled noncommutative gauge theory, both at zero and at finite temperature. Using the gauge-gravity duality and the Ryu-Takayanagi (RT) prescription, we adopt a scheme for defining spatial regions on such noncommutative geometries and subsequently compute the corresponding entanglement entropy. We observe that for regions which do not lie entirely in the noncommutative plane, the RT-prescription yields sensible results. In order to make sense of the divergence structure of the corresponding entanglement entropy, it is essential to introduce an additional cut-off in the theory. For regions which lie entirely in the noncommutative plane, the corresponding minimal area surfaces can only be defined at this cut-off and they have distinctly peculiar properties

Entanglement Properties of a Higher-Integer-Spin AKLT Model with Quantum Group Symmetry

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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.

Half the entanglement in critical systems is distillable from a single specimen

International Nuclear Information System (INIS)

Orus, R.; Latorre, J. I.; Eisert, J.; Cramer, M.

2006-01-01

We establish a quantitative relationship between the entanglement content of a single quantum chain at a critical point and the corresponding entropy of entanglement. We find that, surprisingly, the leading critical scaling of the single-copy entanglement with respect to any bipartitioning is exactly one-half of the entropy of entanglement, in a general setting of conformal field theory and quasifree systems. Conformal symmetry imposes that the single-copy entanglement scales as E 1 (ρ L )=(c/6)ln L-(c/6)(π 2 /ln L)+O(1/L), where L is the number of constituents in a block of an infinite chain and c denotes the central charge. This shows that from a single specimen of a critical chain, already half the entanglement can be distilled compared to the rate that is asymptotically available. The result is substantiated by a quantitative analysis for all translationally invariant quantum spin chains corresponding to all isotropic quasifree fermionic models. An example of the XY spin chain shows that away from criticality the above relation is maintained only near the quantum phase transition

Notes on entanglement entropy in string theory

International Nuclear Information System (INIS)

He, Song; Numasawa, Tokiro; Takayanagi, Tadashi; Watanabe, Kento

2015-01-01

In this paper, we study the conical entropy in string theory in the simplest setup of dividing the nine dimensional space into two halves. This corresponds to the leading quantum correction to the horizon entropy in string theory on the Rindler space. This entropy is also called the conical entropy and includes surface term contributions. We first derive a new simple formula of the conical entropy for any free higher spin fields. Then we apply this formula to computations of conical entropy in open and closed superstring. In our analysis of closed string, we study the twisted conical entropy defined by making use of string theory on Melvin backgrounds. This quantity is easier to calculate owing to the folding trick. Our analysis shows that the conical entropy in closed superstring is UV finite owing to the string scale cutoff.

Large-scale behaviour of local and entanglement entropy of the free Fermi gas at any temperature

Science.gov (United States)

Leschke, Hajo; Sobolev, Alexander V.; Spitzer, Wolfgang

2016-07-01

The leading asymptotic large-scale behaviour of the spatially bipartite entanglement entropy (EE) of the free Fermi gas infinitely extended in multidimensional Euclidean space at zero absolute temperature, T = 0, is by now well understood. Here, we present and discuss the first rigorous results for the corresponding EE of thermal equilibrium states at T> 0. The leading large-scale term of this thermal EE turns out to be twice the first-order finite-size correction to the infinite-volume thermal entropy (density). Not surprisingly, this correction is just the thermal entropy on the interface of the bipartition. However, it is given by a rather complicated integral derived from a semiclassical trace formula for a certain operator on the underlying one-particle Hilbert space. But in the zero-temperature limit T\\downarrow 0, the leading large-scale term of the thermal EE considerably simplifies and displays a {ln}(1/T)-singularity which one may identify with the known logarithmic enhancement at T = 0 of the so-called area-law scaling. birthday of the ideal Fermi gas.

Holographic entanglement entropy in 2D holographic superconductor via AdS3/CFT2

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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.

Quantum entanglement in strong-field ionization

Science.gov (United States)

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.

Entanglement and local extremes at an infinite-order quantum phase transition

International Nuclear Information System (INIS)

Rulli, C. C.; Sarandy, M. S.

2010-01-01

The characterization of an infinite-order quantum phase transition (QPT) by entanglement measures is analyzed. To this aim, we consider two closely related solvable spin-1/2 chains, namely, the Ashkin-Teller and the staggered XXZ models. These systems display a distinct pattern of eigenstates but exhibit the same thermodynamics, that is, the same energy spectrum. By performing exact diagonalization, we investigate the behavior of pairwise and block entanglement in the ground state of both models. In contrast with the XXZ chain, we show that pairwise entanglement fails in the characterization of the infinite-order QPT in the Ashkin-Teller model, although it can be achieved by analyzing the distance of the pair state from the separability boundary. Concerning block entanglement, we show that both XXZ and Ashkin-Teller models exhibit identical von Neumann entropies as long as a suitable choice of blocks is performed. Entanglement entropy is then shown to be able to identify the quantum phase diagram, even though its local extremes (either maximum or minimum) may also appear in the absence of any infinite-order QPT.

On the entropy variation in the scenario of entropic gravity

Science.gov (United States)

Xiao, Yong; Bai, Shi-Yang

2018-05-01

In the scenario of entropic gravity, entropy varies as a function of the location of the matter, while the tendency to increase entropy appears as gravity. We concentrate on studying the entropy variation of a typical gravitational system with different relative positions between the mass and the gravitational source. The result is that the entropy of the system doesn't increase when the mass is displaced closer to the gravitational source. In this way it disproves the proposal of entropic gravity from thermodynamic entropy. It doesn't exclude the possibility that gravity originates from non-thermodynamic entropy like entanglement entropy.

Quantum Entanglement in Neural Network States

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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

Geometric entanglement in topologically ordered states

International Nuclear Information System (INIS)

Orús, Román; Wei, Tzu-Chieh; Buerschaper, Oliver; Nest, Maarten Van den

2014-01-01

Here we investigate the connection between topological order and the geometric entanglement, as measured by the logarithm of the overlap between a given state and its closest product state of blocks. We do this for a variety of topologically ordered systems such as the toric code, double semion, colour code and quantum double models. As happens for the entanglement entropy, we find that for sufficiently large block sizes the geometric entanglement is, up to possible sub-leading corrections, the sum of two contributions: a bulk contribution obeying a boundary law times the number of blocks and a contribution quantifying the underlying pattern of long-range entanglement of the topologically ordered state. This topological contribution is also present in the case of single-spin blocks in most cases, and constitutes an alternative characterization of topological order for these quantum states based on a multipartite entanglement measure. In particular, we see that the topological term for the two-dimensional colour code is twice as much as the one for the toric code, in accordance with recent renormalization group arguments (Bombin et al 2012 New J. Phys. 14 073048). Motivated by these results, we also derive a general formalism to obtain upper- and lower-bounds to the geometric entanglement of states with a non-Abelian group symmetry, and which we explicitly use to analyse quantum double models. Furthermore, we also provide an analysis of the robustness of the topological contribution in terms of renormalization and perturbation theory arguments, as well as a numerical estimation for small systems. Some of the results in this paper rely on the ability to disentangle single sites from the quantum state, which is always possible for the systems that we consider. Additionally we relate our results to the behaviour of the relative entropy of entanglement in topologically ordered systems, and discuss a number of numerical approaches based on tensor networks that could be

Energy entanglement relation for quantum energy teleportation

Energy Technology Data Exchange (ETDEWEB)

Hotta, Masahiro, E-mail: hotta@tuhep.phys.tohoku.ac.j [Department of Physics, Faculty of Science, Tohoku University, Sendai 980-8578 (Japan)

2010-07-26

Protocols of quantum energy teleportation (QET), while retaining causality and local energy conservation, enable the transportation of energy from a subsystem of a many-body quantum system to a distant subsystem by local operations and classical communication through ground-state entanglement. We prove two energy-entanglement inequalities for a minimal QET model. These relations help us to gain a profound understanding of entanglement itself as a physical resource by relating entanglement to energy as an evident physical resource.

Entanglement as a probe of confinement

International Nuclear Information System (INIS)

Klebanov, Igor R.; Kutasov, David; Murugan, Arvind

2008-01-01

We investigate the entanglement entropy in gravity duals of confining large N c gauge theories using the proposal of [S. Ryu, T. Takayanagi, Phys. Rev. Lett. 96 (2006) 181602, (hep-th/0603001); S. Ryu, T. Takayanagi, JHEP 0608 (2006) 045, (hep-th/0605073)]. Dividing one of the directions of space into a line segment of length l and its complement, the entanglement entropy between the two subspaces is given by the classical action of the minimal bulk hypersurface which approaches the endpoints of the line segment at the boundary. We find that in confining backgrounds there are generally two such surfaces. One consists of two disconnected components localized at the endpoints of the line segment. The other contains a tube connecting the two components. The disconnected surface dominates the entropy for l above a certain critical value l crit while the connected one dominates below that value. The change of behavior at l=l crit is reminiscent of the finite temperature deconfinement transition: for l crit the entropy scales as N c 2 , while for l>l crit as N c 0 . We argue that a similar transition should occur in any field theory with a Hagedorn spectrum of non-interacting bound states. The requirement that the entanglement entropy has a phase transition may be useful in constraining gravity duals of confining theories

Tractable Quantification of Entanglement for Multipartite Pure States

International Nuclear Information System (INIS)

Nian-Quan, Jiang; Yu-Jian, Wang; Yi-Zhuang, Zheng; Gen-Chang, Cai

2008-01-01

We present kth-order entanglement measure and global kth-order entanglement measure for multipartite pure states, and extend Bennett's measure of partial entropy for bipartite pure states to a multipartite case. These measures are computable and can effectively classify and quantify the entanglement of multipartite pure states. (general)

Parametric Bayesian Estimation of Differential Entropy and Relative Entropy

OpenAIRE

Gupta; Srivastava

2010-01-01

Given iid samples drawn from a distribution with known parametric form, we propose the minimization of expected Bregman divergence to form Bayesian estimates of differential entropy and relative entropy, and derive such estimators for the uniform, Gaussian, Wishart, and inverse Wishart distributions. Additionally, formulas are given for a log gamma Bregman divergence and the differential entropy and relative entropy for the Wishart and inverse Wishart. The results, as always with Bayesian est...

Entanglement negativity in the multiverse

Energy Technology Data Exchange (ETDEWEB)

Kanno, Sugumi [Department of Theoretical Physics and History of Science, University of the Basque Country UPV/EHU, 48080 Bilbao (Spain); Shock, Jonathan P. [Laboratory for Quantum Gravity and Strings and Astrophysics, Cosmology and Gravity Center, Department of Mathematics and Applied Mathematics, University of Cape Town, Private Bag, Rondebosch 7701 (South Africa); Soda, Jiro, E-mail: sugumi.kanno@ehu.es, E-mail: jonathan.shock@uct.ac.za, E-mail: jiro@phys.sci.kobe-u.ac.jp [Department of Physics, Kobe University, Kobe 657-8501 (Japan)

2015-03-01

We explore quantum entanglement between two causally disconnected regions in the multiverse. We first consider a free massive scalar field, and compute the entanglement negativity between two causally separated open charts in de Sitter space. The qualitative feature of it turns out to be in agreement with that of the entanglement entropy. We then introduce two observers who determine the entanglement between two causally disconnected de Sitter spaces. When one of the observers remains constrained to a region of the open chart in a de Sitter space, we find that the scale dependence enters into the entanglement. We show that a state which is initially maximally entangled becomes more entangled or less entangled on large scales depending on the mass of the scalar field and recovers the initial entanglement in the small scale limit. We argue that quantum entanglement may provide some evidence for the existence of the multiverse.

Entanglement negativity in the multiverse

International Nuclear Information System (INIS)

Kanno, Sugumi; Shock, Jonathan P.; Soda, Jiro

2015-01-01

We explore quantum entanglement between two causally disconnected regions in the multiverse. We first consider a free massive scalar field, and compute the entanglement negativity between two causally separated open charts in de Sitter space. The qualitative feature of it turns out to be in agreement with that of the entanglement entropy. We then introduce two observers who determine the entanglement between two causally disconnected de Sitter spaces. When one of the observers remains constrained to a region of the open chart in a de Sitter space, we find that the scale dependence enters into the entanglement. We show that a state which is initially maximally entangled becomes more entangled or less entangled on large scales depending on the mass of the scalar field and recovers the initial entanglement in the small scale limit. We argue that quantum entanglement may provide some evidence for the existence of the multiverse

Entanglement negativity in the multiverse

Energy Technology Data Exchange (ETDEWEB)

Kanno, Sugumi [Department of Theoretical Physics and History of Science, University of the Basque Country UPV/EHU, 48080 Bilbao (Spain); IKERBASQUE, Basque Foundation for Science, Maria Diaz de Haro 3, 48013, Bilbao (Spain); Laboratory for Quantum Gravity & Strings and Astrophysics, Cosmology & Gravity Center, Department of Mathematics & Applied Mathematics, University of Cape Town, Private Bag, Rondebosch 7701 (South Africa); Shock, Jonathan P. [Laboratory for Quantum Gravity & Strings and Astrophysics, Cosmology & Gravity Center, Department of Mathematics & Applied Mathematics, University of Cape Town, Private Bag, Rondebosch 7701 (South Africa); National Institute for Theoretical Physics, Private Bag X1, Matieland, 7602 (South Africa); Soda, Jiro [Department of Physics, Kobe University, Kobe 657-8501 (Japan)

2015-03-10

We explore quantum entanglement between two causally disconnected regions in the multiverse. We first consider a free massive scalar field, and compute the entanglement negativity between two causally separated open charts in de Sitter space. The qualitative feature of it turns out to be in agreement with that of the entanglement entropy. We then introduce two observers who determine the entanglement between two causally disconnected de Sitter spaces. When one of the observers remains constrained to a region of the open chart in a de Sitter space, we find that the scale dependence enters into the entanglement. We show that a state which is initially maximally entangled becomes more entangled or less entangled on large scales depending on the mass of the scalar field and recovers the initial entanglement in the small scale limit. We argue that quantum entanglement may provide some evidence for the existence of the multiverse.

Gravity as Quantum Entanglement Force

OpenAIRE

Lee, Jae-Weon; Kim, Hyeong-Chan; Lee, Jungjai

2010-01-01

We conjecture that the total quantum entanglement of matter and vacuum in the universe tends to increase with time, like entropy, and that an effective force is associated with this tendency. We also suggest that gravity and dark energy are types of quantum entanglement forces, similar to Verlinde's entropic force, and give holographic dark energy with an equation of state comparable to current observational data. This connection between quantum entanglement and gravity could give some new in...

Entanglement between total intensity and polarization for pairs of coherent states

Science.gov (United States)

Sanchidrián-Vaca, Carlos; Luis, Alfredo

2018-04-01

We examine entanglement between number and polarization, or number and relative phase, in pair coherent states and two-mode squeezed vacuum via linear entropy and covariance criteria. We consider the embedding of the two-mode Hilbert space in a larger space to get a well-defined factorization of the number-phase variables. This can be regarded as a kind of protoentanglement that can be extracted and converted into real particle entanglement via feasible experimental procedures. In particular this reveals interesting entanglement properties of pairs of coherent states.

Topological network entanglement as order parameter for the emergence of geometry

International Nuclear Information System (INIS)

Diamantini, M Cristina; Trugenberger, Carlo A

2017-01-01

We show that, in discrete models of quantum gravity, emergent geometric space can be viewed as the entanglement pattern in a mixed quantum state of the ‘universe’, characterized by a universal topological network entanglement. As a concrete example we analyze the recently proposed model in which geometry emerges due to the condensation of 4-cycles in random regular bipartite graphs, driven by the combinatorial Ollivier–Ricci curvature. Using this model we show that the emergence of geometric order decreases the entanglement entropy of random configurations. The lowest geometric entanglement entropy is realized in four dimensions. (paper)

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.

Photon Entanglement Through Brain Tissue.

Science.gov (United States)

Shi, Lingyan; Galvez, Enrique J; Alfano, Robert R

2016-12-20

Photon entanglement, the cornerstone of quantum correlations, provides a level of coherence that is not present in classical correlations. Harnessing it by study of its passage through organic matter may offer new possibilities for medical diagnosis technique. In this work, we study the preservation of photon entanglement in polarization, created by spontaneous parametric down-conversion, after one entangled photon propagates through multiphoton-scattering brain tissue slices with different thickness. The Tangle-Entropy (TS) plots show the strong preservation of entanglement of photons propagating in brain tissue. By spatially filtering the ballistic scattering of an entangled photon, we find that its polarization entanglement is preserved and non-locally correlated with its twin in the TS plots. The degree of entanglement correlates better with structure and water content than with sample thickness.

Horizon Entropy from Quantum Gravity Condensates.

Science.gov (United States)

Oriti, Daniele; Pranzetti, Daniele; Sindoni, Lorenzo

2016-05-27

We construct condensate states encoding the continuum spherically symmetric quantum geometry of a horizon in full quantum gravity, i.e., without any classical symmetry reduction, in the group field theory formalism. Tracing over the bulk degrees of freedom, we show how the resulting reduced density matrix manifestly exhibits a holographic behavior. We derive a complete orthonormal basis of eigenstates for the reduced density matrix of the horizon and use it to compute the horizon entanglement entropy. By imposing consistency with the horizon boundary conditions and semiclassical thermodynamical properties, we recover the Bekenstein-Hawking entropy formula for any value of the Immirzi parameter. Our analysis supports the equivalence between the von Neumann (entanglement) entropy interpretation and the Boltzmann (statistical) one.

Squashed Entanglement, k-Extendibility, Quantum Markov Chains, and Recovery Maps

Science.gov (United States)

Li, Ke; Winter, Andreas

2018-02-01

Squashed entanglement (Christandl and Winter in J. Math. Phys. 45(3):829-840, 2004) is a monogamous entanglement measure, which implies that highly extendible states have small value of the squashed entanglement. Here, invoking a recent inequality for the quantum conditional mutual information (Fawzi and Renner in Commun. Math. Phys. 340(2):575-611, 2015) greatly extended and simplified in various work since, we show the converse, that a small value of squashed entanglement implies that the state is close to a highly extendible state. As a corollary, we establish an alternative proof of the faithfulness of squashed entanglement (Brandão et al. Commun. Math. Phys. 306:805-830, 2011). We briefly discuss the previous and subsequent history of the Fawzi-Renner bound and related conjectures, and close by advertising a potentially far-reaching generalization to universal and functorial recovery maps for the monotonicity of the relative entropy.

All Inequalities for the Relative Entropy

Science.gov (United States)

Ibinson, Ben; Linden, Noah; Winter, Andreas

2007-01-01

The relative entropy of two n-party quantum states is an important quantity exhibiting, for example, the extent to which the two states are different. The relative entropy of the states formed by reducing two n-party states to a smaller number m of parties is always less than or equal to the relative entropy of the two original n-party states. This is the monotonicity of relative entropy. Using techniques from convex geometry, we prove that monotonicity under restrictions is the only general inequality satisfied by quantum relative entropies. In doing so we make a connection to secret sharing schemes with general access structures: indeed, it turns out that the extremal rays of the cone defined by monotonicity are populated by classical secret sharing schemes. A surprising outcome is that the structure of allowed relative entropy values of subsets of multiparty states is much simpler than the structure of allowed entropy values. And the structure of allowed relative entropy values (unlike that of entropies) is the same for classical probability distributions and quantum states.

The Matter-Gravity Entanglement Hypothesis

Science.gov (United States)

Kay, Bernard S.

2018-05-01

I outline some of my work and results (some dating back to 1998, some more recent) on my matter-gravity entanglement hypothesis, according to which the entropy of a closed quantum gravitational system is equal to the system's matter-gravity entanglement entropy. The main arguments presented are: (1) that this hypothesis is capable of resolving what I call the second-law puzzle, i.e. the puzzle as to how the entropy increase of a closed system can be reconciled with the asssumption of unitary time-evolution; (2) that the black hole information loss puzzle may be regarded as a special case of this second law puzzle and that therefore the same resolution applies to it; (3) that the black hole thermal atmosphere puzzle (which I recall) can be resolved by adopting a radically different-from-usual description of quantum black hole equilibrium states, according to which they are total pure states, entangled between matter and gravity in such a way that the partial states of matter and gravity are each approximately thermal equilibrium states (at the Hawking temperature); (4) that the Susskind-Horowitz-Polchinski string-theoretic understanding of black hole entropy as the logarithm of the degeneracy of a long string (which is the weak string coupling limit of a black hole) cannot be quite correct but should be replaced by a modified understanding according to which it is the entanglement entropy between a long string and its stringy atmosphere, when in a total pure equilibrium state in a suitable box, which (in line with (3)) goes over, at strong-coupling, to a black hole in equilibrium with its thermal atmosphere. The modified understanding in (4) is based on a general result, which I also describe, which concerns the likely state of a quantum system when it is weakly coupled to an energy-bath and the total state is a random pure state with a given energy. This result generalizes Goldstein et al.'s `canonical typicality' result to systems which are not necessarily small.

The Matter-Gravity Entanglement Hypothesis

Science.gov (United States)

Kay, Bernard S.

2018-03-01

I outline some of my work and results (some dating back to 1998, some more recent) on my matter-gravity entanglement hypothesis, according to which the entropy of a closed quantum gravitational system is equal to the system's matter-gravity entanglement entropy. The main arguments presented are: (1) that this hypothesis is capable of resolving what I call the second-law puzzle, i.e. the puzzle as to how the entropy increase of a closed system can be reconciled with the asssumption of unitary time-evolution; (2) that the black hole information loss puzzle may be regarded as a special case of this second law puzzle and that therefore the same resolution applies to it; (3) that the black hole thermal atmosphere puzzle (which I recall) can be resolved by adopting a radically different-from-usual description of quantum black hole equilibrium states, according to which they are total pure states, entangled between matter and gravity in such a way that the partial states of matter and gravity are each approximately thermal equilibrium states (at the Hawking temperature); (4) that the Susskind-Horowitz-Polchinski string-theoretic understanding of black hole entropy as the logarithm of the degeneracy of a long string (which is the weak string coupling limit of a black hole) cannot be quite correct but should be replaced by a modified understanding according to which it is the entanglement entropy between a long string and its stringy atmosphere, when in a total pure equilibrium state in a suitable box, which (in line with (3)) goes over, at strong-coupling, to a black hole in equilibrium with its thermal atmosphere. The modified understanding in (4) is based on a general result, which I also describe, which concerns the likely state of a quantum system when it is weakly coupled to an energy-bath and the total state is a random pure state with a given energy. This result generalizes Goldstein et al.'s `canonical typicality' result to systems which are not necessarily small.

Non-equilibrium entanglement in a driven many-body spin-boson model

Energy Technology Data Exchange (ETDEWEB)

Bastidas, Victor M; Reina, John H [Universidad del Valle, Departamento de Fisica, A. A. 25360, Cali (Colombia); Brandes, Tobias, E-mail: vicmabas@univalle.edu.c, E-mail: j.reina-estupinan@physics.ox.ac.u [Institut fuer Theoretische Physik, Technische Universitaet Berlin, Hardenbergstr. 36, 10623 Berlin (Germany)

2009-05-01

We study the entanglement dynamics in the externally-driven single-mode Dicke model in the thermodynamic limit, when the field is in resonance with the atoms. We compute the correlations in the atoms-field ground state by means of the density operator that represents the pure state of the universe and the reduced density operator for the atoms, which results from taking the partial trace over the field coordinates. As a measure of bipartite entanglement, we calculate the linear entropy, from which we analyze the entanglement dynamics. In particular, we found a strong relation between the stability of the dynamical parameters and the reported entanglement.

Finite-size scaling of the entanglement entropy of the quantum Ising chain with homogeneous, periodically modulated and random couplings

International Nuclear Information System (INIS)

Iglói, Ferenc; Lin, Yu-Cheng

2008-01-01

Using free-fermionic techniques we study the entanglement entropy of a block of contiguous spins in a large finite quantum Ising chain in a transverse field, with couplings of different types: homogeneous, periodically modulated and random. We carry out a systematic study of finite-size effects at the quantum critical point, and evaluate subleading corrections both for open and for periodic boundary conditions. For a block corresponding to a half of a finite chain, the position of the maximum of the entropy as a function of the control parameter (e.g. the transverse field) can define the effective critical point in the finite sample. On the basis of homogeneous chains, we demonstrate that the scaling behavior of the entropy near the quantum phase transition is in agreement with the universality hypothesis, and calculate the shift of the effective critical point, which has different scaling behaviors for open and for periodic boundary conditions

Gravity from entanglement and RG flow in a top-down approach

Science.gov (United States)

Kwon, O.-Kab; Jang, Dongmin; Kim, Yoonbai; Tolla, D. D.

2018-05-01

The duality between a d-dimensional conformal field theory with relevant deformation and a gravity theory on an asymptotically AdS d+1 geometry, has become a suitable tool in the investigation of the emergence of gravity from quantum entanglement in field theory. Recently, we have tested the duality between the mass-deformed ABJM theory and asymptotically AdS4 gravity theory, which is obtained from the KK reduction of the 11-dimensional supergravity on the LLM geometry. In this paper, we extend the KK reduction procedure beyond the linear order and establish non-trivial KK maps between 4-dimensional fields and 11-dimensional fluctuations. We rely on this gauge/gravity duality to calculate the entanglement entropy by using the Ryu-Takayanagi holographic formula and the path integral method developed by Faulkner. We show that the entanglement entropies obtained using these two methods agree when the asymptotically AdS4 metric satisfies the linearized Einstein equation with nonvanishing energy-momentum tensor for two scalar fields. These scalar fields encode the information of the relevant deformation of the ABJM theory. This confirms that the asymptotic limit of LLM geometry is the emergent gravity of the quantum entanglement in the mass-deformed ABJM theory with a small mass parameter. We also comment on the issue of the relative entropy and the Fisher information in our setup.

Quantum entanglement of localized excited states at finite temperature

Energy Technology Data Exchange (ETDEWEB)

Caputa, Paweł [Yukawa Institute for Theoretical Physics (YITP), Kyoto University,Kyoto 606-8502 (Japan); Nordita, KTH Royal Institute of Technology and Stockholm University,Roslagstullsbacken 23, SE-106 91 Stockholm (Sweden); Simón, Joan; Štikonas, Andrius [School of Mathematics and Maxwell Institute for Mathematical Sciences,University of Edinburgh,King’s Buildings, Edinburgh EH9 3FD (United Kingdom); Takayanagi, Tadashi [Yukawa Institute for Theoretical Physics (YITP), Kyoto University,Kyoto 606-8502 (Japan); Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU),University of Tokyo,Kashiwa, Chiba 277-8582 (Japan)

2015-01-20

In this work we study the time evolutions of (Renyi) entanglement entropy of locally excited states in two dimensional conformal field theories (CFTs) at finite temperature. We consider excited states created by acting with local operators on thermal states and give both field theoretic and holographic calculations. In free field CFTs, we find that the growth of Renyi entanglement entropy at finite temperature is reduced compared to the zero temperature result by a small quantity proportional to the width of the localized excitations. On the other hand, in finite temperature CFTs with classical gravity duals, we find that the entanglement entropy approaches a characteristic value at late time. This behaviour does not occur at zero temperature. We also study the mutual information between the two CFTs in the thermofield double (TFD) formulation and give physical interpretations of our results.

E6 and the bipartite entanglement of three qutrits

International Nuclear Information System (INIS)

Duff, M. J.; Ferrara, S.

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 superset of [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 superset of [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

Entangled de Sitter from stringy axionic Bell pair I. An analysis using Bunch-Davies vacuum

International Nuclear Information System (INIS)

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 Renyi 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. (orig.)

Entangled de Sitter from stringy axionic Bell pair I. An analysis using Bunch-Davies vacuum

Energy Technology Data Exchange (ETDEWEB)

Choudhury, Sayantan [Inter-University Centre for Astronomy and Astrophysics, Pune (India); Tata Institute of Fundamental Research, Department of Theoretical Physics, Mumbai (India); Panda, Sudhakar [Institute of Physics, Bhubaneswar, Odisha (India); National Institute of Science Education and Research, Bhubaneswar, Odisha (India); Homi Bhabha National Institute, Mumbai (India)

2018-01-15

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{sup 3}) and in the presence of an NS5 brane. For this computation, we consider a spherical surface S{sup 2}, which divides the spatial slice of de Sitter (dS{sub 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 Renyi 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. (orig.)

Entanglement dynamics following a sudden quench: An exact solution

Science.gov (United States)

Ghosh, Supriyo; Gupta, Kumar S.; Srivastava, Shashi C. L.

2017-12-01

We present an exact and fully analytical treatment of the entanglement dynamics for an isolated system of N coupled oscillators following a sudden quench of the system parameters. The system is analyzed using the solutions of the time-dependent Schrodinger's equation, which are obtained by solving the corresponding nonlinear Ermakov equations. The entanglement entropies exhibit a multi-oscillatory behaviour, where the number of dynamically generated time scales increases with N. The harmonic chains exhibit entanglement revival and for larger values of N (> 10), we find near-critical logarithmic scaling for the entanglement entropy, which is modulated by a time-dependent factor. The N = 2 case is equivalent to the two-site Bose-Hubbard model in the tunneling regime, which is amenable to empirical realization in cold-atom systems.

Entanglement evolution across a conformal interface

Science.gov (United States)

Wen, Xueda; Wang, Yuxuan; Ryu, Shinsei

2018-05-01

For two-dimensional conformal field theories (CFTs) in the ground state, it is known that a conformal interface along the entanglement cut can suppress the entanglement entropy from to , where L is the length of the subsystem A, and is the effective central charge which depends on the transmission property of the conformal interface. In this work, by making use of conformal mappings, we show that a conformal interface has the same effect on entanglement evolution in non-equilibrium cases, including global, local and certain inhomogeneous quantum quenches. I.e. a conformal interface suppresses the time evolution of entanglement entropy by effectively replacing the central charge c with , where is exactly the same as that in the ground state case. We confirm this conclusion by a numerical study on a critical fermion chain. Furthermore, based on the quasi-particle picture, we conjecture that this conclusion holds for an arbitrary quantum quench in CFTs, as long as the initial state can be described by a regularized conformal boundary state.

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.

On entanglement spreading in chaotic systems

Energy Technology Data Exchange (ETDEWEB)

Mezei, Márk [Princeton Center for Theoretical Science, Princeton University,Princeton, NJ 08544 (United States); Stanford, Douglas [Institute for Advanced Study,Princeton, NJ 08540 (United States)

2017-05-11

We discuss the time dependence of subsystem entropies in interacting quantum systems. As a model for the time dependence, we suggest that the entropy is as large as possible given two constraints: one follows from the existence of an emergent light cone, and the other is a conjecture associated to the “entanglement velocity” v{sub E}. We compare this model to new holographic and spin chain computations, and to an operator growth picture. Finally, we introduce a second way of computing the emergent light cone speed in holographic theories that provides a boundary dynamics explanation for a special case of entanglement wedge subregion duality in AdS/CFT.

Parametric Bayesian Estimation of Differential Entropy and Relative Entropy

Directory of Open Access Journals (Sweden)

Maya Gupta

2010-04-01

Full Text Available Given iid samples drawn from a distribution with known parametric form, we propose the minimization of expected Bregman divergence to form Bayesian estimates of differential entropy and relative entropy, and derive such estimators for the uniform, Gaussian, Wishart, and inverse Wishart distributions. Additionally, formulas are given for a log gamma Bregman divergence and the differential entropy and relative entropy for the Wishart and inverse Wishart. The results, as always with Bayesian estimates, depend on the accuracy of the prior parameters, but example simulations show that the performance can be substantially improved compared to maximum likelihood or state-of-the-art nonparametric estimators.

Linear entropy in quantum phase space

International Nuclear Information System (INIS)

Rosales-Zarate, Laura E. C.; Drummond, P. D.

2011-01-01

We calculate the quantum Renyi entropy in a phase-space representation for either fermions or bosons. This can also be used to calculate purity and fidelity, or the entanglement between two systems. We show that it is possible to calculate the entropy from sampled phase-space distributions in normally ordered representations, although this is not possible for all quantum states. We give an example of the use of this method in an exactly soluble thermal case. The quantum entropy cannot be calculated at all using sampling methods in classical symmetric (Wigner) or antinormally ordered (Husimi) phase spaces, due to inner-product divergences. The preferred method is to use generalized Gaussian phase-space methods, which utilize a distribution over stochastic Green's functions. We illustrate this approach by calculating the reduced entropy and entanglement of bosonic or fermionic modes coupled to a time-evolving, non-Markovian reservoir.

Linear entropy in quantum phase space

Energy Technology Data Exchange (ETDEWEB)

Rosales-Zarate, Laura E. C.; Drummond, P. D. [Centre for Atom Optics and Ultrafast Spectroscopy, Swinburne University of Technology, Melbourne 3122 (Australia)

2011-10-15

We calculate the quantum Renyi entropy in a phase-space representation for either fermions or bosons. This can also be used to calculate purity and fidelity, or the entanglement between two systems. We show that it is possible to calculate the entropy from sampled phase-space distributions in normally ordered representations, although this is not possible for all quantum states. We give an example of the use of this method in an exactly soluble thermal case. The quantum entropy cannot be calculated at all using sampling methods in classical symmetric (Wigner) or antinormally ordered (Husimi) phase spaces, due to inner-product divergences. The preferred method is to use generalized Gaussian phase-space methods, which utilize a distribution over stochastic Green's functions. We illustrate this approach by calculating the reduced entropy and entanglement of bosonic or fermionic modes coupled to a time-evolving, non-Markovian reservoir.

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.

Entanglement quantification by local unitary operations

International Nuclear Information System (INIS)

Monras, A.; Giampaolo, S. M.; Gualdi, G.; Illuminati, F.; Adesso, G.; Davies, G. B.

2011-01-01

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. 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.

Attack-Induced Entanglement of Noninteracting Fermi Gas

International Nuclear Information System (INIS)

Ren Jie; Zhu Shiqun

2008-01-01

The bipartite entanglement in Fermi gas without interaction is investigated when there are three fermions in the system. The negativity and the von Neumann entropy are employed to measure the entanglement of the system. The position of the third fermion can affect the entanglement between the first and the second fermions. The entanglement can be enhanced or suppressed when the third fermion changes its position. When the two fermions are at the same position or when their distance is more than 2.0/k F , the third fermion cannot affect them

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.

Quantum Entanglement Growth under Random Unitary Dynamics

Science.gov (United States)

Nahum, Adam; Ruhman, Jonathan; Vijay, Sagar; Haah, Jeongwan

2017-07-01

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.

Machine learning spatial geometry from entanglement features

Science.gov (United States)

You, Yi-Zhuang; Yang, Zhao; Qi, Xiao-Liang

2018-02-01

Motivated by the close relations of the renormalization group with both the holography duality and the deep learning, we propose that the holographic geometry can emerge from deep learning the entanglement feature of a quantum many-body state. We develop a concrete algorithm, call the entanglement feature learning (EFL), based on the random tensor network (RTN) model for the tensor network holography. We show that each RTN can be mapped to a Boltzmann machine, trained by the entanglement entropies over all subregions of a given quantum many-body state. The goal is to construct the optimal RTN that best reproduce the entanglement feature. The RTN geometry can then be interpreted as the emergent holographic geometry. We demonstrate the EFL algorithm on a 1D free fermion system and observe the emergence of the hyperbolic geometry (AdS3 spatial geometry) as we tune the fermion system towards the gapless critical point (CFT2 point).

The concept of entropy. Relation between action and entropy

Directory of Open Access Journals (Sweden)

J.-P.Badiali

2005-01-01

Full Text Available The Boltzmann expression for entropy represents the traditional link between thermodynamics and statistical mechanics. New theoretical developments like the Unruh effect or the black hole theory suggest a new definition of entropy. In this paper we consider the thermodynamics of black holes as seriously founded and we try to see what we can learn from it in the case of ordinary systems for which a pre-relativistic description is sufficient. We introduce a space-time model and a new definition of entropy considering the thermal equilibrium from a dynamic point of view. Then we show that for black hole and ordinary systems we have the same relation relating a change of entropy to a change of action.

Entanglement quantification by local unitary operations

Science.gov (United States)

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.

Universal parity effects in the entanglement entropy of XX chains with open boundary conditions

International Nuclear Information System (INIS)

Fagotti, Maurizio; Calabrese, Pasquale

2011-01-01

We consider the Rényi entanglement entropies in the one-dimensional XX spin-chains with open boundary conditions in the presence of a magnetic field. In the case of a semi-infinite system and a block starting from the boundary, we derive rigorously the asymptotic behavior for large block sizes on the basis of a recent mathematical theorem for the determinant of Toeplitz plus Hankel matrices. We conjecture a generalized Fisher–Hartwig form for the corrections to the asymptotic behavior of this determinant that allows the exact characterization of the corrections to the scaling at order o(l -1 ) for any n. By combining these results with conformal field theory arguments, we derive exact expressions also in finite chains with open boundary conditions and in the case when the block is detached from the boundary

Relation Entropy and Transferable Entropy Think of Aggregation on Group Decision Making

Institute of Scientific and Technical Information of China (English)

CHENG Qi-yue; QIU Wan-hua; LIU Xiao-feng

2002-01-01

In this paper, aggregation question based on group decision making and a single decision making is studied. The theory of entropy is applied to the sets pair analysis. The system of relation entropy and the transferable entropy notion are put. The character is studied. An potential by the relation entropy and transferable entropy are defined. It is the consistency measure on the group between a single decision making. We gained a new aggregation effective definition on the group misjudge.

Entropy, energy and negativity in Fermi-resonance coupled states of substituted methanes

International Nuclear Information System (INIS)

Hou Xiwen; Wan Mingfang; Ma Zhongqi

2010-01-01

Several measures of entanglement have attracted considerable interest in the relationship of a measure of entanglement with other quantities. The dynamics of entropy, energy and negativity is studied for Fermi-resonance coupled vibrations in substituted methanes with three kinds of initial mixed states, which are the mixed density matrices of binomial states, thermal states and squeezed states on two vibrational modes, respectively. It is demonstrated that for mixed binomial states and mixed thermal states with small magnitudes the entropies of the stretch and the bend are anti-correlated in the same oscillatory frequency, so do the energies for each kind of state with small magnitudes, whereas the entropies exhibit positive correlations with the corresponding energies. Furthermore, for small magnitudes quantum mutual entropy is positively correlated with the interacting energy. Analytic forms of entropies and energies are provided with initial conditions in which they are stationary, and the agreement between analytic and numerical simulations is satisfactory. The dynamical entanglement measured by negativity is examined for those states and conditions. It is shown that negativity displays a sudden death for mixed binomial states and mixed thermal states with small magnitudes, and the time-averaged negativity has the minimal value under the conditions of stationary entropies and energies. Moreover, negativity is positively correlated with the mutual entropy and the interacting energy just for mixed squeezed states with small magnitudes. Those are useful for molecular quantum information processing and dynamical entanglement.

Energy spectrum inverse problem of q-deformed harmonic oscillator and entanglement of composite bosons

Science.gov (United States)

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.

Strong subadditivity inequality for quantum entropies and four-particle entanglement

International Nuclear Information System (INIS)

Biswas, Asoka; Agarwal, G.S.

2003-01-01

The strong subadditivity inequality for a three-particle composite system is an important inequality in quantum information theory which can be studied via a four-particle entangled state. We use two three-level atoms in Λ configuration interacting with a two-mode cavity and the Raman adiabatic passage technique for the production of the four-particle entangled state. Using this four-particle entanglement, we study various aspects of the strong subadditivity inequality

Black hole thermodynamical entropy

International Nuclear Information System (INIS)

Tsallis, Constantino; Cirto, Leonardo J.L.

2013-01-01

As early as 1902, Gibbs pointed out that systems whose partition function diverges, e.g. gravitation, lie outside the validity of the Boltzmann-Gibbs (BG) theory. Consistently, since the pioneering Bekenstein-Hawking results, physically meaningful evidence (e.g., the holographic principle) has accumulated that the BG entropy S BG of a (3+1) black hole is proportional to its area L 2 (L being a characteristic linear length), and not to its volume L 3 . Similarly it exists the area law, so named because, for a wide class of strongly quantum-entangled d-dimensional systems, S BG is proportional to lnL if d=1, and to L d-1 if d>1, instead of being proportional to L d (d ≥ 1). These results violate the extensivity of the thermodynamical entropy of a d-dimensional system. This thermodynamical inconsistency disappears if we realize that the thermodynamical entropy of such nonstandard systems is not to be identified with the BG additive entropy but with appropriately generalized nonadditive entropies. Indeed, the celebrated usefulness of the BG entropy is founded on hypothesis such as relatively weak probabilistic correlations (and their connections to ergodicity, which by no means can be assumed as a general rule of nature). Here we introduce a generalized entropy which, for the Schwarzschild black hole and the area law, can solve the thermodynamic puzzle. (orig.)

Multipartite entangled states in particle mixing

International Nuclear Information System (INIS)

Blasone, M.; Dell'Anno, F.; De Siena, S.; Di Mauro, M.; Illuminati, F.

2008-01-01

In the physics of flavor mixing, the flavor states are given by superpositions of mass eigenstates. By using the occupation number to define a multiqubit space, the flavor states can be interpreted as multipartite mode-entangled states. By exploiting a suitable global measure of entanglement, based on the entropies related to all possible bipartitions of the system, we analyze the correlation properties of such states in the instances of three- and four-flavor mixing. Depending on the mixing parameters, and, in particular, on the values taken by the free phases, responsible for the CP-violation, entanglement concentrates in certain bipartitions. We quantify in detail the amount and the distribution of entanglement in the physically relevant cases of flavor mixing in quark and neutrino systems. By using the wave packet description for localized particles, we use the global measure of entanglement, suitably adapted for the instance of multipartite mixed states, to analyze the decoherence, induced by the free evolution dynamics, on the quantum correlations of stationary neutrino beams. We define a decoherence length as the distance associated with the vanishing of the coherent interference effects among massive neutrino states. We investigate the role of the CP-violating phase in the decoherence process.

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.

Accessibility of physical states and non-uniqueness of entanglement measure

International Nuclear Information System (INIS)

Morikoshi, Fumiaki; Santos, Marcelo Franca; Vedral, Vlatko

2004-01-01

Ordering physical states is the key to quantifying some physical property of the states uniquely. Bipartite pure entangled states are totally ordered under local operations and classical communication (LOCC) in the asymptotic limit and uniquely quantified by the well-known entropy of entanglement. However, we show that mixed entangled states are partially ordered under LOCC even in the asymptotic limit. Therefore, non-uniqueness of entanglement measure is understood on the basis of an operational notion of asymptotic convertibility

Entropy and wigner functions

Science.gov (United States)

Manfredi; Feix

2000-10-01

The properties of an alternative definition of quantum entropy, based on Wigner functions, are discussed. Such a definition emerges naturally from the Wigner representation of quantum mechanics, and can easily quantify the amount of entanglement of a quantum state. It is shown that smoothing of the Wigner function induces an increase in entropy. This fact is used to derive some simple rules to construct positive-definite probability distributions which are also admissible Wigner functions.

Entropy and Wigner Functions

OpenAIRE

Manfredi, G.; Feix, M. R.

2002-01-01

The properties of an alternative definition of quantum entropy, based on Wigner functions, are discussed. Such definition emerges naturally from the Wigner representation of quantum mechanics, and can easily quantify the amount of entanglement of a quantum state. It is shown that smoothing of the Wigner function induces an increase in entropy. This fact is used to derive some simple rules to construct positive definite probability distributions which are also admissible Wigner functions

Bound entangled states violate a nonsymmetric local uncertainty relation

International Nuclear Information System (INIS)

Hofmann, Holger F.

2003-01-01

As a consequence of having a positive partial transpose, bound entangled states lack many of the properties otherwise associated with entanglement. It is therefore interesting to identify properties that distinguish bound entangled states from separable states. In this paper, it is shown that some bound entangled states violate a nonsymmetric class of local uncertainty relations [H. F. Hofmann and S. Takeuchi, Phys. Rev. A 68, 032103 (2003)]. This result indicates that the asymmetry of nonclassical correlations may be a characteristic feature of bound entanglement

Correlation and Entanglement in Elliptically Deformed Two-Electron Quantum Dots

International Nuclear Information System (INIS)

Okopinska, A.; Koscik, P.

2011-01-01

We study quantum correlation in a two-dimensional system of two Coulombically interacting electrons trapped in an anisotropic harmonic potential in dependence on the interaction strength. The linear entropy and von Neumann entropy that measure the entanglement between the electrons are compared with the correlation energy and the statistical correlation coefficient. We observe that the entanglement properties are dramatically influenced by the anisotropy of the confining potential. We observe that the energetic and statistical correlations get stronger, whereas the entropic measures show weakening of the correlations with anisotropy. (author)

Single-copy entanglement in critical quantum spin chains

International Nuclear Information System (INIS)

Eisert, J.; Cramer, M.

2005-01-01

We consider the single-copy entanglement as a quantity to assess quantum correlations in the ground state in quantum many-body systems. We show for a large class of models that already on the level of single specimens of spin chains, criticality is accompanied with the possibility of distilling a maximally entangled state of arbitrary dimension from a sufficiently large block deterministically, with local operations and classical communication. These analytical results--which refine previous results on the divergence of block entropy as the rate at which maximally entangled pairs can be distilled from many identically prepared chains--are made quantitative for general isotropic translationally invariant spin chains that can be mapped onto a quasifree fermionic system, and for the anisotropic XY model. For the XX model, we provide the asymptotic scaling of ∼(1/6)log 2 (L), and contrast it with the block entropy

Entanglement-fidelity relations for inaccurate ancilla-driven quantum computation

International Nuclear Information System (INIS)

Morimae, Tomoyuki; Kahn, Jonas

2010-01-01

It was shown by T. Morimae [Phys. Rev. A 81, 060307(R) (2010)] that the gate fidelity of an inaccurate one-way quantum computation is upper bounded by a decreasing function of the amount of entanglement in the register. This means that a strong entanglement causes the low gate fidelity in the one-way quantum computation with inaccurate measurements. In this paper, we derive similar entanglement-fidelity relations for the inaccurate ancilla-driven quantum computation. These relations again imply that a strong entanglement in the register causes the low gate fidelity in the ancilla-driven quantum computation if the measurements on the ancilla are inaccurate.

Calculation of von Neumann entropy for hydrogen and positronium negative ions

International Nuclear Information System (INIS)

Lin, Chien-Hao; Ho, Yew Kam

2014-01-01

In the present work, we carry out calculations of von Neumann entropies and linear entropies for the hydrogen negative ion and the positronium negative ion. We concentrate on the spatial (electron–electron orbital) entanglement in these ions by using highly correlated Hylleraas functions to represent their ground states, and to take care of correlation effects. We apply the Schmidt decomposition method on the partial-wave expanded two-electron wave functions, and from which the one-particle reduced density matrix can be obtained, leading to the quantifications of linear entropy and von Neumann entropy in the H − and Ps − ions. - Highlights: • We calculate von Neumann entropies and linear entropies for hydrogen and positronium negative ions. • We employ highly correlated Hylleraas functions to take into account of correlation effects. • Spatial (electron–electron orbital) entanglement is quantified using the Schmidt decomposition method. • The eigenvalues of the one-particle reduced density matrix are calculated

Spin–spin entanglement in moving frames: Properties of negativity

Indian Academy of Sciences (India)

[8,9], cryptography [10,11], etc. In all such applications, generation and quantification of entanglement are of fundamental importance. To this end, quantification of entan- gled pure states (ensembles) is settled; for instance, through the von Neumann entropy. [12–16]. The von Neumann entropy has indeed the advantage of ...

Asymptotic convertibility of entanglement: An information-spectrum approach to entanglement concentration and dilution

Science.gov (United States)

Jiao, Yong; Wakakuwa, Eyuri; Ogawa, Tomohiro

2018-02-01

We consider asymptotic convertibility of an arbitrary sequence of bipartite pure states into another by local operations and classical communication (LOCC). We adopt an information-spectrum approach to address cases where each element of the sequences is not necessarily a tensor power of a bipartite pure state. We derive necessary and sufficient conditions for the LOCC convertibility of one sequence to another in terms of spectral entropy rates of entanglement of the sequences. Based on these results, we also provide simple proofs for previously known results on the optimal rates of entanglement concentration and dilution of general sequences of bipartite pure states.

More on the rainbow chain: entanglement, space-time geometry and thermal states

International Nuclear Information System (INIS)

Rodríguez-Laguna, Javier; Dubail, Jérôme; Ramírez, Giovanni; Calabrese, Pasquale; Sierra, Germán

2017-01-01

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 . (paper)

Entanglement in Quantum Field Theory: particle mixing and oscillations

International Nuclear Information System (INIS)

Blasone, M; Dell'Anno, F; De Siena, S; Illuminati, F

2013-01-01

The phenomena of particle mixing and flavor oscillations in elementary particle physics are associated with multi-mode entanglement of single-particle states. We show that, in the framework of quantum field theory, these phenomena exhibit a fine structure of quantum correlations, as multi-mode multi-particle entanglement appears. Indeed, the presence of anti-particles adds further degrees of freedom, thus providing nontrivial contributions both to flavor entanglement and, more generally, to multi-partite entanglement. By using the global entanglement measure, based on the linear entropies associated with all the possible bipartitions, we analyze the entanglement in the multiparticle states of two-flavor neutrinos and anti-neutrinos. A direct comparison with the instance of the quantum mechanical Pontecorvo single-particle states is also performed.

Error exponents for entanglement concentration

International Nuclear Information System (INIS)

Hayashi, Masahito; Koashi, Masato; Matsumoto, Keiji; Morikoshi, Fumiaki; Winter, Andreas

2003-01-01

Consider entanglement concentration schemes that convert n identical copies of a pure state into a maximally entangled state of a desired size with success probability being close to one in the asymptotic limit. We give the distillable entanglement, the number of Bell pairs distilled per copy, as a function of an error exponent, which represents the rate of decrease in failure probability as n tends to infinity. The formula fills the gap between the least upper bound of distillable entanglement in probabilistic concentration, which is the well-known entropy of entanglement, and the maximum attained in deterministic concentration. The method of types in information theory enables the detailed analysis of the distillable entanglement in terms of the error rate. In addition to the probabilistic argument, we consider another type of entanglement concentration scheme, where the initial state is deterministically transformed into a (possibly mixed) final state whose fidelity to a maximally entangled state of a desired size converges to one in the asymptotic limit. We show that the same formula as in the probabilistic argument is valid for the argument on fidelity by replacing the success probability with the fidelity. Furthermore, we also discuss entanglement yield when optimal success probability or optimal fidelity converges to zero in the asymptotic limit (strong converse), and give the explicit formulae for those cases

On unified-entropy characterization of quantum channels

International Nuclear Information System (INIS)

Rastegin, A E

2012-01-01

We consider properties of quantum channels with the use of unified entropies. Extremal unravelings of quantum channel with respect to these entropies are examined. The concept of map entropy is extended in terms of the unified entropies. The map (q, s)-entropy is naturally defined as the unified (q, s)-entropy of a rescaled dynamical matrix of given quantum channel. Inequalities of Fannes type are obtained for introduced entropies in terms of both the trace and Frobenius norms of difference between corresponding dynamical matrices. Additivity properties of introduced map entropies are discussed. The known inequality of Lindblad with the entropy exchange is generalized to many of the unified entropies. For the tensor product of a pair of quantum channels, we derive a two-sided estimate on the output entropy of a maximally entangled input state. (paper)

Charged Rényi entropies in CFTs with Einstein-Gauss-Bonnet holographic duals

Science.gov (United States)

Pastras, Georgios; Manolopoulos, Dimitrios

2014-11-01

We calculate the Rényi entropy S q ( μ, λ), for spherical entangling surfaces in CFT's with Einstein-Gauss-Bonnet-Maxwell holographic duals. Rényi entropies must obey some interesting inequalities by definition. However, for Gauss-Bonnet couplings λ, larger than specific value, but still allowed by causality, we observe a violation of the inequality , which is related to the existence of negative entropy black holes, providing interesting restrictions in the bulk theory. Moreover, we find an interesting distinction of the behaviour of the analytic continuation of S q ( μ, λ) for imaginary chemical potential, between negative and non-negative λ.

Entanglement of purification: from spin chains to holography

Science.gov (United States)

Nguyen, Phuc; Devakul, Trithep; Halbasch, Matthew G.; Zaletel, Michael P.; Swingle, Brian

2018-01-01

Purification is a powerful technique in quantum physics whereby a mixed quantum state is extended to a pure state on a larger system. This process is not unique, and in systems composed of many degrees of freedom, one natural purification is the one with minimal entanglement. Here we study the entropy of the minimally entangled purification, called the entanglement of purification, in three model systems: an Ising spin chain, conformal field theories holographically dual to Einstein gravity, and random stabilizer tensor networks. We conjecture values for the entanglement of purification in all these models, and we support our conjectures with a variety of numerical and analytical results. We find that such minimally entangled purifications have a number of applications, from enhancing entanglement-based tensor network methods for describing mixed states to elucidating novel aspects of the emergence of geometry from entanglement in the AdS/CFT correspondence.

Soft-Hair-Enhanced Entanglement Beyond Page Curves in a Black Hole Evaporation Qubit Model

Science.gov (United States)

Hotta, Masahiro; Nambu, Yasusada; Yamaguchi, Koji

2018-05-01

We propose a model with multiple qubits that reproduces the thermal properties of four-dimensional Schwarzschild black holes (BHs) by simultaneously taking account of the emission of Hawking particles and the zero-energy soft-hair evaporation at the horizon. The results verify that the entanglement entropy between a qubit and other subsystems, including emitted radiation, is much larger than the BH entropy analogue of the qubit, as opposed to the Page curve prediction. Our result suggests that early Hawking radiation is entangled with soft hair and that late Hawking radiation can be highly entangled with the degrees of freedom of a BH, avoiding the emergence of a firewall at the horizon.

Effect of atomic spontaneous decay on entanglement in the generalized Jaynes-Cummings model

International Nuclear Information System (INIS)

Hessian, H.A.; Obada, A.-S.F.; Mohamed, A.-B.A.

2010-01-01

Some aspects of the irreversible dynamics of a generalized Jaynes-Cummings model are addressed. By working in the dressed-state representation, it is possible to split the dynamics of the entanglement and coherence. The exact solution of the master equation in the case of a high-Q cavity with atomic decay is found. Effects of the atomic spontaneous decay on the temporal evolution of partial entropies of the atom or the field and the total entropy as a quantitative measure entanglement are elucidated. The degree of entanglement, through the sum of the negative eigenvalues of the partially transposed density matrix and the negative mutual information has been studied and compared with other measures.

Properties of von Neumann entropy

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 ...

Low Streamflow Forcasting using Minimum Relative Entropy

Science.gov (United States)

Cui, H.; Singh, V. P.

2013-12-01

Minimum relative entropy spectral analysis is derived in this study, and applied to forecast streamflow time series. Proposed method extends the autocorrelation in the manner that the relative entropy of underlying process is minimized so that time series data can be forecasted. Different prior estimation, such as uniform, exponential and Gaussian assumption, is taken to estimate the spectral density depending on the autocorrelation structure. Seasonal and nonseasonal low streamflow series obtained from Colorado River (Texas) under draught condition is successfully forecasted using proposed method. Minimum relative entropy determines spectral of low streamflow series with higher resolution than conventional method. Forecasted streamflow is compared to the prediction using Burg's maximum entropy spectral analysis (MESA) and Configurational entropy. The advantage and disadvantage of each method in forecasting low streamflow is discussed.

Holographic Rényi entropy in AdS3/LCFT2 correspondence

International Nuclear Information System (INIS)

Chen, Bin; Song, Feng-yan; Zhang, Jia-ju

2014-01-01

The recent study in AdS 3 /CFT 2 correspondence shows that the tree level contribution and 1-loop correction of holographic Rényi entanglement entropy (HRE) exactly match the direct CFT computation in the large central charge limit. This allows the Rényi entanglement entropy to be a new window to study the AdS/CFT correspondence. In this paper we generalize the study of Rényi entanglement entropy in pure AdS 3 gravity to the massive gravity theories at the critical points. For the cosmological topological massive gravity (CTMG), the dual conformal field theory (CFT) could be a chiral conformal field theory or a logarithmic conformal field theory (LCFT), depending on the asymptotic boundary conditions imposed. In both cases, by studying the short interval expansion of the Rényi entanglement entropy of two disjoint intervals with small cross ratio x, we find that the classical and 1-loop HRE are in exact match with the CFT results, up to order x 6 . To this order, the difference between the massless graviton and logarithmic mode can be seen clearly. Moreover, for the cosmological new massive gravity (CNMG) at critical point, which could be dual to a logarithmic CFT as well, we find the similar agreement in the CNMG/LCFT correspondence. Furthermore we read the 2-loop correction of graviton and logarithmic mode to HRE from CFT computation. It has distinct feature from the one in pure AdS 3 gravity

A universal feature of CFT Rényi entropy

Energy Technology Data Exchange (ETDEWEB)

Perlmutter, Eric [DAMTP, Centre for Mathematical Sciences, University of Cambridge,Cambridge, CB3 0WA (United Kingdom)

2014-03-26

We show that for a d-dimensional CFT in flat space, the Rényi entropy S{sub q} across a spherical entangling surface has the following property: in an expansion around q=1, the first correction to the entanglement entropy is proportional to C{sub T}, the coefficient of the stress tensor vacuum two-point function, with a fixed d-dependent coefficient. This is equivalent to a similar statement about the free energy of CFTs living on S{sup 1}×ℍ{sup d−1} with inverse temperature β=2πq. In addition to furnishing a direct argument applicable to all CFTs, we exhibit this result using a handful of gravity and field theory computations. Knowledge of C{sub T} thus doubles as knowledge of Rényi entropies in the neighborhood of q=1, which we use to establish new results in 3d vector models at large N.

Entropy function and universality of entropy-area relation for small black holes

International Nuclear Information System (INIS)

Cai Ronggen; Chen, C.-M.; Maeda, Kei-ichi; Ohta, Nobuyoshi; Pang Dawei

2008-01-01

We discuss the entropy-area relation for the small black holes with higher curvature corrections by using the entropy function formalism and field redefinition method. We show that the entropy S BH of the small black hole is proportional to its horizon area A. In particular, we find a universal result that S BH =A/2G, the ratio is 2 times of Bekenstein-Hawking entropy-area formula in many cases of physical interest. In four dimensions, the universal relation is always true irrespective of the coefficients of the higher-order terms if the dilaton couplings are the same, which is the case for string effective theory, while in five dimensions, the relation again holds irrespective of the overall coefficient if the higher-order corrections are in the GB combination. We also discuss how this result generalizes to known physically interesting cases with Lovelock correction terms in various dimensions, and possible implications of the universal relation.

Entanglement dynamics of J-aggregate systems

Energy Technology Data Exchange (ETDEWEB)

Thilagam, A, E-mail: Thilagam.Lohe@unisa.edu.au [Information Technology, Engineering and the Environment, Mawson Institute, University of South Australia, South Australia 5095 (Australia)

2011-04-01

The entanglement dynamics of one-dimensional J-aggregate systems are examined using entanglement measures such as the von Neumann entropy and Wootters concurrence. The effect of dispersion and resonance terms associated with the exciton-phonon interaction are analyzed using Green's function formalism. A probability propagator term, derived using the Markovian approximation, presents J-aggregate systems as potential channels for large scale energy propagation for a select range of parameters. We highlight the role of a critical number of coherently coupled monomer sites and two-exciton states in determining superradiance in J-aggregate systems.

Quantum entanglement and a metaphysics of relations

Science.gov (United States)

Esfeld, Michael

This paper argues for a metaphysics of relations based on a characterization of quantum entanglement in terms of non-separability, thereby regarding entanglement as a sort of holism. By contrast to a radical metaphysics of relations, the position set out in this paper recognizes things that stand in the relations, but claims that, as far as the relations are concerned, there is no need for these things to have qualitative intrinsic properties underlying the relations. This position thus opposes a metaphysics of individual things that are characterized by intrinsic properties. A principal problem of the latter position is that it seems that we cannot gain any knowledge of these properties insofar as they are intrinsic. Against this background, the rationale behind a metaphysics of relations is to avoid a gap between epistemology and metaphysics.

Black hole entropy in the O(N) model

International Nuclear Information System (INIS)

Kabat, D.; Shenker, S.H.; Strassler, M.J.

1995-01-01

We consider corrections to the entropy of a black hole from an O(N)-invariant linear σ model. We obtain the entropy from a 1/N expansion of the partition function on a cone. The entropy arises from diagrams which are analogous to those introduced by Susskind and Uglum to explain black hole entropy in string theory. The interpretation of the σ-model entropy depends on scale. At short distances, it has a state counting interpretation, as the entropy of entanglement of the N fields φ a . In the infrared, the effective theory has a single composite field σ∼φ a φ a , and the state counting interpretation of the entropy is lost. copyright 1995 The American Physical Society

Entanglement detection via tighter local uncertainty relations

International Nuclear Information System (INIS)

Zhang Chengjie; Zhang Yongsheng; Guo Guangcan; Nha, Hyunchul

2010-01-01

We propose an entanglement criterion based on local uncertainty relations (LURs) in a stronger form than the original LUR criterion introduced by Hofmann and Takeuchi [H. F. Hofmann and S. Takeuchi, Phys. Rev. A 68, 032103 (2003)]. Using arbitrarily chosen operators (A k ) and (B k ) of subsystems A and B, the tighter LUR criterion, which may be used not only for discrete variables but also for continuous variables, can detect more entangled states than the original criterion.

New constraints for holographic entropy from maximin: A no-go theorem

Science.gov (United States)

Rota, Massimiliano; Weinberg, Sean J.

2018-04-01

The Ryu-Takayanagi (RT) formula for static spacetimes arising in the AdS/CFT correspondence satisfies inequalities that are not yet proven in the case of the Rangamani-Hubeny-Takayanagi (HRT) formula, which applies to general dynamical spacetimes. Wall's maximin construction is the only known technique for extending inequalities of holographic entanglement entropy from the static to dynamical case. We show that this method currently has no further utility when dealing with inequalities for five or fewer regions. Despite this negative result, we propose the validity of one new inequality for covariant holographic entanglement entropy for five regions. This inequality, while not maximin provable, is much weaker than many of the inequalities satisfied by the RT formula and should therefore be easier to prove. If it is valid, then there is strong evidence that holographic entanglement entropy plays a role in general spacetimes including those that arise in cosmology. Our new inequality is obtained by the assumption that the HRT formula satisfies every known balanced inequality obeyed by the Shannon entropies of classical probability distributions. This is a property that the RT formula has been shown to possess and which has been previously conjectured to hold for quantum mechanics in general.

Entanglement contour perspective for "strong area-law violation" in a disordered long-range hopping model

Science.gov (United States)

Roy, Nilanjan; Sharma, Auditya

2018-03-01

We numerically investigate the link between the delocalization-localization transition and entanglement in a disordered long-range hopping model of spinless fermions by studying various static and dynamical quantities. This includes the inverse participation ratio, level statistics, entanglement entropy, and number fluctuations in the subsystem along with quench and wave-packet dynamics. Finite systems show delocalized, quasilocalized, and localized phases. The delocalized phase shows strong area-law violation, whereas the (quasi)localized phase adheres to (for large subsystems) the strict area law. The idea of "entanglement contour" nicely explains the violation of area law and its relationship with "fluctuation contour" reveals a signature at the transition point. The relationship between entanglement entropy and number fluctuations in the subsystem also carries signatures for the transition in the model. Results from the Aubry-Andre-Harper model are compared in this context. The propagation of charge and entanglement are contrasted by studying quench and wave-packet dynamics at the single-particle and many-particle levels.

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 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.

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 Capacity of Two-Qubit Unitary Operator with the Help of Auxiliary System

International Nuclear Information System (INIS)

Hu Baolin; Di Yaomin

2007-01-01

The entanglement capacity of general two-qubit unitary operators is studied when auxiliary systems are allowed, and the analytical results based on linear entropy when input states are disentangled are given. From the results the condition for perfect entangler, α 1 = α 2 = π/4, is obtained. Contrary to the case without auxiliary system, the parameter α 3 may play active role to the entanglement capacity when auxiliary systems are allowed.

The relative entropy in the quantum mechanics

International Nuclear Information System (INIS)

Lecomte Montes, A.

1983-06-01

Relative Entropy is a generalization of entropy which substitutes the Liouville measure from classical mechanics or the trace from quantum mechanics by an arbitrary state. There are many different defintions of it in quantum mechanics because the algebra of observables is not commutative. In this work, three known defintions of the quantum relative entropy are studied and compared but specifically their common properties are presented. The best known defintion was proposed many years ago by Umegaki and later on by Lindblad. This defintion can be realized through a functional calculus for quadratic forms introduced by Pusz and Woronowicz, for two arbitrary states on a Csup(*)-algebra. The two other definitions investigated are the Naudt's entropy and the inference function of Marchand and Wyss. The first one can be expressed through the functional calculus too, it has then almost the same properties as the Umegaki-Lindblad defintion. The inference function can be considered only as some kind of 1/2-relative entropy. The function is nevertheless very important because it can be expressed as the logarithm of the transition probability between the basis state and the actual state. A general theory which includes the three defintions is not found yet, but it is shown that the functional calculus provides a great family of relative entropies. This is important for a unified theory of all defintions and their properties. (Author)

Entanglement witness via quantum-memory-assisted entropic uncertainty relation

Science.gov (United States)

Shi, Jiadong; Ding, Zhiyong; Wu, Tao; He, Juan; Yu, Lizhi; Sun, Wenyang; Wang, Dong; Ye, Liu

2017-12-01

By virtue of the quantum-memory-assisted entropic uncertainty relation (EUR), we analyze entanglement witness via the efficiencies of the estimates proposed by Berta (2010 Nat. Phys. 6 659) and Pati (2012 Phys. Rev. A 86 042105). The results show that, without a structured reservoir, the entanglement regions witnessed by these EUR estimates are only determined by the chosen estimated setup, and have no correlation with the explicit form of the initial state. On the other hand, with the structured reservoirs, the time regions during which the entanglement can be witnessed, and the corresponding entanglement regions closely depend on the choice of the estimated setup, the initial state and the state purity p . Concretely, for a pure state with p=1 , the entanglement can be witnessed by both estimates, while for mixed states with p=0.78 , it can only be witnessed using the Pati estimate. What is more, we find that the time regions incorporating the Pati estimate become discontinuous for the initial state with ≤ft| {{φ }\\prime } \\right> ={≤ft(≤ft| 01 \\right> +≤ft| 10 \\right> \\right)}/{\\sqrt{2}} , and the corresponding entanglement regions remain the same; however the entanglement can only be witnessed once by utilizing the Berta estimate.

Operational classification and quantification of multipartite entangled states

International Nuclear Information System (INIS)

Rigolin, Gustavo; Oliveira, Thiago R. de; Oliveira, Marcos C. de

2006-01-01

We formalize and extend an operational multipartite entanglement measure introduced by T. R. Oliveira, G. Rigolin, and M. C. de Oliveira, Phys. Rev. A 73, 010305(R) (2006), through the generalization of global entanglement (GE) [D. A. Meyer and N. R. Wallach, J. Math. Phys. 43, 4273 (2002)]. Contrarily to GE the main feature of this measure lies in the fact that we study the mean linear entropy of all possible partitions of a multipartite system. This allows the construction of an operational multipartite entanglement measure which is able to distinguish among different multipartite entangled states that GE failed to discriminate. Furthermore, it is also maximum at the critical point of the Ising chain in a transverse magnetic field, being thus able to detect a quantum phase transition

Anderson localization and momentum-space entanglement

International Nuclear Information System (INIS)

Andrade, Eric C; Steudtner, Mark; Vojta, Matthias

2014-01-01

We consider Anderson localization and the associated metal–insulator transition for non-interacting fermions in D = 1, 2 space dimensions in the presence of spatially correlated on-site random potentials. To assess the nature of the wave function, we follow a recent proposal to study momentum-space entanglement. For a D = 1 model with long-range disorder correlations, both the entanglement spectrum and the entanglement entropy allow us to clearly distinguish between extended and localized states based upon a single realization of disorder. However, for other models, including the D = 2 case with long-range correlated disorder, we find that the method is not similarly successful. We analyze the reasons for its failure, concluding that the much desired generalization to higher dimensions may be problematic. (paper)

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

Quantum entanglement: theory and applications

International Nuclear Information System (INIS)

Schuch, N.

2007-01-01

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

Constant conditional entropy and related hypotheses

International Nuclear Information System (INIS)

Ferrer-i-Cancho, Ramon; Dębowski, Łukasz; Moscoso del Prado Martín, Fermín

2013-01-01

Constant entropy rate (conditional entropies must remain constant as the sequence length increases) and uniform information density (conditional probabilities must remain constant as the sequence length increases) are two information theoretic principles that are argued to underlie a wide range of linguistic phenomena. Here we revise the predictions of these principles in the light of Hilberg’s law on the scaling of conditional entropy in language and related laws. We show that constant entropy rate (CER) and two interpretations for uniform information density (UID), full UID and strong UID, are inconsistent with these laws. Strong UID implies CER but the reverse is not true. Full UID, a particular case of UID, leads to costly uncorrelated sequences that are totally unrealistic. We conclude that CER and its particular cases are incomplete hypotheses about the scaling of conditional entropies. (letter)

Holographic Rényi entropy in AdS{sub 3}/LCFT{sub 2} correspondence

Energy Technology Data Exchange (ETDEWEB)

Chen, Bin [Department of Physics and State Key Laboratory of Nuclear Physics and Technology,Peking University, 5 Yiheyuan Rd, 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,105 W 3rd Ring Rd N, Beijing 100048 (China); Song, Feng-yan; Zhang, Jia-ju [Department of Physics and State Key Laboratory of Nuclear Physics and Technology,Peking University, 5 Yiheyuan Rd, Beijing 100871 (China)

2014-03-31

The recent study in AdS{sub 3}/CFT{sub 2} correspondence shows that the tree level contribution and 1-loop correction of holographic Rényi entanglement entropy (HRE) exactly match the direct CFT computation in the large central charge limit. This allows the Rényi entanglement entropy to be a new window to study the AdS/CFT correspondence. In this paper we generalize the study of Rényi entanglement entropy in pure AdS{sub 3} gravity to the massive gravity theories at the critical points. For the cosmological topological massive gravity (CTMG), the dual conformal field theory (CFT) could be a chiral conformal field theory or a logarithmic conformal field theory (LCFT), depending on the asymptotic boundary conditions imposed. In both cases, by studying the short interval expansion of the Rényi entanglement entropy of two disjoint intervals with small cross ratio x, we find that the classical and 1-loop HRE are in exact match with the CFT results, up to order x{sup 6}. To this order, the difference between the massless graviton and logarithmic mode can be seen clearly. Moreover, for the cosmological new massive gravity (CNMG) at critical point, which could be dual to a logarithmic CFT as well, we find the similar agreement in the CNMG/LCFT correspondence. Furthermore we read the 2-loop correction of graviton and logarithmic mode to HRE from CFT computation. It has distinct feature from the one in pure AdS{sub 3} gravity.

Holographic entanglement for Chern-Simons terms

International Nuclear Information System (INIS)

Azeyanagi, Tatsuo; Loganayagam, R.; Ng, Gim Seng

2017-01-01

We derive the holographic entanglement entropy contribution from pure and mixed gravitational Chern-Simons(CS) terms in AdS 2k+1 . This is done through two different methods: first, by a direct evaluation of CS action in a holographic replica geometry and second by a descent of Dong’s derivation applied to the corresponding anomaly polynomial. In lower dimensions (k=1,2), the formula coincides with the Tachikawa formula for black hole entropy from gravitational CS terms. New extrinsic curvature corrections appear for k≥3: we give explicit and concise expressions for the two pure gravitational CS terms in AdS 7 and present various consistency checks, including agreements with the black hole entropy formula when evaluated at the bifurcation surface.

Holographic entanglement for Chern-Simons terms

Energy Technology Data Exchange (ETDEWEB)

Azeyanagi, Tatsuo [Département de Physique, Ecole Normale Supérieure, CNRS,24 rue Lhomond, 75005 Paris (France); Loganayagam, R. [School of Natural Sciences, Institute for Advanced Study,Princeton, NJ 08540 (United States); Ng, Gim Seng [Department of Physics, McGill University,Montréal, QC H3A 2T8 (Canada)

2017-02-01

We derive the holographic entanglement entropy contribution from pure and mixed gravitational Chern-Simons(CS) terms in AdS{sub 2k+1}. This is done through two different methods: first, by a direct evaluation of CS action in a holographic replica geometry and second by a descent of Dong’s derivation applied to the corresponding anomaly polynomial. In lower dimensions (k=1,2), the formula coincides with the Tachikawa formula for black hole entropy from gravitational CS terms. New extrinsic curvature corrections appear for k≥3: we give explicit and concise expressions for the two pure gravitational CS terms in AdS{sub 7} and present various consistency checks, including agreements with the black hole entropy formula when evaluated at the bifurcation surface.

Holographic entanglement for Chern-Simons terms

Science.gov (United States)

Azeyanagi, Tatsuo; Loganayagam, R.; Ng, Gim Seng

2017-02-01

We derive the holographic entanglement entropy contribution from pure and mixed gravitational Chern-Simons(CS) terms in AdS2 k+1. This is done through two different methods: first, by a direct evaluation of CS action in a holographic replica geometry and second by a descent of Dong's derivation applied to the corresponding anomaly polynomial. In lower dimensions ( k = 1 , 2), the formula coincides with the Tachikawa formula for black hole entropy from gravitational CS terms. New extrinsic curvature corrections appear for k ≥ 3: we give explicit and concise expressions for the two pure gravitational CS terms in AdS7 and present various consistency checks, including agreements with the black hole entropy formula when evaluated at the bifurcation surface.

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.

Damped driven coupled oscillators: entanglement, decoherence and the classical limit

International Nuclear Information System (INIS)

Mancilla, R D Guerrero; Rey-Gonzalez, R R; Fonseca-Romero, K M

2009-01-01

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

Decoherence, entanglement, and chaos in the Dicke model

International Nuclear Information System (INIS)

Hou Xiwen; Hu Bambi

2004-01-01

The dynamical properties of quantum entanglement in the Dicke model without rotating-wave approximation are investigated in terms of the reduced-density linear entropy. The characteristic time of decoherence process in the early-time evolution is numerically obtained and it is shown that the characteristic time decreases as the coupling parameter increases. The mean entanglement, which is defined to be averaged over time, is employed to describe the influences of both quantum phase transition and corresponding classical chaos on the behavior of entanglement. For a given energy, initial conditions are taken to be minimum uncertainty wave packets centered at regular and chaotic regions of the classical phase space. It is shown that the entanglement has a distinct change at the quantum phase transition, and that the entanglement for regular initial conditions is smaller than that for chaotic ones in the case of weak coupling, while it fluctuates with small amplitude in strong coupling and for chaotic initial conditions

Bulk entanglement gravity without a boundary: Towards finding Einstein's equation in Hilbert space

Science.gov (United States)

Cao, ChunJun; Carroll, Sean M.

2018-04-01

We consider the emergence from quantum entanglement of spacetime geometry in a bulk region. For certain classes of quantum states in an appropriately factorized Hilbert space, a spatial geometry can be defined by associating areas along codimension-one surfaces with the entanglement entropy between either side. We show how radon transforms can be used to convert these data into a spatial metric. Under a particular set of assumptions, the time evolution of such a state traces out a four-dimensional spacetime geometry, and we argue using a modified version of Jacobson's "entanglement equilibrium" that the geometry should obey Einstein's equation in the weak-field limit. We also discuss how entanglement equilibrium is related to a generalization of the Ryu-Takayanagi formula in more general settings, and how quantum error correction can help specify the emergence map between the full quantum-gravity Hilbert space and the semiclassical limit of quantum fields propagating on a classical spacetime.

Perturbative entanglement thermodynamics for AdS spacetime: renormalization

International Nuclear Information System (INIS)

Mishra, Rohit; Singh, Harvendra

2015-01-01

We study the effect of charged excitations in the AdS spacetime on the first law of entanglement thermodynamics. It is found that ‘boosted’ AdS black holes give rise to a more general form of first law which includes chemical potential and charge density. To obtain this result we have to resort to a second order perturbative calculation of entanglement entropy for small size subsystems. At first order the form of entanglement law remains unchanged even in the presence of charged excitations. But the thermodynamic quantities have to be appropriately ‘renormalized’ at the second order due to the corrections. We work in the perturbative regime where T thermal ≪T E .

Quantum entanglement and thermal reduced density matrices in fermion and spin systems on ladders

International Nuclear Information System (INIS)

Chen, Xiao; Fradkin, Eduardo

2013-01-01

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. (paper)

On entanglement spreading from holography

Energy Technology Data Exchange (ETDEWEB)

Mezei, Márk [Princeton Center for Theoretical Science, Princeton University,Princeton, NJ 08544 (United States)

2017-05-11

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: We prove holographic bounds on the entanglement velocity v{sub E} and the butterfly effect speed v{sub B} that arises in the study of chaos. We obtain the EE as a function of time for large spherical entangling surfaces analytically. We show that the EE is insensitive to the details of the initial state or quench protocol. In a thermofield double state we determine analytically the two-sided mutual information between two large concentric spheres separated in time. We derive a bound on the rate of growth of EE for arbitrary shapes, and develop an expansion for EE at early times. In a companion paper https://arxiv.org/abs/1608.05101, these results are put in the broader context of EE growth in chaotic systems: we relate EE growth to the chaotic spreading of operators, derive bounds on EE at a given time, and compare the holographic results to spin chain numerics and toy models. In this paper, we perform holographic calculations that provide the basis of arguments presented in that paper. We prove holographic bounds on the entanglement velocity v{sub E} and the butterfly effect speed v{sub B} that arises in the study of chaos. We obtain the EE as a function of time for large spherical entangling surfaces analytically. We show that the EE is insensitive to the details of the initial state or quench protocol. In a thermofield double state we determine analytically the two-sided mutual information between two large concentric spheres separated in time. We derive a bound on the rate of growth of EE for arbitrary shapes, and develop an expansion for EE at early times.

Escort entropies and divergences and related canonical distribution

International Nuclear Information System (INIS)

Bercher, J.-F.

2011-01-01

We discuss two families of two-parameter entropies and divergences, derived from the standard Renyi and Tsallis entropies and divergences. These divergences and entropies are found as divergences or entropies of escort distributions. Exploiting the nonnegativity of the divergences, we derive the expression of the canonical distribution associated to the new entropies and a observable given as an escort-mean value. We show that this canonical distribution extends, and smoothly connects, the results obtained in nonextensive thermodynamics for the standard and generalized mean value constraints. -- Highlights: → Two-parameter entropies are derived from q-entropies and escort distributions. → The related canonical distribution is derived. → This connects and extends known results in nonextensive statistics.

Optimal control of orientation and entanglement for two dipole-dipole coupled quantum planar rotors.

Science.gov (United States)

Yu, Hongling; Ho, Tak-San; Rabitz, Herschel

2018-05-09

Optimal control simulations are performed for orientation and entanglement of two dipole-dipole coupled identical quantum rotors. The rotors at various fixed separations lie on a model non-interacting plane with an applied control field. It is shown that optimal control of orientation or entanglement represents two contrasting control scenarios. In particular, the maximally oriented state (MOS) of the two rotors has a zero entanglement entropy and is readily attainable at all rotor separations. Whereas, the contrasting maximally entangled state (MES) has a zero orientation expectation value and is most conveniently attainable at small separations where the dipole-dipole coupling is strong. It is demonstrated that the peak orientation expectation value attained by the MOS at large separations exhibits a long time revival pattern due to the small energy splittings arising form the extremely weak dipole-dipole coupling between the degenerate product states of the two free rotors. Moreover, it is found that the peak entanglement entropy value attained by the MES remains largely unchanged as the two rotors are transported to large separations after turning off the control field. Finally, optimal control simulations of transition dynamics between the MOS and the MES reveal the intricate interplay between orientation and entanglement.

Entropy of entangled states and SU(1,1) and SU(2) symmetries

International Nuclear Information System (INIS)

Santana, A.E.; Khanna, F.C.; Revzen, M.

2002-01-01

Based on a recent definition of a measure for entanglement [Plenio and Vedral, Contemp. Phys. 39, 431 (1998)], examples of maximum entangled states are presented. The construction of such states, which have symmetry SU(1,1) and SU(2), follows the guidance of thermofield dynamics formalism

Higher-curvature corrections to holographic entanglement with momentum dissipation

Energy Technology Data Exchange (ETDEWEB)

Tanhayi, M.R. [Islamic Azad University Central Tehran Branch (IAUCTB), Department of Physics, Faculty of Basic Science, Tehran (Iran, Islamic Republic of); Institute for Research in Fundamental Sciences (IPM), School of Physics, Tehran (Iran, Islamic Republic of); Vazirian, R. [Islamic Azad University Central Tehran Branch (IAUCTB), Department of Physics, Faculty of Basic Science, Tehran (Iran, Islamic Republic of)

2018-02-15

We study the effects of Gauss-Bonnet corrections on some nonlocal probes (entanglement entropy, n-partite information and Wilson loop) in the holographic model with momentum relaxation. Higher-curvature terms as well as scalar fields make in fact nontrivial corrections to the coefficient of the universal term in entanglement entropy. We use holographic methods to study such corrections. Moreover, holographic calculation indicates that mutual and tripartite information undergo a transition beyond which they identically change their values. We find that the behavior of the transition curves depends on the sign of the Gauss-Bonnet coupling λ. The transition for λ > 0 takes place in larger separation of subsystems than that of λ < 0. Finally, we examine the behavior of modified part of the force between external point-like objects as a function of Gauss-Bonnet coupling and its sign. (orig.)

Entropy and Quantum Gravity

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.

Relative entropy of steering: on its definition and properties

International Nuclear Information System (INIS)

Kaur, Eneet; Wilde, Mark M

2017-01-01

In Gallego and Aolita (2015 Phys. Rev . X 5 041008), the authors proposed a definition for the relative entropy of steering and showed that the resulting quantity is a convex steering monotone. Here we advocate for a different definition for relative entropy of steering, based on well grounded concerns coming from quantum Shannon theory. We prove that this modified relative entropy of steering is a convex steering monotone. Furthermore, we establish that it is uniformly continuous and faithful, in both cases giving quantitative bounds that should be useful in applications. We also consider a restricted relative entropy of steering which is relevant for the case in which the free operations in the resource theory of steering have a more restricted form (the restricted operations could be more relevant in practical scenarios). The restricted relative entropy of steering is convex, monotone with respect to these restricted operations, uniformly continuous, and faithful. (paper)

Supersymmetric Rényi entropy and Anomalies in 6d (1,0) SCFTs

Energy Technology Data Exchange (ETDEWEB)

Yankielowicz, Shimon; Zhou, Yang [School of Physics and Astronomy, Tel-Aviv University,Ramat-Aviv 69978 (Israel)

2017-04-21

A closed formula of the universal part of supersymmetric Rényi entropy S{sub q} for six-dimensional (1,0) superconformal theories is proposed. Within our arguments, S{sub q} across a spherical entangling surface is a cubic polynomial of ν=1/q, with 4 coefficients expressed as linear combinations of the ’t Hooft anomaly coefficients for the R-symmetry and gravitational anomalies. As an application, we establish linear relations between the c-type Weyl anomalies and the ’t Hooft anomaly coefficients. We make a conjecture relating the supersymmetric Rényi entropy to an equivariant integral of the anomaly polynomial in even dimensions and check it against known data in 4d and 6d.

Properties of Linear Entropy in k-Photon Jaynes-Cummings Model with Stark Shift and Kerr-Like Medium

International Nuclear Information System (INIS)

Liao Qinghong; Wang Yueyuan; Liu Shutian; Ahmad, Muhammad Ashfaq

2010-01-01

The time evolution of the linear entropy of an atom in k-photon Jaynes-Cummings model is investigated taking into consideration Stark shift and Kerr-like medium. The effect of both the Stark shift and Kerr-like medium on the linear entropy is analyzed using a numerical technique for the field initially in coherent state and in even coherent state. The results show that the presence of the Kerr-like medium and Stark shift has an important effect on the properties of the entropy and entanglement. It is also shown that the setting of the initial state plays a significant role in the evolution of the linear entropy and entanglement. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

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.

Correlation properties of entangled multiphoton states and Bernstein’s paradox

International Nuclear Information System (INIS)

Chirkin, A. S.; Belyaeva, O. V.; Belinsky, A. V.

2013-01-01

A normally ordered characteristic function (NOCF) of Bose operators is calculated for a number of discrete-variable entangled states (Greenberger-Horne-Zeilinger (GHZ) and Werner (W) qubit states and a cluster state). It is shown that such NOCFs contain visual information on two types of correlations: pseudoclassical and quantum correlations. The latter manifest themselves in the interference terms of the NOCFs and lead to quantum paradoxes, whereas the pseudoclassical correlations of photons and their cumulants satisfy the relations for classical random variables. Three- and four-qubit states are analyzed in detail. An implementation of an analog of Bernstein’s paradox on discrete quantum variables is discussed. A measure of quantumness of an entangled state is introduced that is not related to the entropy approach. It is established that the maximum of the degree of quantumness substantiates the numerical values of the coefficients in multiqubit vector states derived from intuitive considerations.

Universal corrections to scaling for block entanglement in spin-1/2 XX chains

International Nuclear Information System (INIS)

Calabrese, Pasquale; Essler, Fabian H L

2010-01-01

We consider the Rényi entropies S n (l) in the one-dimensional spin-1/2 Heisenberg XX chain in a magnetic field. The case n = 1 corresponds to the von Neumann 'entanglement' entropy. Using a combination of methods based on the generalized Fisher–Hartwig conjecture and a recurrence relation connected to the Painlevé VI differential equation we obtain the asymptotic behaviour, accurate to order O(l -3 ), of the Rényi entropies S n (l) for large block lengths l. For n = 1, 2, 3, 10 this constitutes the 3, 6, 10, 48 leading terms respectively. The o(1) contributions are found to exhibit a rich structure of oscillatory behaviour, which we analyse in some detail both for finite n and in the limit n→∞

Entanglement of two blocks of spins in the critical Ising model

Science.gov (United States)

Facchi, P.; Florio, G.; Invernizzi, C.; Pascazio, S.

2008-11-01

We compute the entropy of entanglement of two blocks of L spins at a distance d in the ground state of an Ising chain in an external transverse magnetic field. We numerically study the von Neumann entropy for different values of the transverse field. At the critical point we obtain analytical results for blocks of size L=1 and 2. In the general case, the critical entropy is shown to be additive when d→∞ . Finally, based on simple arguments, we derive an expression for the entropy at the critical point as a function of both L and d . This formula is in excellent agreement with numerical results.

Von Neumann Entropy of an Electron in One-Dimensional Determined Potentials

Institute of Scientific and Technical Information of China (English)

GONG Long-Yan; TONG Pei-Qing

2005-01-01

@@ By using the measure of von Neumann entropy, we numerically investigate quantum entanglement of an electronmoving in the one-dimensional Harper model and in the one-dimensional slowly varying potential model. Thedelocalized and localized eigenstates can be distinguished by von Neumann entropy of the individual eigenstates.There are drastic decreases in yon Neumann entropy of the individual eigenstates at mobility edges. In the curveof the spectrum averaged yon Neumann entropy as a function of potential parameter λ, a sharp transition existsat the metal-insulator transition point λc = 2. It is found that the yon Neumann entropy is a good quantity toreflect localization and metal-insulator transition.

Quantum entanglement in inhomogeneous 1D systems

Science.gov (United States)

Ramírez, Giovanni

2018-04-01

The entanglement entropy of the ground state of a quantum lattice model with local interactions usually satisfies an area law. However, in 1D systems some violations may appear in inhomogeneous systems or in random systems. In our inhomogeneous system, the inhomogeneity parameter, h, allows us to tune different regimes where a volumetric violation of the area law appears. We apply the strong disorder renormalization group to describe the maximally entangled state of the system in a strong inhomogeneity regime. Moreover, in a weak inhomogeneity regime, we use a continuum approximation to describe the state as a thermo-field double in a conformal field theory with an effective temperature which is proportional to the inhomogeneity parameter of the system. The latter description also shows 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 = h2, providing another example of the relation between quantum entanglement and space-time geometry. The results we discuss here were already published before, but here we present a more didactic exposure of basic concepts of the rainbow system for the students attending the Latin American School of Physics "Marcos Moshinsky" 2017.

Generalizing entanglement

Science.gov (United States)

Jia, Ding

2017-12-01

The expected indefinite causal structure in quantum gravity poses a challenge to the notion of entanglement: If two parties are in an indefinite causal relation of being causally connected and not, can they still be entangled? If so, how does one measure the amount of entanglement? We propose to generalize the notions of entanglement and entanglement measure to address these questions. Importantly, the generalization opens the path to study quantum entanglement of states, channels, networks, and processes with definite or indefinite causal structure in a unified fashion, e.g., we show that the entanglement distillation capacity of a state, the quantum communication capacity of a channel, and the entanglement generation capacity of a network or a process are different manifestations of one and the same entanglement measure.

Entropy of Reissner–Nordström–de Sitter black hole

Energy Technology Data Exchange (ETDEWEB)

Zhang, Li-Chun [Department of Physics, Shanxi Datong University, Datong 037009 (China); Institute of Theoretical Physics, Shanxi Datong University, Datong 037009 (China); Zhao, Ren [Institute of Theoretical Physics, Shanxi Datong University, Datong 037009 (China); Ma, Meng-Sen, E-mail: mengsenma@gmail.com [Department of Physics, Shanxi Datong University, Datong 037009 (China); Institute of Theoretical Physics, Shanxi Datong University, Datong 037009 (China)

2016-10-10

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.

Correlation properties of entangled multiphoton states and Bernstein's paradox

Energy Technology Data Exchange (ETDEWEB)

Chirkin, A. S., E-mail: aschirkin@rambler.ru; Belyaeva, O. V., E-mail: lisenok.msu@gmail.com; Belinsky, A. V., E-mail: belinsky@inbox.ru [Moscow State University (Russian Federation)

2013-01-15

A normally ordered characteristic function (NOCF) of Bose operators is calculated for a number of discrete-variable entangled states (Greenberger-Horne-Zeilinger (GHZ) and Werner (W) qubit states and a cluster state). It is shown that such NOCFs contain visual information on two types of correlations: pseudoclassical and quantum correlations. The latter manifest themselves in the interference terms of the NOCFs and lead to quantum paradoxes, whereas the pseudoclassical correlations of photons and their cumulants satisfy the relations for classical random variables. Three- and four-qubit states are analyzed in detail. An implementation of an analog of Bernstein's paradox on discrete quantum variables is discussed. A measure of quantumness of an entangled state is introduced that is not related to the entropy approach. It is established that the maximum of the degree of quantumness substantiates the numerical values of the coefficients in multiqubit vector states derived from intuitive considerations.

Entanglement versus Stosszahlansatz: disappearance of the thermodynamic arrow in a high-correlation environment.

Science.gov (United States)

Partovi, M Hossein

2008-02-01

The crucial role of ambient correlations in determining thermodynamic behavior is established. A class of entangled states of two macroscopic systems is constructed such that each component is in a state of thermal equilibrium at a given temperature, and when the two are allowed to interact heat can flow from the colder to the hotter system. A dilute gas model exhibiting this behavior is presented. This reversal of the thermodynamic arrow is a consequence of the entanglement between the two systems, a condition that is opposite to molecular chaos and shown to be unlikely in a low-entropy environment. By contrast, the second law is established by proving Clausius' inequality in a low-entropy environment. These general results strongly support the expectation, first expressed by Boltzmann and subsequently elaborated by others, that the second law is an emergent phenomenon which requires a low-entropy cosmological environment, one that can effectively function as an ideal information sink.

Entanglement and purity of two-mode Gaussian states in noisy channels

International Nuclear Information System (INIS)

Serafini, Alessio; Illuminati, Fabrizio; De Siena, Silvio; Paris, Matteo G.A.

2004-01-01

We study the evolution of purity, entanglement, and total correlations of general two-mode continuous variable Gaussian states in arbitrary uncorrelated Gaussian environments. The time evolution of purity, von Neumann entropy, logarithmic negativity, and mutual information is analyzed for a wide range of initial conditions. In general, we find that a local squeezing of the bath leads to a faster degradation of purity and entanglement, while it can help to preserve the mutual information between the modes

Some relations between entropy and approximation numbers

Institute of Scientific and Technical Information of China (English)

郑志明

1999-01-01

A general result is obtained which relates the entropy numbers of compact maps on Hilbert space to its approximation numbers. Compared with previous works in this area, it is particularly convenient for dealing with the cases where the approximation numbers decay rapidly. A nice estimation between entropy and approximation numbers for noncompact maps is given.

Partial recovery of entanglement in bipartite-entanglement transformations

International Nuclear Information System (INIS)

Bandyopadhyay, Somshubhro; Roychowdhury, Vwani; Vatan, Farrokh

2002-01-01

Any deterministic bipartite-entanglement transformation involving finite copies of pure states and carried out using local operations and classical communication (LOCC) results in a net loss of entanglement. We show that for almost all such transformations, partial recovery of lost entanglement is achievable by using 2x2 auxiliary entangled states, no matter how large the dimensions of the parent states are. For the rest of the special cases of deterministic LOCC transformations, we show that the dimension of the auxiliary entangled state depends on the presence of equalities in the majorization relations of the parent states. We show that genuine recovery is still possible using auxiliary states in dimensions less than that of the parent states for all patterns of majorization relations except only one special case

Dual entanglement measures based on no local cloning and no local deleting

International Nuclear Information System (INIS)

Horodecki, Michal; Sen, Aditi; Sen, Ujjwal

2004-01-01

The impossibility of cloning and deleting of unknown states constitute important restrictions on processing of information in the quantum world. On the other hand, a known quantum state can always be cloned or deleted. However, if we restrict the class of allowed operations, there will arise restrictions on the ability of cloning and deleting machines. We have shown that cloning and deleting of known states is in general not possible by local operations. This impossibility hints at quantum correlation in the state. We propose dual measures of quantum correlation based on the dual restrictions of no local cloning and no local deleting. The measures are relative entropy distances of the desired states in a (generally impossible) perfect local cloning or local deleting process from the best approximate state that is actually obtained by imperfect local cloning or deleting machines. Just like the dual measures of entanglement cost and distillable entanglement, the proposed measures are based on important processes in quantum information. We discuss their properties. For the case of pure states, estimations of these two measures are also provided. Interestingly, the entanglement of cloning for a maximally entangled state of two two-level systems is not unity

Entropy generation in a condenser and related correlations

Directory of Open Access Journals (Sweden)

Askowski Rafał

2015-06-01

Full Text Available The paper presents an analysis of relations describing entropy generation in a condenser of a steam unit. Connections between entropy generation, condenser ratio, and heat exchanger effectiveness, as well as relations implied by them are shown. Theoretical considerations allowed to determine limits of individual parameters which describe the condenser operation. Various relations for average temperature of the cold fluid were compared. All the proposed relations were verified against data obtained using a simulator and actual measurement data from a 200 MW unit condenser. Based on data from a simulator it was examined how the sum of entropy rates, steam condenser effectiveness, terminal temperature difference and condenser ratio vary with the change in the inlet cooling water temperature, mass flow rate of steam and the cooling water mass flow rate.

Entanglement transitions induced by large deviations

Science.gov (United States)

Bhosale, Udaysinh T.

2017-12-01

The probability of large deviations of the smallest Schmidt eigenvalue for random pure states of bipartite systems, denoted as A and B , is computed analytically using a Coulomb gas method. It is shown that this probability, for large N , goes as exp[-β N2Φ (ζ ) ] , where the parameter β is the Dyson index of the ensemble, ζ is the large deviation parameter, while the rate function Φ (ζ ) is calculated exactly. Corresponding equilibrium Coulomb charge density is derived for its large deviations. Effects of the large deviations of the extreme (largest and smallest) Schmidt eigenvalues on the bipartite entanglement are studied using the von Neumann entropy. Effect of these deviations is also studied on the entanglement between subsystems 1 and 2, obtained by further partitioning the subsystem A , using the properties of the density matrix's partial transpose ρ12Γ. The density of states of ρ12Γ is found to be close to the Wigner's semicircle law with these large deviations. The entanglement properties are captured very well by a simple random matrix model for the partial transpose. The model predicts the entanglement transition across a critical large deviation parameter ζ . Log negativity is used to quantify the entanglement between subsystems 1 and 2. Analytical formulas for it are derived using the simple model. Numerical simulations are in excellent agreement with the analytical results.

Photonic simulation of entanglement growth and engineering after a spin chain quench.

Science.gov (United States)

Pitsios, Ioannis; Banchi, Leonardo; Rab, Adil S; Bentivegna, Marco; Caprara, Debora; Crespi, Andrea; Spagnolo, Nicolò; Bose, Sougato; Mataloni, Paolo; Osellame, Roberto; Sciarrino, Fabio

2017-11-17

The time evolution of quantum many-body systems is one of the most important processes for benchmarking quantum simulators. The most curious feature of such dynamics is the growth of quantum entanglement to an amount proportional to the system size (volume law) even when interactions are local. This phenomenon has great ramifications for fundamental aspects, while its optimisation clearly has an impact on technology (e.g., for on-chip quantum networking). Here we use an integrated photonic chip with a circuit-based approach to simulate the dynamics of a spin chain and maximise the entanglement generation. The resulting entanglement is certified by constructing a second chip, which measures the entanglement between multiple distant pairs of simulated spins, as well as the block entanglement entropy. This is the first photonic simulation and optimisation of the extensive growth of entanglement in a spin chain, and opens up the use of photonic circuits for optimising quantum devices.

Quantum states and their marginals. From multipartite entanglement to quantum error-correcting codes

International Nuclear Information System (INIS)

Huber, Felix Michael

2017-01-01

At the heart of the curious phenomenon of quantum entanglement lies the relation between the whole and its parts. In my thesis, I explore different aspects of this theme in the multipartite setting by drawing connections to concepts from statistics, graph theory, and quantum error-correcting codes: first, I address the case when joint quantum states are determined by their few-body parts and by Jaynes' maximum entropy principle. This can be seen as an extension of the notion of entanglement, with less complex states already being determined by their few-body marginals. Second, I address the conditions for certain highly entangled multipartite states to exist. In particular, I present the solution of a long-standing open problem concerning the existence of an absolutely maximally entangled state on seven qubits. This sheds light on the algebraic properties of pure quantum states, and on the conditions that constrain the sharing of entanglement amongst multiple particles. Third, I investigate Ulam's graph reconstruction problems in the quantum setting, and obtain legitimacy conditions of a set of states to be the reductions of a joint graph state. Lastly, I apply and extend the weight enumerator machinery from quantum error correction to investigate the existence of codes and highly entangled states in higher dimensions. This clarifies the physical interpretation of the weight enumerators and of the quantum MacWilliams identity, leading to novel applications in multipartite entanglement.

The application of asymmetric entangled states in quantum games

International Nuclear Information System (INIS)

Li Ye; Qin Gan; Zhou Xianyi; Du Jiangfeng

2006-01-01

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

Relations Among Some Fuzzy Entropy Formulae

Institute of Scientific and Technical Information of China (English)

卿铭

2004-01-01

Fuzzy entropy has been widely used to analyze and design fuzzy systems, and many fuzzy entropy formulae have been proposed. For further in-deepth analysis of fuzzy entropy, the axioms and some important formulae of fuzzy entropy are introduced. Some equivalence results among these fuzzy entropy formulae are proved, and it is shown that fuzzy entropy is a special distance measurement.

The effect of a coupling field on the entanglement dynamics of a three-level atom

International Nuclear Information System (INIS)

Mortezapour, Ali; Mahmoudi, Mohammad; Abedi, Majid; Khajehpour, M R H

2011-01-01

The effect of a coupling laser field on the entanglement of a three-level quantum system and its spontaneous emission is investigated via the reduced quantum entropy. We consider two schemes: the upper- and lower-level couplings. By calculating the degree of entanglement (DEM) for both systems, it is shown that the entanglement between the atom and its spontaneous emission can be controlled by the coupling laser field. This field, however, affects the entanglement differently in the two schemes; it is only the lower-level coupling scheme that shows a non-zero steady state DEM which can be controlled by the intensity and detuning of the coupling laser field.

The effect of a coupling field on the entanglement dynamics of a three-level atom

Energy Technology Data Exchange (ETDEWEB)

Mortezapour, Ali; Mahmoudi, Mohammad [Physics Department, Zanjan University, PO Box 45195-313, Zanjan (Iran, Islamic Republic of); Abedi, Majid; Khajehpour, M R H, E-mail: mahmoudi@iasbs.ac.ir, E-mail: pour@iasbs.ac.ir [Institute for Advanced Studies in Basic Sciences, PO Box 45195-159, Zanjan (Iran, Islamic Republic of)

2011-04-28

The effect of a coupling laser field on the entanglement of a three-level quantum system and its spontaneous emission is investigated via the reduced quantum entropy. We consider two schemes: the upper- and lower-level couplings. By calculating the degree of entanglement (DEM) for both systems, it is shown that the entanglement between the atom and its spontaneous emission can be controlled by the coupling laser field. This field, however, affects the entanglement differently in the two schemes; it is only the lower-level coupling scheme that shows a non-zero steady state DEM which can be controlled by the intensity and detuning of the coupling laser field.

Entanglement across extended random defects in the XX spin chain

Science.gov (United States)

Juhász, Róbert

2017-08-01

We study the half-chain entanglement entropy in the ground state of the spin-1/2 XX chain across an extended random defect, where the strength of disorder decays with the distance from the interface algebraically as Δ_l∼ l-κ . In the whole regime κ≥slant 0 , the average entanglement entropy is found to increase logarithmically with the system size L as S_L≃\\frac{c_eff(κ)}{6}\\ln L+const , where the effective central charge c_eff(κ) depends on κ. In the regime κ<1/2 , where the extended defect is a relevant perturbation, the strong-disorder renormalization group method gives c_eff(κ)=(1-2κ)\\ln2 , while, in the regime κ≥slant 1/2 , where the extended defect is irrelevant in the bulk, numerical results indicate a non-zero effective central charge, which increases with κ. The variation of c_eff(κ) is thus found to be non-monotonic and discontinuous at κ=1/2 .

Quantum Rényi relative entropies affirm universality of thermodynamics.

Science.gov (United States)

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.

Entanglement, holography and causal diamonds

Science.gov (United States)

de Boer, Jan; Haehl, Felix M.; Heller, Michal P.; Myers, Robert C.

2016-08-01

We argue that the degrees of freedom in a d-dimensional CFT can be reorganized 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 2 d-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 entanglemententropy 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.

Ellipses of constant entropy in the XY spin chain

International Nuclear Information System (INIS)

Franchini, F; Its, A R; Jin, B-Q; Korepin, V E

2007-01-01

Entanglement in the ground state of the XY model on the infinite chain can be measured by the von Neumann entropy of a block of neighbouring spins. We study a double scaling limit: the size of the block is much larger than 1 but much smaller than the length of the whole chain. The entropy of the block has an asymptotic limit in the gapped regimes. We study this limiting entropy as a function of the anisotropy and of the magnetic field. We identify its minima at product states and its divergencies at the quantum phase transitions. We find that the curves of constant entropy are ellipses and hyperbolas, and that they all meet at one point (essential critical point). Depending on the approach to the essential critical point, the entropy can take any value between 0 and ∞. In the vicinity of this point, small changes in the parameters cause large change of the entropy

Spin-resolved entanglement spectroscopy of critical spin chains and Luttinger liquids

International Nuclear Information System (INIS)

Laflorencie, Nicolas; Rachel, Stephan

2014-01-01

Quantum critical chains are well-described and understood by virtue of conformal field theory. Still, the meaning of the real space entanglement spectrum—the eigenvalues of the reduced density matrix—of such systems remains elusive in general, even when there is an additional quantum number available such as the spin or particle number. In this paper, we explore in detail the properties and structure of the reduced density matrix of critical XXZ spin- (1/2) chains. We investigate the quantum/thermal correspondence between the reduced density matrix of a T = 0 pure quantum state and the thermal density matrix of an effective entanglement Hamiltonian. Using large scale DMRG and QMC simulations, we investigate the conformal structure of the spectra, the entanglement Hamiltonian, and temperature. We then introduce the notion of spin-resolved entanglement entropies, which display interesting scaling features. (paper)

Entropy of Iterated Function Systems and Their Relations with Black Holes and Bohr-Like Black Holes Entropies

Directory of Open Access Journals (Sweden)

Christian Corda

2018-01-01

Full Text Available In this paper we consider the metric entropies of the maps of an iterated function system deduced from a black hole which are known the Bekenstein–Hawking entropies and its subleading corrections. More precisely, we consider the recent model of a Bohr-like black hole that has been recently analysed in some papers in the literature, obtaining the intriguing result that the metric entropies of a black hole are created by the metric entropies of the functions, created by the black hole principal quantum numbers, i.e., by the black hole quantum levels. We present a new type of topological entropy for general iterated function systems based on a new kind of the inverse of covers. Then the notion of metric entropy for an Iterated Function System ( I F S is considered, and we prove that these definitions for topological entropy of IFS’s are equivalent. It is shown that this kind of topological entropy keeps some properties which are hold by the classic definition of topological entropy for a continuous map. We also consider average entropy as another type of topological entropy for an I F S which is based on the topological entropies of its elements and it is also an invariant object under topological conjugacy. The relation between Axiom A and the average entropy is investigated.

On numerical calculation of Rényi entropy for a sphere

Energy Technology Data Exchange (ETDEWEB)

Kim, Nakwoo, E-mail: nkim@khu.ac.kr

2014-06-02

We numerically compute the Rényi entropy for four-dimensional free scalar field theory with a spherical entangling surface. As is well known, the Rényi entropy as a function of the boundary area exhibits linear dependence in the leading order. The coefficient of the subleading logarithmic term from our numerical data, as a function of the Rényi order q, agrees nicely with the general prediction of conformal field theory computation. The motivation of this work is also partly to see how the efficiency of numerical computation changes as a function of q. For q<1 the summation over eigenvalues of reduced density matrix takes longer since the series converges more slowly than for q=1. For q>1 the convergence is faster, but the relative error becomes large as a general trend.

Fidelity, entanglement, and information complementarity relation

International Nuclear Information System (INIS)

Cai, Jian-Ming; Zhou, Zheng-Wei; Guo, Guang-Can

2007-01-01

We investigate the dynamics of information in isolated multi-qubit systems. It is shown that information is in not only local form but also nonlocal form. We apply a measure of local information based on fidelity, and demonstrate that nonlocal information can be directly related to some appropriate well defined entanglement measures. Under general unitary transformations, local and nonlocal information will exhibit unambiguous complementary behavior with the total information conserved

Entropy of a rotating and charged black string to all orders in the Planck length

International Nuclear Information System (INIS)

Ren, Zhao; Yue-Qin, Wu; Li-Chun, Zhang

2009-01-01

By using the entanglement entropy method, this paper calculates the statistical entropy of the Bose and Fermi fields in thin films, and derives the Bekenstein–Hawking entropy and its correction term on the background of a rotating and charged black string. Here, the quantum field is entangled with quantum states in the black string and thin film to the event horizon from outside the rotating and charged black string. Taking into account the effect of the generalized uncertainty principle on quantum state density, it removes the difficulty of the divergence of state density near the event horizon in the brick-wall model. These calculations and discussions imply that high density quantum states near the event horizon of a black string are strongly correlated with the quantum states in a black string and that black string entropy is a quantum effect. The ultraviolet cut-off in the brick-wall model is not reasonable. The generalized uncertainty principle should be considered in the high energy quantum field near the event horizon. From the viewpoint of quantum statistical mechanics, the correction value of Bekenstein–Hawking entropy is obtained. This allows the fundamental recognition of the correction value of black string entropy at nonspherical coordinates

Quasi-exact solvability and entropies of the one-dimensional regularised Calogero model

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Pont, Federico M.; Osenda, Omar; Serra, Pablo

2018-05-01

The Calogero model can be regularised through the introduction of a cutoff parameter which removes the divergence in the interaction term. In this work we show that the one-dimensional two-particle regularised Calogero model is quasi-exactly solvable and that for certain values of the Hamiltonian parameters the eigenfunctions can be written in terms of Heun’s confluent polynomials. These eigenfunctions are such that the reduced density matrix of the two-particle density operator can be obtained exactly as well as its entanglement spectrum. We found that the number of non-zero eigenvalues of the reduced density matrix is finite in these cases. The limits for the cutoff distance going to zero (Calogero) and infinity are analysed and all the previously obtained results for the Calogero model are reproduced. Once the exact eigenfunctions are obtained, the exact von Neumann and Rényi entanglement entropies are studied to characterise the physical traits of the model. The quasi-exactly solvable character of the model is assessed studying the numerically calculated Rényi entropy and entanglement spectrum for the whole parameter space.

Entropy, extremality, euclidean variations, and the equations of motion

Science.gov (United States)

Dong, Xi; Lewkowycz, Aitor

2018-01-01

We study the Euclidean gravitational path integral computing the Rényi entropy and analyze its behavior under small variations. We argue that, in Einstein gravity, the extremality condition can be understood from the variational principle at the level of the action, without having to solve explicitly the equations of motion. This set-up is then generalized to arbitrary theories of gravity, where we show that the respective entanglement entropy functional needs to be extremized. We also extend this result to all orders in Newton's constant G N , providing a derivation of quantum extremality. Understanding quantum extremality for mixtures of states provides a generalization of the dual of the boundary modular Hamiltonian which is given by the bulk modular Hamiltonian plus the area operator, evaluated on the so-called modular extremal surface. This gives a bulk prescription for computing the relative entropies to all orders in G N . We also comment on how these ideas can be used to derive an integrated version of the equations of motion, linearized around arbitrary states.

Relative entropy of excited states in two dimensional conformal field theories

Energy Technology Data Exchange (ETDEWEB)

Sárosi, Gábor [Department of Theoretical Physics, Institute of Physics, Budapest University of Technology,Budapest, H-1521 (Hungary); Ugajin, Tomonori [Kavli Institute for Theoretical Physics, University of California,Santa Barbara,CA 93106 (United States)

2016-07-21

We study the relative entropy and the trace square distance, both of which measure the distance between reduced density matrices of two excited states in two dimensional conformal field theories. We find a general formula for the relative entropy between two primary states with the same conformal dimension in the limit of a single small interval and find that in this case the relative entropy is proportional to the trace square distance. We check our general formulae by calculating the relative entropy between two generalized free fields and the trace square distance between the spin and disorder operators of the critical Ising model. We also give the leading term of the relative entropy in the small interval expansion when the two operators have different conformal dimensions. This turns out to be universal when the CFT has no primaires lighter than the stress tensor. The result reproduces the previously known special cases.

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}.

Ergodicity, Maximum Entropy Production, and Steepest Entropy Ascent in the Proofs of Onsager's Reciprocal Relations

Science.gov (United States)

Benfenati, Francesco; Beretta, Gian Paolo

2018-04-01

We show that to prove the Onsager relations using the microscopic time reversibility one necessarily has to make an ergodic hypothesis, or a hypothesis closely linked to that. This is true in all the proofs of the Onsager relations in the literature: from the original proof by Onsager, to more advanced proofs in the context of linear response theory and the theory of Markov processes, to the proof in the context of the kinetic theory of gases. The only three proofs that do not require any kind of ergodic hypothesis are based on additional hypotheses on the macroscopic evolution: Ziegler's maximum entropy production principle (MEPP), the principle of time reversal invariance of the entropy production, or the steepest entropy ascent principle (SEAP).

Machine learning with quantum relative entropy

International Nuclear Information System (INIS)

Tsuda, Koji

2009-01-01

Density matrices are a central tool in quantum physics, but it is also used in machine learning. A positive definite matrix called kernel matrix is used to represent the similarities between examples. Positive definiteness assures that the examples are embedded in an Euclidean space. When a positive definite matrix is learned from data, one has to design an update rule that maintains the positive definiteness. Our update rule, called matrix exponentiated gradient update, is motivated by the quantum relative entropy. Notably, the relative entropy is an instance of Bregman divergences, which are asymmetric distance measures specifying theoretical properties of machine learning algorithms. Using the calculus commonly used in quantum physics, we prove an upperbound of the generalization error of online learning.

Machine learning with quantum relative entropy

Energy Technology Data Exchange (ETDEWEB)

Tsuda, Koji [Max Planck Institute for Biological Cybernetics, Spemannstr. 38, Tuebingen, 72076 (Germany)], E-mail: koji.tsuda@tuebingen.mpg.de

2009-12-01

Density matrices are a central tool in quantum physics, but it is also used in machine learning. A positive definite matrix called kernel matrix is used to represent the similarities between examples. Positive definiteness assures that the examples are embedded in an Euclidean space. When a positive definite matrix is learned from data, one has to design an update rule that maintains the positive definiteness. Our update rule, called matrix exponentiated gradient update, is motivated by the quantum relative entropy. Notably, the relative entropy is an instance of Bregman divergences, which are asymmetric distance measures specifying theoretical properties of machine learning algorithms. Using the calculus commonly used in quantum physics, we prove an upperbound of the generalization error of online learning.

On variational definition of quantum entropy

International Nuclear Information System (INIS)

Belavkin, Roman V.

2015-01-01

Entropy of distribution P can be defined in at least three different ways: 1) as the expectation of the Kullback-Leibler (KL) divergence of P from elementary δ-measures (in this case, it is interpreted as expected surprise); 2) as a negative KL-divergence of some reference measure ν from the probability measure P; 3) as the supremum of Shannon’s mutual information taken over all channels such that P is the output probability, in which case it is dual of some transportation problem. In classical (i.e. commutative) probability, all three definitions lead to the same quantity, providing only different interpretations of entropy. In non-commutative (i.e. quantum) probability, however, these definitions are not equivalent. In particular, the third definition, where the supremum is taken over all entanglements of two quantum systems with P being the output state, leads to the quantity that can be twice the von Neumann entropy. It was proposed originally by V. Belavkin and Ohya [1] and called the proper quantum entropy, because it allows one to define quantum conditional entropy that is always non-negative. Here we extend these ideas to define also quantum counterpart of proper cross-entropy and cross-information. We also show inequality for the values of classical and quantum information

The fall of the black hole firewall: natural nonmaximal entanglement for the Page curve

Science.gov (United States)

Hotta, Masahiro; Sugita, Ayumu

2015-12-01

The black hole firewall conjecture is based on the Page curve hypothesis, which claims that entanglement between a black hole and its Hawking radiation is almost maximum. Adopting canonical typicality for nondegenerate systems with nonvanishing Hamiltonians, we show the entanglement becomes nonmaximal, and energetic singularities (firewalls) do not emerge for general systems. An evaporating old black hole must evolve in Gibbs states with exponentially small error probability after the Page time as long as the states are typical. This means that the ordinarily used microcanonical states are far from typical. The heat capacity computed from the Gibbs states should be nonnegative in general. However, the black hole heat capacity is actually negative due to the gravitational instability. Consequently the states are not typical until the last burst. This requires inevitable modification of the Page curve, which is based on the typicality argument. For static thermal pure states of a large AdS black hole and its Hawking radiation, the entanglement entropy equals the thermal entropy of the smaller system.

Comments on Jacobson’s “entanglement equilibrium and the Einstein equation”

Energy Technology Data Exchange (ETDEWEB)

Casini, Horacio [Centro Atómico Bariloche and CONICET,S.C. de Bariloche, Rio Negro, R8402AGP (Argentina); Galante, Damián A. [Department of Applied Mathematics, University of Western Ontario,London, ON N6A 5B7 (Canada); Perimeter Institute for Theoretical Physics,Waterloo, ON N2L 2Y5 (Canada); Myers, Robert C. [Perimeter Institute for Theoretical Physics,Waterloo, ON N2L 2Y5 (Canada)

2016-03-30

Using holographic calculations, we examine a key assumption made in Jacobson’s recent argument for deriving Einstein’s equations from vacuum entanglement entropy. Our results involving relevant operators with low conformal dimensions seem to conflict with Jacobson’s assumption. However, we discuss ways to circumvent this problem.

Relation between entropy functional of Keizer and information theory

International Nuclear Information System (INIS)

Freidkin, E.S.; Nettleton, R.E.

1990-01-01

An equation given by Keizer which relates the second-order functional derivative of the steady-state entropy to the inverse fluctuation correlation function is satisified by the information-theoretic entropy if the equation is extended to arbitrary nonequilibrium states

Thermal entanglement in an orthogonal dimer-plaquette chain with alternating Ising–Heisenberg coupling

International Nuclear Information System (INIS)

Paulinelli, H G; De Souza, S M; Rojas, Onofre

2013-01-01

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. (paper)

Shape Dependence of Holographic Rényi Entropy in Conformal Field Theories

Science.gov (United States)

Dong, Xi

2016-06-01

We develop a framework for studying the well-known universal term in the Rényi entropy for an arbitrary entangling region in four-dimensional conformal field theories that are holographically dual to gravitational theories. The shape dependence of the Rényi entropy Sn is described by two coefficients: fb(n ) for traceless extrinsic curvature deformations and fc(n ) for Weyl tensor deformations. We provide the first calculation of the coefficient fb(n ) in interacting theories by relating it to the stress tensor one-point function in a deformed hyperboloid background. The latter is then determined by a straightforward holographic calculation. Our results show that a previous conjecture fb(n )=fc(n ), motivated by surprising evidence from a variety of free field theories and studies of conical defects, fails holographically.

Upper bounds on entangling rates of bipartite Hamiltonians

International Nuclear Information System (INIS)

Bravyi, Sergey

2007-01-01

We discuss upper bounds on the rate at which unitary evolution governed by a nonlocal Hamiltonian can generate entanglement in a bipartite system. Given a bipartite Hamiltonian H coupling two finite dimensional particles A and B, the entangling rate is shown to be upper bounded by c log(d) parallel H parallel, where d is the smallest dimension of the interacting particles parallel H parallel is the operator norm of H, and c is a constant close to 1. Under certain restrictions on the initial state we prove an analogous upper bound for the ancilla-assisted entangling rate with a constant c that does not depend upon dimensions of local ancillas. The restriction is that the initial state has at most two distinct Schmidt coefficients (each coefficient may have arbitrarily large multiplicity). Our proof is based on analysis of a mixing rate - a functional measuring how fast entropy can be produced if one mixes a time-independent state with a state evolving unitarily

Where are the black-hole entropy degrees of freedom?

International Nuclear Information System (INIS)

Das, Saurya; Shankaranarayanan, S

2007-01-01

Understanding the area proportionality of black-hole entropy (the 'area law') from an underlying fundamental theory has been one of the goals of all models of quantum gravity. A key question that one asks is: where are the degrees of freedom giving rise to black-hole entropy located? Taking the point of view that entanglement between field degrees of freedom inside and outside the horizon can be a source of this entropy, we show that when the field is in its ground state, the degrees of freedom near the horizon contribute most to the entropy, and the area law is obeyed. However, when it is in an excited state, degrees of freedom far from the horizon contribute more significantly, and deviations from the area law are observed. In other words, we demonstrate that horizon degrees of freedom are responsible for the area law

Entanglement from topology in Chern-Simons theory

Science.gov (United States)

Salton, Grant; Swingle, Brian; Walter, Michael

2017-05-01

The way in which geometry encodes entanglement is a topic of much recent interest in quantum many-body physics and the AdS/CFT duality. This relation is particularly pronounced in the case of topological quantum field theories, where topology alone determines the quantum states of the theory. In this work, we study the set of quantum states that can be prepared by the Euclidean path integral in three-dimensional Chern-Simons theory. Specifically, we consider arbitrary three-manifolds with a fixed number of torus boundaries in both Abelian U (1 ) and non-Abelian S O (3 ) Chern-Simons theory. For the Abelian theory, we find that the states that can be prepared coincide precisely with the set of stabilizer states from quantum information theory. This constrains the multipartite entanglement present in this theory, but it also reveals that stabilizer states can be described by topology. In particular, we find an explicit expression for the entanglement entropy of a many-torus subsystem using only a single replica, as well as a concrete formula for the number of GHZ states that can be distilled from a tripartite state prepared through path integration. For the non-Abelian theory, we find a notion of "state universality," namely that any state can be prepared to an arbitrarily good approximation. The manifolds we consider can also be viewed as toy models of multiboundary wormholes in AdS/CFT.

Discrimination strategies for inequivalent classes of multipartite entangled states

International Nuclear Information System (INIS)

Niekamp, Soenke; Kleinmann, Matthias; Guehne, Otfried

2010-01-01

How can one discriminate different inequivalent classes of multiparticle entanglement experimentally? We present an approach for the discrimination of an experimentally prepared state from the equivalence class of another state. We consider two possible measures for the discrimination strength of an observable. The first measure is based on the difference of expectation values, the second on the relative entropy of the probability distributions of the measurement outcomes. The interpretation of these measures and their usefulness for experiments with limited resources are discussed. In the case of graph states, the stabilizer formalism is employed to compute these quantities and to find sets of observables that result in the most decisive discrimination.

Deformed Fredkin spin chain with extensive entanglement

Science.gov (United States)

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\

Eigenvalue and Entropy Statistics for Products of Conjugate Random Quantum Channels

Directory of Open Access Journals (Sweden)

Benoît Collins

2010-06-01

Full Text Available Using the graphical calculus and integration techniques introduced by the authors, we study the statistical properties of outputs of products of random quantum channels for entangled inputs. In particular, we revisit and generalize models of relevance for the recent counterexamples to the minimum output entropy additivity problems. Our main result is a classification of regimes for which the von Neumann entropy is lower on average than the elementary bounds that can be obtained with linear algebra techniques.

Quantum entanglement of baby universes

International Nuclear Information System (INIS)

Aganagic, Mina; Okuda, Takuya; Ooguri, Hirosi

2007-01-01

We study quantum entanglements of baby universes which appear in non-perturbative corrections to the OSV formula for the entropy of extremal black holes in type IIA string theory compactified on the local Calabi-Yau manifold defined as a rank 2 vector bundle over an arbitrary genus G Riemann surface. This generalizes the result for G=1 in hep-th/0504221. Non-perturbative terms can be organized into a sum over contributions from baby universes, and the total wave-function is their coherent superposition in the third quantized Hilbert space. We find that half of the universes preserve one set of supercharges while the other half preserve a different set, making the total universe stable but non-BPS. The parent universe generates baby universes by brane/anti-brane pair creation, and baby universes are correlated by conservation of non-normalizable D-brane charges under the process. There are no other source of entanglement of baby universes, and all possible states are superposed with the equal weight

Quantum entanglement of baby universes

International Nuclear Information System (INIS)

Essman, Eric P.; Aganagic, Mina; Okuda, Takuya; Ooguri, Hirosi

2006-01-01

We study quantum entanglements of baby universes which appear in non-perturbative corrections to the OSV formula for the entropy of extremal black holes in type IIA string theory compactified on the local Calabi-Yau manifold defined as a rank 2 vector bundle over an arbitrary genus G Riemann surface. This generalizes the result for G=1 in hep-th/0504221. Non-perturbative terms can be organized into a sum over contributions from baby universes, and the total wave-function is their coherent superposition in the third quantized Hilbert space. We find that half of the universes preserve one set of supercharges while the other half preserve a different set, making the total universe stable but non-BPS. The parent universe generates baby universes by brane/anti-brane pair creation, and baby universes are correlated by conservation of non-normalizable D-brane charges under the process. There are no other source of entanglement of baby universes, and all possible states are superposed with the equal weight

Entanglement in holographic dark energy models

Energy Technology Data Exchange (ETDEWEB)

Horvat, R., E-mail: horvat@lei3.irb.h [Rudjer Boskovic Institute, P.O. Box 180, 10002 Zagreb (Croatia)

2010-10-18

We study a process of equilibration of holographic dark energy (HDE) with the cosmic horizon around the dark-energy dominated epoch. This process is characterized by a huge amount of information conveyed across the horizon, filling thereby a large gap in entropy between the system on the brink of experiencing a sudden collapse to a black hole and the black hole itself. At the same time, even in the absence of interaction between dark matter and dark energy, such a process marks a strong jump in the entanglement entropy, measuring the quantum-mechanical correlations between the horizon and its interior. Although the effective quantum field theory (QFT) with a peculiar relationship between the UV and IR cutoffs, a framework underlying all HDE models, may formally account for such a huge shift in the number of distinct quantum states, we show that the scope of such a framework becomes tremendously restricted, devoid virtually any application in other cosmological epochs or particle-physics phenomena. The problem of negative entropies for the non-phantom stuff is also discussed.

Entanglement in holographic dark energy models

International Nuclear Information System (INIS)

Horvat, R.

2010-01-01

We study a process of equilibration of holographic dark energy (HDE) with the cosmic horizon around the dark-energy dominated epoch. This process is characterized by a huge amount of information conveyed across the horizon, filling thereby a large gap in entropy between the system on the brink of experiencing a sudden collapse to a black hole and the black hole itself. At the same time, even in the absence of interaction between dark matter and dark energy, such a process marks a strong jump in the entanglement entropy, measuring the quantum-mechanical correlations between the horizon and its interior. Although the effective quantum field theory (QFT) with a peculiar relationship between the UV and IR cutoffs, a framework underlying all HDE models, may formally account for such a huge shift in the number of distinct quantum states, we show that the scope of such a framework becomes tremendously restricted, devoid virtually any application in other cosmological epochs or particle-physics phenomena. The problem of negative entropies for the non-phantom stuff is also discussed.

Relative entropy differences in bacterial chromosomes, plasmids, phages and genomic islands

DEFF Research Database (Denmark)

Bohlin, Jon; van Passel, Mark W. J.; Snipen, Lars

2012-01-01

with the strongest association being in phages. Relative entropy was also found to be lower in the obligate intracellular Mycobacterium leprae than in the related M. tuberculosis when measured on a shared set of highly conserved genes. Conclusions: We argue that relative entropy differences reflect how plasmids...

Multipartite entangled quantum states: Transformation, Entanglement monotones and Application

Science.gov (United States)

Cui, Wei

Entanglement is one of the fundamental features of quantum information science. Though bipartite entanglement has been analyzed thoroughly in theory and shown to be an important resource in quantum computation and communication protocols, the theory of entanglement shared between more than two parties, which is called multipartite entanglement, is still not complete. Specifically, the classification of multipartite entanglement and the transformation property between different multipartite states by local operators and classical communications (LOCC) are two fundamental questions in the theory of multipartite entanglement. In this thesis, we present results related to the LOCC transformation between multipartite entangled states. Firstly, we investigate the bounds on the LOCC transformation probability between multipartite states, especially the GHZ class states. By analyzing the involvement of 3-tangle and other entanglement measures under weak two-outcome measurement, we derive explicit upper and lower bound on the transformation probability between GHZ class states. After that, we also analyze the transformation between N-party W type states, which is a special class of multipartite entangled states that has an explicit unique expression and a set of analytical entanglement monotones. We present a necessary and sufficient condition for a known upper bound of transformation probability between two N-party W type states to be achieved. We also further investigate a novel entanglement transformation protocol, the random distillation, which transforms multipartite entanglement into bipartite entanglement ii shared by a non-deterministic pair of parties. We find upper bounds for the random distillation protocol for general N-party W type states and find the condition for the upper bounds to be achieved. What is surprising is that the upper bounds correspond to entanglement monotones that can be increased by Separable Operators (SEP), which gives the first set of

Entanglement Generation with Deformed Barut-Girardello Coherent States as Input States in a Unitary Beam Splitter

International Nuclear Information System (INIS)

Berrada, K.; Benmoussa, A.; Hassouni, Y.

2010-07-01

Using linear entropy as a measure of entanglement, we investigate the entanglement generated via a beam splitter using deformed Barut-Girardello coherent states. We show that the degree of entanglement depends strongly on the q-deformation parameter and amplitude Z of the states. We compute the Mandel Q parameter to examine the quantum statistical properties of these coherent states and make a comparison with the Glauber coherent states. It is shown that these states are useful to describe the states of real and ideal lasers by a proper choice of their characterizing parameters, using an alteration of the Holstein-Primakoff realization. (author)

Charcterization of multipartite entanglement

Energy Technology Data Exchange (ETDEWEB)

Chong, Bo

2006-06-23

In this thesis, we discuss several aspects of the characterization of entanglement in multipartite quantum systems, including detection, classification and quantification of entanglement. First, we discuss triqubit pure entanglement and propose a special true tripartite entanglement, the mixed entanglement, besides the Greenberger-Horne-Zeilinger (GHZ) entanglement and the W entanglement. Then, based on quantitative complementarity relations, we draw entanglement Venn diagrams for triqubit pure states with different entanglements and introduce the total tangle {tau}{sup (T)} to quantify total entanglement of triqubit pure states by defining the union I that is equivalent to the total tangle {tau}{sup (T)} from the mathematical point of view. The generalizations of entanglement Venn diagrams and the union I to N-qubit pure states are also discussed. Finally, based on the ranks of reduced density matrices, we discuss the separability of multiparticle arbitrary-dimensional pure and mixed states, respectively. (orig.)

Charcterization of multipartite entanglement

International Nuclear Information System (INIS)

Chong, Bo

2006-01-01

In this thesis, we discuss several aspects of the characterization of entanglement in multipartite quantum systems, including detection, classification and quantification of entanglement. First, we discuss triqubit pure entanglement and propose a special true tripartite entanglement, the mixed entanglement, besides the Greenberger-Horne-Zeilinger (GHZ) entanglement and the W entanglement. Then, based on quantitative complementarity relations, we draw entanglement Venn diagrams for triqubit pure states with different entanglements and introduce the total tangle τ (T) to quantify total entanglement of triqubit pure states by defining the union I that is equivalent to the total tangle τ (T) from the mathematical point of view. The generalizations of entanglement Venn diagrams and the union I to N-qubit pure states are also discussed. Finally, based on the ranks of reduced density matrices, we discuss the separability of multiparticle arbitrary-dimensional pure and mixed states, respectively. (orig.)

Quantum entanglement and criticality of the antiferromagnetic Heisenberg model in an external field

International Nuclear Information System (INIS)

Liu Guanghua; Li Ruoyan; Tian Guangshan

2012-01-01

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 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 < 2.0), a logarithmically divergent 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. (paper)

Entanglement criterion for tripartite systems based on local sum uncertainty relations

Science.gov (United States)

Akbari-Kourbolagh, Y.; Azhdargalam, M.

2018-04-01

We propose a sufficient criterion for the entanglement of tripartite systems based on local sum uncertainty relations for arbitrarily chosen observables of subsystems. This criterion generalizes the tighter criterion for bipartite systems introduced by Zhang et al. [C.-J. Zhang, H. Nha, Y.-S. Zhang, and G.-C. Guo, Phys. Rev. A 81, 012324 (2010), 10.1103/PhysRevA.81.012324] and can be used for both discrete- and continuous-variable systems. It enables us to detect the entanglement of quantum states without having a complete knowledge of them. Its utility is illustrated by some examples of three-qubit, qutrit-qutrit-qubit, and three-mode Gaussian states. It is found that, in comparison with other criteria, this criterion is able to detect some three-qubit bound entangled states more efficiently.

Relative Entropy, Interaction Energy and the Nature of Dissipation

Directory of Open Access Journals (Sweden)

Bernard Gaveau

2014-06-01

Full Text Available Many thermodynamic relations involve inequalities, with equality if a process does not involve dissipation. In this article we provide equalities in which the dissipative contribution is shown to involve the relative entropy (a.k.a. Kullback-Leibler divergence. The processes considered are general time evolutions both in classical and quantum mechanics, and the initial state is sometimes thermal, sometimes partially so. By calculating a transport coefficient we show that indeed—at least in this case—the source of dissipation in that coefficient is the relative entropy.

Geometric characterization of separability and entanglement in pure Gaussian states by single-mode unitary operations

Science.gov (United States)

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.

Geometric characterization of separability and entanglement in pure Gaussian states by single-mode unitary operations

International Nuclear Information System (INIS)

Adesso, Gerardo; Giampaolo, Salvatore M.; Illuminati, Fabrizio

2007-01-01

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 1xM 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

Thermal excitation spectrum from entanglement in an expanding quantum string

Directory of Open Access Journals (Sweden)

Jürgen Berges

2018-03-01

Full Text Available A surprising result in e+e− collisions is that the particle spectra from the string formed between the expanding quark–antiquark pair have thermal properties even though scatterings appear not to be frequent enough to explain this. We address this problem by considering the finite observable interval of a relativistic quantum string in terms of its reduced density operator by tracing over the complement region. We show how quantum entanglement in the presence of a horizon in spacetime for the causal transfer of information leads locally to a reduced mixed-state density operator. For very early proper time τ, we show that the entanglement entropy becomes extensive and scales with the rapidity. At these early times, the reduced density operator is of thermal form, with an entanglement temperature Tτ=ħ/(2πkBτ, even in the absence of any scatterings.

Gaussian measures of entanglement versus negativities: Ordering of two-mode Gaussian states

International Nuclear Information System (INIS)

Adesso, Gerardo; Illuminati, Fabrizio

2005-01-01

We study the entanglement of general (pure or mixed) two-mode Gaussian states of continuous-variable systems by comparing the two available classes of computable measures of entanglement: entropy-inspired Gaussian convex-roof measures and positive partial transposition-inspired measures (negativity and logarithmic negativity). We first review the formalism of Gaussian measures of entanglement, adopting the framework introduced in M. M. Wolf et al., Phys. Rev. A 69, 052320 (2004), where the Gaussian entanglement of formation was defined. We compute explicitly Gaussian measures of entanglement for two important families of nonsymmetric two-mode Gaussian state: namely, the states of extremal (maximal and minimal) negativities at fixed global and local purities, introduced in G. Adesso et al., Phys. Rev. Lett. 92, 087901 (2004). This analysis allows us to compare the different orderings induced on the set of entangled two-mode Gaussian states by the negativities and by the Gaussian measures of entanglement. We find that in a certain range of values of the global and local purities (characterizing the covariance matrix of the corresponding extremal states), states of minimum negativity can have more Gaussian entanglement of formation than states of maximum negativity. Consequently, Gaussian measures and negativities are definitely inequivalent measures of entanglement on nonsymmetric two-mode Gaussian states, even when restricted to a class of extremal states. On the other hand, the two families of entanglement measures are completely equivalent on symmetric states, for which the Gaussian entanglement of formation coincides with the true entanglement of formation. Finally, we show that the inequivalence between the two families of continuous-variable entanglement measures is somehow limited. Namely, we rigorously prove that, at fixed negativities, the Gaussian measures of entanglement are bounded from below. Moreover, we provide some strong evidence suggesting that they

Symplectic entropy

International Nuclear Information System (INIS)

De Nicola, Sergio; Fedele, Renato; Man'ko, Margarita A; Man'ko, Vladimir I

2007-01-01

The tomographic-probability description of quantum states is reviewed. The symplectic tomography of quantum states with continuous variables is studied. The symplectic entropy of the states with continuous variables is discussed and its relation to Shannon entropy and information is elucidated. The known entropic uncertainty relations of the probability distribution in position and momentum of a particle are extended and new uncertainty relations for symplectic entropy are obtained. The partial case of symplectic entropy, which is optical entropy of quantum states, is considered. The entropy associated to optical tomogram is shown to satisfy the new entropic uncertainty relation. The example of Gaussian states of harmonic oscillator is studied and the entropic uncertainty relations for optical tomograms of the Gaussian state are shown to minimize the uncertainty relation

Generation and control of electronic hybrid entanglement via a two-dimensional Rashba anisotropic nanodot

Energy Technology Data Exchange (ETDEWEB)

Amiri, F.; Rastgoo, S.; Golshan, M.M., E-mail: golshan@susc.ac.ir

2014-06-13

In the present article we report the dynamics of electronic spin–subbands, as well as subband–subband, hybrid entanglements in a two-dimensional anisotropic quantum dot. The dot is under the influence of Rashba effect and an external magnetic field. To study the hybrid entanglements, we partition the system into two categories in which either spatial degrees of freedom, subbands, entangle with the spin or the subbands become entangled amongst themselves. For the first case we calculate the von Neumann entropy, while for the latter the negativity is calculated. Our calculations show that for both cases information is periodically distributed between the corresponding subspaces. Effects of Rashba parameter and magnetic field on the characteristics of such oscillatory behavior are also discussed. For spin–subband entanglement the oscillations include dips, surrounded by plateaus of maximal entanglement. The subband–subband entanglement shows vanishingly small plateaus. The duration of plateaus is controlled by Rashba coupling and the external field. - Highlights: • Dynamics of hybrid entanglements in a parabolic 2-dimensional electron gas is reported. • The electron gas is influenced by the Rashba spin–orbit coupling and a magnetic field. • Spin–subband entanglement exhibits oscillations with dips and maximal plateaus. • Subband–subband entanglement also oscillates, but with vanishingly small plateaus. • The vigilance of plateaus is controllable by the Rashba effect and/or the field.

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.

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 ...

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.

Entanglement in correlated random spin chains, RNA folding and kinetic roughening

International Nuclear Information System (INIS)

Rodríguez-Laguna, Javier; Santalla, Silvia N; Ramírez, Giovanni; Sierra, Germán

2016-01-01

Average block entanglement in the 1D XX-model with uncorrelated random couplings is known to grow as the logarithm of the block size, in similarity to conformal systems. In this work we study random spin chains whose couplings present long range correlations, generated as gaussian fields with a power-law spectral function. Ground states are always planar valence bond states, and their statistical ensembles are characterized in terms of their block entropy and their bond-length distribution, which follow power-laws. We conjecture the existence of a critical value for the spectral exponent, below which the system behavior is identical to the case of uncorrelated couplings. Above that critical value, the entanglement entropy violates the area law and grows as a power law of the block size, with an exponent which increases from zero to one. Interestingly, we show that XXZ models with positive anisotropy present the opposite behavior, and strong correlations in the couplings lead to lower entropies. Similar planar bond structures are also found in statistical models of RNA folding and kinetic roughening, and we trace an analogy between them and quantum valence bond states. Using an inverse renormalization procedure we determine the optimal spin-chain couplings which give rise to a given planar bond structure, and study the statistical properties of the couplings whose bond structures mimic those found in RNA folding. (paper)

Relationship of Quantum Entanglement to Density Functional Theory

OpenAIRE

Rajagopal, A. K.; Rendell, R. W.

2005-01-01

The maximum von Neumann entropy principle subject to given constraints of mean values of some physical observables determines the density matrix. Similarly the stationary action principle in the case of time-dependent (dissipative) situations under similar constraints yields the density matrix. The free energy and measures of entanglement are expressed in terms of such a density matrix and thus define respective functionals of the mean values. In the light of several model calculations, it is...

Studying entanglement-assisted entanglement transformation

International Nuclear Information System (INIS)

Hsu Liyi

2004-01-01

In this paper, we study catalysis of entanglement transformations for n-level pure entangled states. We propose an algorithm of finding the required catalystic entanglement. We introduce several examples by way of demonstration. We evaluate the lower and upper bound of the required inequalities for deciding whether there are m-level appropriate catalyst states for entanglement transformations for two n-level pure entangled states

Relative entropy and waiting time for continuous-time Markov processes

NARCIS (Netherlands)

Chazottes, J.R.; Giardinà, C.; Redig, F.H.J.

2006-01-01

For discrete-time stochastic processes, there is a close connection between return (resp. waiting) times and entropy (resp. relative entropy). Such a connection cannot be straightforwardly extended to the continuous-time setting. Contrarily to the discrete-time case one needs a reference measure on

Entropy and Its Correlations with Other Related Quantities

Directory of Open Access Journals (Sweden)

Jing Wu

2014-02-01

Full Text Available In order to find more correlations between entropy and other related quantities, an analogical analysis is conducted between thermal science and other branches of physics. Potential energy in various forms is the product of a conserved extensive quantity (for example, mass or electric charge and an intensive quantity which is its potential (for example, gravitational potential or electrical voltage, while energy in specific form is a dissipative quantity during irreversible transfer process (for example mechanical or electrical energy will be dissipated as thermal energy. However, it has been shown that heat or thermal energy, like mass or electric charge, is conserved during heat transfer processes. When a heat transfer process is for object heating or cooling, the potential of internal energy U is the temperature T and its potential “energy” is UT/2 (called entransy and it is the simplified expression of thermomass potential energy; when a heat transfer process is for heat-work conversion, the potential of internal energy U is (1 − T0/T, and the available potential energy of a system in reversible heat interaction with the environment is U − U0 − T0(S − S0, then T0/T and T0(S − S0 are the unavailable potential and the unavailable potential energy of a system respectively. Hence, entropy is related to the unavailable potential energy per unit environmental temperature for heat-work conversion during reversible heat interaction between the system and its environment. Entropy transfer, like other forms of potential energy transfer, is the product of the heat and its potential, the reciprocal of temperature, although it is in form of the quotient of the heat and the temperature. Thus, the physical essence of entropy transfer is the unavailable potential energy transfer per unit environmental temperature. Entropy is a non-conserved, extensive, state quantity of a system, and entropy generation in an irreversible heat transfer process

State-independent uncertainty relations and entanglement detection

Science.gov (United States)

Qian, Chen; Li, Jun-Li; Qiao, Cong-Feng

2018-04-01

The uncertainty relation is one of the key ingredients of quantum theory. Despite the great efforts devoted to this subject, most of the variance-based uncertainty relations are state-dependent and suffering from the triviality problem of zero lower bounds. Here we develop a method to get uncertainty relations with state-independent lower bounds. The method works by exploring the eigenvalues of a Hermitian matrix composed by Bloch vectors of incompatible observables and is applicable for both pure and mixed states and for arbitrary number of N-dimensional observables. The uncertainty relation for the incompatible observables can be explained by geometric relations related to the parallel postulate and the inequalities in Horn's conjecture on Hermitian matrix sum. Practical entanglement criteria are also presented based on the derived uncertainty relations.

Characterization of separability and entanglement in (2xD)- and (3xD)-dimensional systems by single-qubit and single-qutrit unitary transformations

International Nuclear Information System (INIS)

Giampaolo, Salvatore M.; Illuminati, Fabrizio

2007-01-01

We investigate the geometric characterization of pure state bipartite entanglement of (2xD)- and (3xD)-dimensional composite quantum systems. To this aim, we analyze the relationship between states and their images under the action of particular classes of local unitary operations. We find that invariance of states under the action of single-qubit and single-qutrit transformations is a necessary and sufficient condition for separability. We demonstrate that in the (2xD)-dimensional case the von Neumann entropy of entanglement is a monotonic function of the minimum squared Euclidean distance between states and their images over the set of single qubit unitary transformations. Moreover, both in the (2xD)- and in the (3xD)-dimensional cases the minimum squared Euclidean distance exactly coincides with the linear entropy [and thus as well with the tangle measure of entanglement in the (2xD)-dimensional case]. These results provide a geometric characterization of entanglement measures originally established in informational frameworks. Consequences and applications of the formalism to quantum critical phenomena in spin systems are discussed

Generalization of Gibbs Entropy and Thermodynamic Relation

OpenAIRE

Park, Jun Chul

2010-01-01

In this paper, we extend Gibbs's approach of quasi-equilibrium thermodynamic processes, and calculate the microscopic expression of entropy for general non-equilibrium thermodynamic processes. Also, we analyze the formal structure of thermodynamic relation in non-equilibrium thermodynamic processes.

Entropy-power uncertainty relations: towards a tight inequality for all Gaussian pure states

International Nuclear Information System (INIS)

Hertz, Anaelle; Jabbour, Michael G; Cerf, Nicolas J

2017-01-01

We show that a proper expression of the uncertainty relation for a pair of canonically-conjugate continuous variables relies on entropy power, a standard notion in Shannon information theory for real-valued signals. The resulting entropy-power uncertainty relation is equivalent to the entropic formulation of the uncertainty relation due to Bialynicki-Birula and Mycielski, but can be further extended to rotated variables. Hence, based on a reasonable assumption, we give a partial proof of a tighter form of the entropy-power uncertainty relation taking correlations into account and provide extensive numerical evidence of its validity. Interestingly, it implies the generalized (rotation-invariant) Schrödinger–Robertson uncertainty relation exactly as the original entropy-power uncertainty relation implies Heisenberg relation. It is saturated for all Gaussian pure states, in contrast with hitherto known entropic formulations of the uncertainty principle. (paper)

Entropy is in Flux V3.4

Science.gov (United States)

Kadanoff, Leo P.

2017-05-01

of kinetic entropy. However, when the system is outside of local equilibrium, this definition fails. It is speculated that quantum entanglement is the source of this failure.

Teleporting entanglement during black hole evaporation

International Nuclear Information System (INIS)

Brustein, Ram; Medved, A.J.M.

2016-01-01

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.

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.

Multiple-copy entanglement transformation and entanglement catalysis

International Nuclear Information System (INIS)

Duan Runyao; Feng Yuan; Li Xin; Ying Mingsheng

2005-01-01

We prove that any multiple-copy entanglement transformation [S. Bandyopadhyay, V. Roychowdhury, and U. Sen, Phys. Rev. A 65, 052315 (2002)] can be implemented by a suitable entanglement-assisted local transformation [D. Jonathan and M. B. Plenio, Phys. Rev. Lett. 83, 3566 (1999)]. Furthermore, we show that the combination of multiple-copy entanglement transformation and the entanglement-assisted one is still equivalent to the pure entanglement-assisted one. The mathematical structure of multiple-copy entanglement transformations then is carefully investigated. Many interesting properties of multiple-copy entanglement transformations are presented, which exactly coincide with those satisfied by the entanglement-assisted ones. Most interestingly, we show that an arbitrarily large number of copies of state should be considered in multiple-copy entanglement transformations

Conservation law for distributed entanglement of formation and quantum discord

International Nuclear Information System (INIS)

Fanchini, Felipe F.; Cornelio, Marcio F.; Oliveira, Marcos C. de; Caldeira, Amir O.

2011-01-01

We present a direct relation, based upon a monogamic principle, between entanglement of formation (EOF) and quantum discord (QD), showing how they are distributed in an arbitrary tripartite pure system. By extending it to a paradigmatic situation of a bipartite system coupled to an environment, we demonstrate that the EOF and the QD obey conservation relation. By means of this relation we show that in the deterministic quantum computer with one pure qubit the protocol has the ability to rearrange the EOF and the QD, which implies that quantum computation can be understood on a different basis as a coherent dynamics where quantum correlations are distributed between the qubits of the computer. Furthermore, for a tripartite mixed state we show that the balance between distributed EOF and QD results in a stronger version of the strong subadditivity of entropy.

Uncertainty relations for information entropy in wave mechanics

International Nuclear Information System (INIS)

Bialynicki-Birula, I.; Pittsburgh Univ., Pa.; Mycielski, J.

1975-01-01

New uncertainty relations in quantum mechanics are derived. They express restrictions imposed by quantum theory on probability distributions of canonically conjugate variables in terms of corresponding information entropies. The Heisenberg uncertainty relation follows from those inequalities and so does the Gross-Nelson inequality. (orig.) [de

Entanglement in bipartite pure states of an interacting boson gas obtained by local projective measurements

International Nuclear Information System (INIS)

Paraan, Francis N. C.; Korepin, Vladimir E.; Molina-Vilaplana, Javier; Bose, Sougato

2011-01-01

We quantify the extractable entanglement of excited states of a Lieb-Liniger gas that are obtained from coarse-grained measurements on the ground state in which the boson number in one of two complementary contiguous partitions of the gas is determined. Numerically exact results obtained from the coordinate Bethe ansatz show that the von Neumann entropy of the resulting bipartite pure state increases monotonically with the strength of repulsive interactions and saturates to the impenetrable-boson limiting value. We also present evidence indicating that the largest amount of entanglement can be extracted from the most probable projected state having half the number of bosons in a given partition. Our study points to a fundamental difference between the nature of the entanglement in free-bosonic and free-fermionic systems, with the entanglement in the former being zero after projection, while that in the latter (corresponding to the impenetrable-boson limit) being nonzero.

Entanglement dynamics and position-momentum entropic uncertainty relation of a Λ-type three-level atom interacting with a two-mode cavity field in the presence of nonlinearities

Science.gov (United States)

Faghihi, M. J.; Tavassoly, M. K.; Hooshmandasl, M. R.

2013-05-01

In this paper, the interaction between a $\\Lambda$-type three-level atom and two-mode cavity field is discussed. The detuning parameters and cross-Kerr nonlinearity are taken into account and it is assumed that atom-field coupling and Kerr medium to be $f$-deformed. Even though the system seems to be complicated, the analytical form of the state vector of the entire system for considered model is exactly obtained. The time evolution of nonclassical properties such as quantum entanglement and position-momentum entropic uncertainty relation (entropy squeezing) of the field are investigated. In each case, the influences of the detuning parameters, generalized Kerr medium and intensity-dependent coupling on the latter nonclassicality signs are analyzed, in detail.

Multipartite entanglement in neutrino oscillations

International Nuclear Information System (INIS)

Blasone, Massimo; Dell'Anno, Fabio; De Siena, Silvio; Illuminati, Fabrizio

2009-01-01

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.

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 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.

Unification of Quantum and Gravity by Non Classical Information Entropy Space

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Davide Fiscaletti

2013-09-01

Full Text Available A quantum entropy space is suggested as the fundamental arena describing the quantum effects. In the quantum regime the entropy is expressed as the superposition of many different Boltzmann entropies that span the space of the entropies before any measure. When a measure is performed the quantum entropy collapses to one component. A suggestive reading of the relational interpretation of quantum mechanics and of Bohm’s quantum potential in terms of the quantum entropy are provided. The space associated with the quantum entropy determines a distortion in the classical space of position, which appears as a Weyl-like gauge potential connected with Fisher information. This Weyl-like gauge potential produces a deformation of the moments which changes the classical action in such a way that Bohm’s quantum potential emerges as consequence of the non classical definition of entropy, in a non-Euclidean information space under the constraint of a minimum condition of Fisher information (Fisher Bohm- entropy. Finally, the possible quantum relativistic extensions of the theory and the connections with the problem of quantum gravity are investigated. The non classical thermodynamic approach to quantum phenomena changes the geometry of the particle phase space. In the light of the representation of gravity in ordinary phase space by torsion in the flat space (Teleparallel gravity, the change of geometry in the phase space introduces quantum phenomena in a natural way. This gives a new force to F. Shojai’s and A. Shojai’s theory where the geometry of space-time is highly coupled with a quantum potential whose origin is not the Schrödinger equation but the non classical entropy of a system of many particles that together change the geometry of the phase space of the positions (entanglement. In this way the non classical thermodynamic changes the classical geodetic as a consequence of the quantum phenomena and quantum and gravity are unified. Quantum

Entropy, related thermodynamic properties, and structure of methylisocyanate

International Nuclear Information System (INIS)

Davis, Phil S.; Kilpatrick, John E.

2013-01-01

Highlights: ► The thermodynamic properties of methylisocyanate have been determined by isothermal calorimetry from 15 to 298.15 K. ► The third law entropy has been compared with the entropy calculated by statistical thermodynamics. ► The comparisons are consistent with selected proposed molecular structures and vibrational frequencies. -- Abstract: The entropy and related thermodynamic properties of methylisocyanate, CH 3 NCO, have been determined by isothermal calorimetry. The entropy in the ideal gas state at 298.15 K and 1 atmosphere is S m o = 284.3 ± 0.6 J/K · mol. Other thermodynamic properties determined include: the heat capacity from 15 to 300 K, the temperature of fusion (T fus = 178.461 ± 0.024 K), the enthalpy of fusion (ΔH fus = 7455.2 ± 14.0 J/mol), the enthalpy of vaporization at 298.15 K (ΔH vap = 28768 ± 54 J/mol), and the vapor pressure from fusion to 300 K. Using statistical thermodynamics, the entropy in this same state has been calculated for various assumed structures for methylisocyante which have been proposed based on several spectroscopic and ab initio results. Comparisons between the experimental and calculated entropy have led to the following conclusions concerning historical differences among problematic structural properties: (1) The CNC/CNO angles can have the paired values of 140/180° or 135/173° respectively. It is not possible to distinguish between the two by this thermodynamic analysis. (2) The methyl group functions as a free rotor or near free rotor against the NCO rigid frame. The barrier to internal rotation is less than 2100 J/mol. (3) The CNC vibrational bending frequency is consistent with the more recently observed assignments at 165 and 172 cm −1 with some degree of anharmonicity or with a pure harmonic at about 158 cm −1

Mechanism of the generation of black hole entropy in Sakharov's induced gravity

International Nuclear Information System (INIS)

Frolov, V.P.; Fursaev, D.V.

1997-01-01

The mechanism of the generation of Bekenstein-Hawking entropy S BH of a black hole in the Sakharov's induced gravity is proposed. It is suggested that the physical degrees of freedom, which explain the entropy S BH , form only a finite subset of the standard Rindler-like modes defined outside the black hole horizon. The entropy S R of the Rindler modes, or entanglement entropy, is always ultraviolet divergent, while the entropy of the physical modes is finite and coincides in the induced gravity with S BH . The two entropies S BH and S R differ by a surface integral Q interpreted as a Noether charge of nonminimally coupled scalar constituents of the model. We demonstrate that energy E and Hamiltonian H of the fields localized in a part of space-time, restricted by the Killing horizon Σ, differ by the quantity T H Q, where T H is the temperature of a black hole. The first law of black hole thermodynamics enables one to relate the probability distribution of fluctuations of the black hole mass, caused by the quantum fluctuations of the fields, to the probability distribution of physical modes over energy E. The latter turns out to be different from the distribution of the Rindler modes. We show that the probability distribution of the physical degrees of freedom has a sharp peak at E=0 with the width proportional to the Planck mass. The logarithm of number of physical states at the peak coincides exactly with the black hole entropy S BH . This enables us to argue that the energy distribution of the physical modes and distribution of the black hole mass are equivalent in induced gravity. Finally it is shown that the Noether charge Q is related to the entropy of the low-frequency modes propagating in the vicinity of the bifurcation surface Σ of the horizon. (Abstract Truncated)

The quantum entropic uncertainty relation and entanglement witness in the two-atom system coupling with the non-Markovian environments

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