Pseudo-Hermitian quantum mechanics with unbounded metric operators.
Mostafazadeh, Ali
2013-04-28
I extend the formulation of pseudo-Hermitian quantum mechanics to η(+)-pseudo-Hermitian Hamiltonian operators H with an unbounded metric operator η(+). In particular, I give the details of the construction of the physical Hilbert space, observables and equivalent Hermitian Hamiltonian for the case that H has a real and discrete spectrum and its eigenvectors belong to the domain of η(+) and consequently √η(+).
Holographic computations of the Quantum Information Metric
Trivella, Andrea
2016-01-01
In this note we show how the Quantum Information Metric can be computed holographically using a perturbative approach. In particular when the deformation of the conformal field theory state is induced by a scalar operator the corresponding bulk configuration reduces to a scalar field perturbatively probing the unperturbed background. We study two concrete examples: a CFT ground state deformed by a primary operator and thermofield double state in $d=2$ deformed by a marginal operator. Finally, we generalize the bulk construction to the case of a multi dimensional parameter space and show that the Quantum Information Metric coincides with the metric of the non-linear sigma model for the corresponding scalar fields.
Rainbow metric from quantum gravity
Assaniousssi, Mehdi; Lewandowski, Jerzy
2014-01-01
In this letter, we describe a general mechanism for emergence of a rainbow metric from a quantum cosmological model. This idea is based on QFT on a quantum space-time. Under general assumptions, we discover that the quantum space-time on which the field propagates can be replaced by a classical space-time, whose metric depends explicitly on the energy of the field: as shown by an analysis of dispersion relations, quanta of different energy propagate on different metrics, similar to photons in a refractive material (hence the name "rainbow" used in the literature). In deriving this result, we do not consider any specific theory of quantum gravity: the qualitative behavior of high-energy particles on quantum space-time relies only on the assumption that the quantum space-time is described by a wave-function $\\Psi_o$ in a Hilbert space $\\mathcal{H}_G$.
Gravity Dual of Quantum Information Metric
Miyaji, Masamichi; Shiba, Noburo; Takayanagi, Tadashi; Watanabe, Kento
2015-01-01
We study a quantum information metric (or fidelity susceptibility) in conformal field theories with respect to a small perturbation by a primary operator. We argue that its gravity dual is approximately given by a volume of maximal time slice in an AdS spacetime when the perturbation is exactly marginal. We confirm our claim in several examples.
Metric for Estimating Congruity between Quantum Images
Directory of Open Access Journals (Sweden)
Abdullah M. Iliyasu
2016-10-01
Full Text Available An enhanced quantum-based image fidelity metric, the QIFM metric, is proposed as a tool to assess the “congruity” between two or more quantum images. The often confounding contrariety that distinguishes between classical and quantum information processing makes the widely accepted peak-signal-to-noise-ratio (PSNR ill-suited for use in the quantum computing framework, whereas the prohibitive cost of the probability-based similarity score makes it imprudent for use as an effective image quality metric. Unlike the aforementioned image quality measures, the proposed QIFM metric is calibrated as a pixel difference-based image quality measure that is sensitive to the intricacies inherent to quantum image processing (QIP. As proposed, the QIFM is configured with in-built non-destructive measurement units that preserve the coherence necessary for quantum computation. This design moderates the cost of executing the QIFM in order to estimate congruity between two or more quantum images. A statistical analysis also shows that our proposed QIFM metric has a better correlation with digital expectation of likeness between images than other available quantum image quality measures. Therefore, the QIFM offers a competent substitute for the PSNR as an image quality measure in the quantum computing framework thereby providing a tool to effectively assess fidelity between images in quantum watermarking, quantum movie aggregation and other applications in QIP.
Curved noncommutative tori as Leibniz quantum compact metric spaces
Energy Technology Data Exchange (ETDEWEB)
Latrémolière, Frédéric, E-mail: frederic@math.du.edu [Department of Mathematics, University of Denver, Denver, Colorado 80208 (United States)
2015-12-15
We prove that curved noncommutative tori are Leibniz quantum compact metric spaces and that they form a continuous family over the group of invertible matrices with entries in the image of the quantum tori for the conjugation by modular conjugation operator in the regular representation, when this group is endowed with a natural length function.
Curved noncommutative tori as Leibniz quantum compact metric spaces
Latrémolière, Frédéric
2015-12-01
We prove that curved noncommutative tori are Leibniz quantum compact metric spaces and that they form a continuous family over the group of invertible matrices with entries in the image of the quantum tori for the conjugation by modular conjugation operator in the regular representation, when this group is endowed with a natural length function.
Quantum entanglement and quantum operation
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
It is a simple introduction to quantum entanglement and quantum operations. The authors focus on some applications of quantum entanglement and relations between two-qubit entangled states and unitary operations. It includes remote state preparation by using any pure entangled states, nonlocal operation implementation using entangled states, entanglement capacity of two-qubit gates and two-qubit gates construction.
Quantum Operations as Quantum States
Arrighi, P; Arrighi, Pablo; Patricot, Christophe
2004-01-01
In this article we formalize the correspondence between quantum states and quantum operations, and harness its consequences. This correspondence was already implicit in Choi's proof of the operator sum representation of Completely Positive-preserving linear maps; we go further and show that all of the important theorems concerning quantum operations can be derived as simple corollaries of those concerning quantum states. As we do so the discussion first provides an elegant and original review of the main features of quantum operations. Next (in the second half of the paper) we search for more results to arise from the correspondence. Thus we propose a factorizability condition and an extremal trace-preservedness condition for quantum operations, give two novel Schmidt-type decompositions of bipartite pure states and two interesting composition laws for which the set of quantum operations and quantum states remain stable. The latter enables us to define a group structure upon the set of totally entangled state...
Geons and the quantum information metric
Sinamuli, Musema; Mann, Robert B.
2017-07-01
We investigate the proposed duality between a quantum information metric in a CFTd +1 and the volume of a maximum time slice in the dual AdSd +2 for topological geons. Examining the specific cases of Banados-Teitelboim-Zannelli (BTZ) black holes and planar Schwarzschild-anti-de Sitter black holes, along with their geon counterparts, we find that the proposed duality relation for geons is the same apart from a factor of 4. The information metric therefore provides a probe of the topology of the bulk spacetime.
Modified gravity from the quantum part of the metric
Energy Technology Data Exchange (ETDEWEB)
Dzhunushaliev, Vladimir [KazNU, Department of Theoretical and Nuclear Physics, Almaty (Kazakhstan); IETP, Al-Farabi Kazakh National University, Almaty (Kazakhstan); NAS of the Kyrgyz Republic, Bishkek (Kyrgyzstan). Institute of Physicotechnical Problems and Material Science; Universitaet Oldenburg, Institut fuer Physik, Oldenburg (Germany); Folomeev, Vladimir [IETP, Al-Farabi Kazakh National University, Almaty (Kazakhstan); NAS of the Kyrgyz Republic, Bishkek (Kyrgyzstan). Institute of Physicotechnical Problems and Material Science; Kleihaus, Burkhard; Kunz, Jutta [Universitaet Oldenburg, Institut fuer Physik, Oldenburg (Germany)
2014-01-15
It is shown that if a metric in quantum gravity can be decomposed as a sum of classical and quantum parts, then Einstein quantum gravity looks approximately like modified gravity with a nonminimal interaction between gravity and matter. (orig.)
Quantum entanglement and quantum operation
Institute of Scientific and Technical Information of China (English)
2008-01-01
It is a simple introduction to quantum entanglement and quantum operations.The authors focus on some applications of quantum entanglement and relations between two-qubit entangled states and unitary operations.It includes remote state preparation by using any pure entangled states,nonlocal operation implementation using entangled states,entanglement capacity of two-qubit gates and two-qubit gates construction.
Metrics for Offset Printing Press Operation.
Cooper, Gloria S., Ed.; Magisos, Joel H., Ed.
Designed to meet the job-related metric measurement needs of offset printing press operation students, this instructional package is one of six for the communication media occupations cluster, part of a set of 55 packages for metric instruction in different occupations. The package is intended for students who already know the occupational…
Rainbow metric from quantum gravity: anisotropic cosmology
Assanioussi, Mehdi
2016-01-01
In this paper we present a construction of effective cosmological models which describe the propagation of a massive quantum scalar field on a quantum anisotropic cosmological spacetime. Each obtained effective model is represented by a rainbow metric in which particles of distinct momenta propagate on different classical geometries. Our analysis shows that upon certain assumptions and conditions on the parameters determining such anisotropic models, we surprisingly obtain a unique deformation parameter $\\beta$ in the modified dispersion relation of the modes. Hence inducing an isotropic deformation despite the general starting considerations. We then ensure the recovery of the dispersion relation realized in the isotropic case, studied in [arXiv:1412.6000], when some proper symmetry constraints are imposed, and we estimate the value of the deformation parameter for this case in loop quantum cosmology context.
Rainbow metric from quantum gravity: Anisotropic cosmology
Assanioussi, Mehdi; Dapor, Andrea
2017-03-01
In this paper we present a construction of effective cosmological models which describe the propagation of a massive quantum scalar field on a quantum anisotropic cosmological spacetime. Each obtained effective model is represented by a rainbow metric in which particles of distinct momenta propagate on different classical geometries. Our analysis shows that upon certain assumptions and conditions on the parameters determining such anisotropic models, we surprisingly obtain a unique deformation parameter β in the modified dispersion relation of the modes, hence, inducing an isotropic deformation despite the general starting considerations. We then ensure the recovery of the dispersion relation realized in the isotropic case, studied in [M. Assanioussi, A. Dapor, and J. Lewandowski, Phys. Lett. B 751, 302 (2015), 10.1016/j.physletb.2015.10.043], when some proper symmetry constraints are imposed, and we estimate the value of the deformation parameter for this case in loop quantum cosmology context.
Cosmological implications of modified gravity induced by quantum metric fluctuations
Liu, Xing; Liang, Shi-Dong
2016-01-01
We investigate the cosmological implications of modified gravities induced by the quantum fluctuations of the gravitational metric. If the metric can be decomposed as the sum of the classical and of a fluctuating part, of quantum origin, then the corresponding Einstein quantum gravity generates at the classical level modified gravity models with a nonminimal coupling between geometry and matter. As a first step in our study, after assuming that the expectation value of the quantum correction can be generally expressed in terms of an arbitrary second order tensor constructed from the metric and from the thermodynamic quantities characterizing the matter content of the Universe, we derive the (classical) gravitational field equations in their general form. We analyze in detail the cosmological models obtained by assuming that the quantum correction tensor is given by the coupling of a scalar field and of a scalar function to the metric tensor, and by a term proportional to the matter energy-momentum tensor. For...
Quantum Mechanical Corrections to the Schwarzschild Black Hole Metric
Bargueño, P; Nowakowski, M; Batic, D
2016-01-01
Motivated by quantum mechanical corrections to the Newtonian potential, which can be translated into an $\\hbar$-correction to the $g_{00}$ component of the Schwarzschild metric, we construct a quantum mechanically corrected metric assuming $-g_{00}=g^{rr}$. We show how the Bekenstein black hole entropy $S$ receives its logarithmic contribution provided the quantum mechanical corrections to the metric are negative. In this case the standard horizon at the Schwarzschild radius $r_S$ increases by small terms proportional to $\\hbar$ and a remnant of the order of Planck mass emerges. We contrast these results with a positive correction to the metric which, apart from a corrected Schwarzschild horizon, leads to a new purely quantum mechanical horizon. In such a case the quantum mechanical corrections to the entropy are logarithmic and polynomial.
Cohering power of quantum operations
Energy Technology Data Exchange (ETDEWEB)
Bu, Kaifeng, E-mail: bkf@zju.edu.cn [School of Mathematical Sciences, Zhejiang University, Hangzhou 310027 (China); Kumar, Asutosh, E-mail: asukumar@hri.res.in [Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211019 (India); Homi Bhabha National Institute, Anushaktinagar, Mumbai 400094 (India); Zhang, Lin, E-mail: linyz@zju.edu.cn [Institute of Mathematics, Hangzhou Dianzi University, Hangzhou 310018 (China); Wu, Junde, E-mail: wjd@zju.edu.cn [School of Mathematical Sciences, Zhejiang University, Hangzhou 310027 (China)
2017-05-18
Highlights: • Quantum coherence. • Cohering power: production of quantum coherence by quantum operations. • Study of cohering power and generalized cohering power, and their comparison for differentmeasures of quantum coherence. • Operational interpretation of cohering power. • Bound on cohering power of a generic quantum operation. - Abstract: Quantum coherence and entanglement, which play a crucial role in quantum information processing tasks, are usually fragile under decoherence. Therefore, the production of quantum coherence by quantum operations is important to preserve quantum correlations including entanglement. In this paper, we study cohering power–the ability of quantum operations to produce coherence. First, we provide an operational interpretation of cohering power. Then, we decompose a generic quantum operation into three basic operations, namely, unitary, appending and dismissal operations, and show that the cohering power of any quantum operation is upper bounded by the corresponding unitary operation. Furthermore, we compare cohering power and generalized cohering power of quantum operations for different measures of coherence.
Isometric Coactions of Compact Quantum Groups on Compact Quantum Metric Spaces
Indian Academy of Sciences (India)
Johan Quaegebeur; Marie Sabbe
2012-08-01
We propose a notion of isometric coaction of a compact quantum group on a compact quantum metric space in the framework of Rieffel, where the metric structure is given by a Lipnorm. Within this setting we study the problem of the existence of a quantum isometry group.
Quantum corrections in massive bigravity and new effective composite metrics
Heisenberg, Lavinia
2015-05-01
We compute the one-loop quantum corrections to the interactions between the two metrics of the ghost-free massive bigravity. When considering gravitons running in the loops, we show how the structure of the interactions gets destabilized at the quantum level, exactly in the same way as in its massive gravity limit. A priori one might have expected a better quantum behavior, however, the broken diffeomorphism invariance out of the two initial diffeomorphisms in bigravity has similar consequences at the quantum level as the broken diffeomorphism in massive gravity. From lessons of the generated quantum corrections through matter loops we propose yet other types of effective composite metrics to which the matter fields can couple. Among these new effective metrics there might be one or more that could provide interesting phenomenology and important cosmological implications.
Quantum corrections in massive bigravity and new effective composite metrics
Heisenberg, Lavinia
2014-01-01
We compute the one-loop quantum corrections to the interactions between the two metrics of the ghost-free massive bigravity. When considering gravitons running in the loops, we show how the structure of the interactions gets destabilized at the quantum level, exactly in the same way as in its massive gravity limit. A priori one might have expected a better quantum behavior, however the broken diffeomorphism invariance out of the two initial diffeomorphisms in bigravity has similar consequences at the quantum level as the broken diffeomorphism in massive gravity. From lessons of the generated quantum corrections through matter loops we propose yet other types of effective composite metrics to which the matter fields can couple. Among these new effective metrics there might be one or more that could provide interesting phenomenology and important cosmological implications.
Operator-based metric for nuclear operations automation assessment
Energy Technology Data Exchange (ETDEWEB)
Zacharias, G.L.; Miao, A.X.; Kalkan, A. [Charles River Analytics Inc., Cambridge, MA (United States)] [and others
1995-04-01
Continuing advances in real-time computational capabilities will support enhanced levels of smart automation and AI-based decision-aiding systems in the nuclear power plant (NPP) control room of the future. To support development of these aids, we describe in this paper a research tool, and more specifically, a quantitative metric, to assess the impact of proposed automation/aiding concepts in a manner that can account for a number of interlinked factors in the control room environment. In particular, we describe a cognitive operator/plant model that serves as a framework for integrating the operator`s information-processing capabilities with his procedural knowledge, to provide insight as to how situations are assessed by the operator, decisions made, procedures executed, and communications conducted. Our focus is on the situation assessment (SA) behavior of the operator, the development of a quantitative metric reflecting overall operator awareness, and the use of this metric in evaluating automation/aiding options. We describe the results of a model-based simulation of a selected emergency scenario, and metric-based evaluation of a range of contemplated NPP control room automation/aiding options. The results demonstrate the feasibility of model-based analysis of contemplated control room enhancements, and highlight the need for empirical validation.
Cosmological implications of modified gravity induced by quantum metric fluctuations
Energy Technology Data Exchange (ETDEWEB)
Liu, Xing [Sun Yat-Sen University, School of Physics, Guangzhou (China); Sun Yat-Sen University, Yat Sen School, Guangzhou (China); Harko, Tiberiu [Babes-Bolyai University, Department of Physics, Cluj-Napoca (Romania); University College London, Department of Mathematics, London (United Kingdom); Liang, Shi-Dong [Sun Yat-Sen University, School of Physics, Guangzhou (China); Sun Yat-Sen University, State Key Laboratory of Optoelectronic Material and Technology, Guangdong Province Key Laboratory of Display Material and Technology, School of Physics, Guangzhou (China)
2016-08-15
We investigate the cosmological implications of modified gravities induced by the quantum fluctuations of the gravitational metric. If the metric can be decomposed as the sum of the classical and of a fluctuating part, of quantum origin, then the corresponding Einstein quantum gravity generates at the classical level modified gravity models with a non-minimal coupling between geometry and matter. As a first step in our study, after assuming that the expectation value of the quantum correction can be generally expressed in terms of an arbitrary second order tensor constructed from the metric and from the thermodynamic quantities characterizing the matter content of the Universe, we derive the (classical) gravitational field equations in their general form. We analyze in detail the cosmological models obtained by assuming that the quantum correction tensor is given by the coupling of a scalar field and of a scalar function to the metric tensor, and by a term proportional to the matter energy-momentum tensor. For each considered model we obtain the gravitational field equations, and the generalized Friedmann equations for the case of a flat homogeneous and isotropic geometry. In some of these models the divergence of the matter energy-momentum tensor is non-zero, indicating a process of matter creation, which corresponds to an irreversible energy flow from the gravitational field to the matter fluid, and which is direct consequence of the non-minimal curvature-matter coupling. The cosmological evolution equations of these modified gravity models induced by the quantum fluctuations of the metric are investigated in detail by using both analytical and numerical methods, and it is shown that a large variety of cosmological models can be constructed, which, depending on the numerical values of the model parameters, can exhibit both accelerating and decelerating behaviors. (orig.)
Cosmological implications of modified gravity induced by quantum metric fluctuations
Liu, Xing; Harko, Tiberiu; Liang, Shi-Dong
2016-08-01
We investigate the cosmological implications of modified gravities induced by the quantum fluctuations of the gravitational metric. If the metric can be decomposed as the sum of the classical and of a fluctuating part, of quantum origin, then the corresponding Einstein quantum gravity generates at the classical level modified gravity models with a non-minimal coupling between geometry and matter. As a first step in our study, after assuming that the expectation value of the quantum correction can be generally expressed in terms of an arbitrary second order tensor constructed from the metric and from the thermodynamic quantities characterizing the matter content of the Universe, we derive the (classical) gravitational field equations in their general form. We analyze in detail the cosmological models obtained by assuming that the quantum correction tensor is given by the coupling of a scalar field and of a scalar function to the metric tensor, and by a term proportional to the matter energy-momentum tensor. For each considered model we obtain the gravitational field equations, and the generalized Friedmann equations for the case of a flat homogeneous and isotropic geometry. In some of these models the divergence of the matter energy-momentum tensor is non-zero, indicating a process of matter creation, which corresponds to an irreversible energy flow from the gravitational field to the matter fluid, and which is direct consequence of the non-minimal curvature-matter coupling. The cosmological evolution equations of these modified gravity models induced by the quantum fluctuations of the metric are investigated in detail by using both analytical and numerical methods, and it is shown that a large variety of cosmological models can be constructed, which, depending on the numerical values of the model parameters, can exhibit both accelerating and decelerating behaviors.
Integration using invariant operators Conformally flat radiation metrics
Edgar, S B
1999-01-01
A new method is presented for obtaining the general conformally flat radiation metric by using the differential operators of Machado Ramos and Vickers (a generalisation of the GHP operators) which are invariant under null rotations and spin and boosts. The solution is found by constructing involutive tables of these derivatives applied to the quantities which arise in the Karlhede classification of metrics.
Energy Emission by Quantum Systems in an Expanding FRW Metric
Sheehan, D P
2004-01-01
Bound quantum mechanical systems not expanding with the comoving frame of an expanding, flat FRW metric are found to release energy at a rate linearly proportional to the local Hubble constant ($H_{o}$) and the systems' binding energy ($E_{b}$); {\\em i.e.}, $\\dot{E} = H_{o} E_{b}$. Three exemplary quantum systems are examined. For systems with early cosmological condensation times | notably hadrons | time-integrated energy release could have been significant and could account for an appreciable fraction of the dark matter inventory.
Monge Metric on the Sphere and Geometry of Quantum States
Zyczkowski, Karol; Slomczynski, Wojciech
2000-01-01
Topological and geometrical properties of the set of mixed quantum states in the N-dimensional Hilbert space are analysed. Assuming that the corresponding classical dynamics takes place on the sphere we use the vector SU(2) coherent states and the generalised Husimi distributions to define the Monge distance between arbitrary two density matrices. The Monge metric has a simple semiclassical interpretation and induces a non-trivial geometry. Among all pure states the distance from the maximall...
Eigentensors of the Lichnerowicz operator in Euclidean Schwarzschild metrics
Energy Technology Data Exchange (ETDEWEB)
Martinez-Morales, J.L. [Instituto de Matematicas, Universidad Nacional Autonoma de Mexico, A. P. 273, Admon. de correos 3, C. P. 62251 Cuernavaca, Morelos (Mexico)
2006-09-01
Properties of the eigentensors of the Lichnerowicz Laplacian for the Euclidean Schwarzschild metric are discussed together with possible applications to the linear stability of higher-dimensional instantons. The main statement of the article is that any eigentensor of the Lichnerowicz operator in a Euclidean (possibly higher-dimensional) Schwarzschild metric is essentially singular at infinity. (Abstract Copyright [2006], Wiley Periodicals, Inc.)
Operational interpretations of quantum discord
Cavalcanti, D; Boixo, S; Modi, K; Piani, M; Winter, A
2010-01-01
Quantum discord is a quantifier of non-classical correlations that goes beyond the standard classification of quantum states into entangled and unentangled ones. Although it has received considerable attention, it still lacks any precise interpretation in terms of some protocol in which quantum features are relevant. Here we give quantum discord its first operational meaning in terms on consumption of entanglement in an extended quantum state merging protocol. We go on to show that the asymmetry of quantum discord is related to the performance imbalance in quantum state merging and dense coding.
Eigenfunction expansion for Schrodinger operators on metric graphs
Lenz, Daniel; Stollmann, Peter
2008-01-01
We construct an expansion in generalized eigenfunctions for Schrodinger operators on metric graphs. We require rather minimal assumptions concerning the graph structure and the boundary conditions at the vertices.
Monge Metric on the Sphere and Geometry of Quantum States
Zyczkowski, K; Zyczkowski, Karol; Slomczynski, Wojciech
2001-01-01
Topological and geometrical properties of the set of mixed quantum states in the N-dimensional Hilbert space are analysed. Assuming that the corresponding classical dynamics takes place on the sphere we use the vector SU(2) coherent states to define the Monge distance between two arbitrary density matrices. The Monge metric has a simple semiclassical interpretation and induce$ a non-trivial geometry. Among all pure states the distance from the maximally mixed state \\rho_*, proportional to the identity matrix, admits the largest value for the coherent states, while the delocalized 'chaotic' states are close to \\rho_*. This contrasts the geometry induced by the standard (trace, Hilbert-Schmidt or Bures) metrics, for which the distance from \\rho_* is the same for all pure states. We discuss possible physical consequences including unitary time evolution and the process of decoherence.
Fredholm Operators and Einstein Metrics on Conformally Compact Manifolds
2001-01-01
The main purpose of this monograph is to give an elementary and self-contained account of the existence of asymptotically hyperbolic Einstein metrics with prescribed conformal infinities sufficiently close to that of a given asymptotically hyperbolic Einstein metric with nonpositive curvature. The proof is based on an elementary derivation of sharp Fredholm theorems for self-adjoint geometric linear elliptic operators on asymptotically hyperbolic manifolds.
Modelling Metrics for Mine Counter Measure Operations
2014-08-01
Refs [22][25]) that was initially developed at DRDC Atlantic and was recently upgraded at DRDC CORA under the Technology Investment Fund (TIF) project...and Yip H. Autonomous underwater vehicles conducting mine countermeasure operations, DRDC CORA TM 2008-42, Oct 08, 54 pages. [14] Nguyen, B. U. and...Contract Report, Jun 06. 46 DRDC-RDDC-2014-R58 List of symbols/abbreviations/acronyms/initialisms CAF Canadian Forces CORA Centre for Operational
Effects of quantum fluctuations of metric on the universe
Yang, Rongjia
2016-09-01
We consider a model of modified gravity from the nonperturbative quantization of a metric. We obtain the modified gravitational field equations and the modified conservational equations. We apply it to the FLRW spacetime and find that due to the quantum fluctuations a bounce universe can be obtained and a decelerated expansion can also possibly be obtained in a dark energy dominated epoch. We also discuss the effects of quantum fluctuations on inflation parameters (such as slow-roll parameters, spectral index, and the spectrum of the primordial curvature perturbation) and find values of parameters in the comparing the predictions of inflation can also work to drive the current epoch of acceleration. We obtain the constraints on the parameter of the theory from the observation of the big bang nucleosynthesis.
Quantum quadratic operators and processes
Mukhamedov, Farrukh
2015-01-01
Covering both classical and quantum approaches, this unique and self-contained book presents the most recent developments in the theory of quadratic stochastic operators and their Markov and related processes. The asymptotic behavior of dynamical systems generated by classical and quantum quadratic operators is investigated and various properties of quantum quadratic operators are studied, providing an insight into the construction of quantum channels. This book is suitable as a textbook for an advanced undergraduate/graduate level course or summer school in quantum dynamical systems. It can also be used as a reference book by researchers looking for interesting problems to work on, or useful techniques and discussions of particular problems. Since it includes the latest developments in the fields of quadratic dynamical systems, Markov processes and quantum stochastic processes, researchers at all levels are likely to find the book inspiring and useful.
Singular Soliton Operators and Indefinite Metrics
Grinevich, P. G.; Novikov, S. P.
2011-01-01
The singular real second order 1D Schrodinger operators are considered here with such potentials that all local solutions near singularities to the eigenvalue problem are meromorphic for all values of the spectral parameter. All algebro-geometrical or "singular finite-gap" potentials satisfy to this condition. A Spectral Theory is constructed here for the periodic and rapidly decreasing cases in the special classes of functions with singularities and indefinite inner product. It has a finite ...
Energy Technology Data Exchange (ETDEWEB)
Bruzda, Wojciech [Mark Kac Complex Systems Research Centre, Institute of Physics, Jagiellonian University, ul. Reymonta 4, 30-059 Krakow (Poland)], E-mail: wojtek@gorce.if.uj.edu.pl; Cappellini, Valerio [Mark Kac Complex Systems Research Centre, Institute of Physics, Jagiellonian University, ul. Reymonta 4, 30-059 Krakow (Poland); Sommers, Hans-Juergen [Fachbereich Physik, Universitaet Duisburg-Essen, Campus Duisburg, 47048 Duisburg (Germany); Zyczkowski, Karol [Mark Kac Complex Systems Research Centre, Institute of Physics, Jagiellonian University, ul. Reymonta 4, 30-059 Krakow (Poland); Centrum Fizyki Teoretycznej, Polska Akademia Nauk, Al. Lotnikow 32/44, 02-668 Warszawa (Poland)
2009-01-12
We define a natural ensemble of trace preserving, completely positive quantum maps and present algorithms to generate them at random. Spectral properties of the superoperator {phi} associated with a given quantum map are investigated and a quantum analogue of the Frobenius-Perron theorem is proved. We derive a general formula for the density of eigenvalues of {phi} and show the connection with the Ginibre ensemble of real non-symmetric random matrices. Numerical investigations of the spectral gap imply that a generic state of the system iterated several times by a fixed generic map converges exponentially to an invariant state.
Remote implementation of quantum operations
Energy Technology Data Exchange (ETDEWEB)
Huelga, Susana F [Quantum Physics Group, STRI, Department of Physics, Astrophysics and Mathematics, University of Hertfordshire, Hatfield, Herts AL10 9AB (United Kingdom); Plenio, Martin B [QOLS, Blackett Laboratory, Imperial College London, London SW7 2BW (United Kingdom); Xiang Guoyong [Key Laboratory of Quantum Information and Department of Physics, University of Science and Technology of China, Hefei 230026 (China); Li Jian [Key Laboratory of Quantum Information and Department of Physics, University of Science and Technology of China, Hefei 230026 (China); Guo Guangcan [Key Laboratory of Quantum Information and Department of Physics, University of Science and Technology of China, Hefei 230026 (China)
2005-10-01
Shared entanglement allows, under certain conditions, the remote implementation of quantum operations. We revise and extend recent theoretical results on the remote control of quantum systems as well as experimental results on the remote manipulation of photonic qubits via linear optical elements.
Remote Implementation of Quantum Operations
Huelga, S F; Xiang, G Y; Guo, J L G C; Huelga, Susana F.; Plenio, Martin B.; Xiang, Guo-Yong; Guo, Jian Li}and Guang-Can
2005-01-01
Shared entanglement allows, under certain conditions, the remote implementation of quantum operations. We revise and extend recent theoretical results on the remote control of quantum systems as well as experimental results on the remote manipulation of photonic qubits via linear optical elements.
Linear operators for quantum mechanics
Jordan, Thomas F
2006-01-01
This compact treatment highlights the logic and simplicity of the mathematical structure of quantum mechanics. Suitable for advanced undergraduates and graduate students, it treats the language of quantum mechanics as expressed in the mathematics of linear operators.Originally oriented toward atomic physics, quantum mechanics became a basic language for solid-state, nuclear, and particle physics. Its grammar consists of the mathematics of linear operators, and with this text, students will find it easier to understand and use the language of physics. Topics include linear spaces and linear fun
Non-selfadjoint operators in quantum physics mathematical aspects
Gazeau, Jean Pierre; Szafraniec, Franciszek Hugon; Znojil, Miloslav
2015-01-01
A unique discussion of mathematical methods with applications to quantum mechanics Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects presents various mathematical constructions influenced by quantum mechanics and emphasizes the spectral theory of non-adjoint operators. Featuring coverage of functional analysis and algebraic methods in contemporary quantum physics, the book discusses recent emergence of the unboundedness of metric operators, which is a serious issue in the study of parity-time-symmetric quantum mechanics. The book also answers mathematical questions that are currently the subject of rigorous analysis, with potentially significant physical consequences. In addition to prompting a discussion of the role of mathematical methods in the contemporary development of quantum physics, the book features: * Chapter contributions written by well-known mathematical physicists who clarify numerous misunderstandings and misnomers while shedding light on new approaches in this growing area *...
Eye Tracking Metrics for Workload Estimation in Flight Deck Operation
Ellis, Kyle; Schnell, Thomas
2010-01-01
Flight decks of the future are being enhanced through improved avionics that adapt to both aircraft and operator state. Eye tracking allows for non-invasive analysis of pilot eye movements, from which a set of metrics can be derived to effectively and reliably characterize workload. This research identifies eye tracking metrics that correlate to aircraft automation conditions, and identifies the correlation of pilot workload to the same automation conditions. Saccade length was used as an indirect index of pilot workload: Pilots in the fully automated condition were observed to have on average, larger saccadic movements in contrast to the guidance and manual flight conditions. The data set itself also provides a general model of human eye movement behavior and so ostensibly visual attention distribution in the cockpit for approach to land tasks with various levels of automation, by means of the same metrics used for workload algorithm development.
Hierarchies of incoherent quantum operations
Streltsov, Alexander; Bera, Manabendra Nath; Lewenstein, Maciej
2015-01-01
The search for a simple description of fundamental physical processes is an important part of quantum theory. One example for such an abstraction can be found in the distance lab paradigm: if two separated parties are connected via a classical channel, it is notoriously difficult to characterize all possible operations these parties can perform. This class of operations is widely known as local operations and classical communication (LOCC). Surprisingly, the situation becomes comparably simple if the more general class of separable operations is considered, a finding which has been extensively used in quantum information theory for many years. Here, we propose a related approach for the resource theory of quantum coherence, where two distant parties can only perform measurements which do not create coherence and can communicate their outcomes via a classical channel. We call this class local incoherent operations and classical communication (LICC). While the characterization of this class is also difficult in...
Quantum Cosmology of Quadratic f(R Theories with a FRW Metric
Directory of Open Access Journals (Sweden)
V. Vázquez-Báez
2017-01-01
Full Text Available We study the quantum cosmology of a quadratic fR theory with a FRW metric, via one of its equivalent Horndeski type actions, where the dynamic of the scalar field is induced. The classical equations of motion and the Wheeler-DeWitt equation, in their exact versions, are solved numerically. There is a free parameter in the action from which two cases follow: inflation + exit and inflation alone. The numerical solution of the Wheeler-DeWitt equation depends strongly on the boundary conditions, which can be chosen so that the resulting wave function of the universe is normalizable and consistent with Hermitian operators.
Unknowability of Quantum State forbids perfectly quantum operations
Institute of Scientific and Technical Information of China (English)
CAIQing-yu; LIBai-wen
2004-01-01
We analyze the oonnection between quantum operations and accessible information. And we find that the accessible information decreases under quantum operations. We show that it is impossible to perfectly manipulate an unknown state in an open quantum system. That the accessible information decreases under quantum operations gives a fundamental limitation in the microscopic world.
Unknowability of Quantum State forbids perfectly quantum operations
Institute of Scientific and Technical Information of China (English)
CAI Qing-yu; LI Bai-wen
2004-01-01
We analyze the connection between quantum operations and accessible information. And we find that the accessible information decreases under quantum operations. We show that it is impossible to perfectly manipulate an unknown state in an open quantum system. That the accessible information decreases under quantum operations gives a fundamental limitation in the microscopic world.
Klauder, J R
1998-01-01
Canonical quantization may be approached from several different starting points. The usual approaches involve promotion of c-numbers to q-numbers, or path integral constructs, each of which generally succeeds only in Cartesian coordinates. All quantization schemes that lead to Hilbert space vectors and Weyl operators---even those that eschew Cartesian coordinates---implicitly contain a metric on a flat phase space. This feature is demonstrated by studying the classical and quantum ``aggregations'', namely, the set of all facts and properties resident in all classical and quantum theories, respectively. Metrical quantization is an approach that elevates the flat phase space metric inherent in any canonical quantization to the level of a postulate. Far from being an unwanted structure, the flat phase space metric carries essential physical information. It is shown how the metric, when employed within a continuous-time regularization scheme, gives rise to an unambiguous quantization procedure that automatically ...
Quantum Hall effect, Quillen metric and holomorphic anomaly
Klevtsov, Semyon; Marinescu, George; Wiegmann, Paul
2015-01-01
We study the generating functional, the adiabatic curvature and the adiabatic phase for the integer quantum Hall effect (QHE) on a compact Riemann surface. For the generating functional we derive its asymptotic expansion for the large flux of the magnetic field, i.e., for the large degree k of the positive Hermitian line bundle $L^k$. The expansion consists of the anomalous and exact terms. The anomalous terms are the leading terms of the expansion. This part is responsible for the quantization of the adiabatic transport coefficients in QHE. We then identify the anomalous part of the expansion with the Quillen metric on the determinant line bundle, and the subleading exact part with the asymptotics of the regularized spectral determinant of the Laplacian for the line bundle $L^k$, at large k. Finally, we show how the generating functional of the integer QHE is related to the gauge and gravitational (2+1)d Chern-Simons functionals. We observe the relation between the Bismut-Gillet-Soul\\'e curvature formula for...
Operator methods in quantum mechanics
Schechter, Martin
2003-01-01
This advanced undergraduate and graduate-level text introduces the power of operator theory as a tool in the study of quantum mechanics, assuming only a working knowledge of advanced calculus and no background in physics. The author presents a few simple postulates describing quantum theory, gradually introducing the mathematical techniques that help answer questions important to the physical theory; in this way, readers see clearly the purpose of the method and understand the accomplishment. The entire book is devoted to the study of a single particle moving along a straight line. By posing q
Metric Extension Operators, Vertex Sparsifiers and Lipschitz Extendability
Makarychev, Konstantin
2010-01-01
We study vertex cut and flow sparsifiers that were recently introduced by Moitra, and Leighton and Moitra. We improve and generalize their results. We give a new polynomial-time algorithm for constructing O(log k / log log k) cut and flow sparsifiers, matching the best existential upper bound on the quality of a sparsifier, and improving the previous algorithmic upper bound of O(log^2 k / log log k). We show that flow sparsifiers can be obtained from linear operators approximating minimum metric extensions. We introduce the notion of (linear) metric extension operators, prove that they exist, and give an exact polynomial-time algorithm for finding optimal operators. We then establish a direct connection between flow and cut sparsifiers and Lipschitz extendability of maps in Banach spaces, a notion studied in functional analysis since 1950s. Using this connection, we prove a lower bound of \\Omega(\\sqrt{log k/log log k}) for flow sparsifiers and a lower bound of \\Omega(\\sqrt[4]{log k/log log k}) for cut sparsif...
Quadratic relativistic invariant and metric form in quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Pissondes, Jean-Claude [DAEC, Observatoire de Paris-Meudon, Meudon (France)
1999-04-16
The Klein-Gordon equation is recovered in the framework of the theory of scale-relativity, first in the absence, then in the presence of an electromagnetic field. In this framework, spacetime at quantum scales is characterized by non-differentiability and continuity, which involves the introduction of explicit resolution-dependent fractal coordinates. Such a description leads to the notion of scale-covariance and its corresponding tool, a scale-covariant; derivative operator {theta}/ds. Due to it, the Klein-Gordon equation is written as an equation of free motion and interpreted as a geodesic equation in fractal spacetime. However, we obtain a new form for the corresponding relativistic invariant, which differs from that of special and general relativity. Characterizing quantum mechanics in the present approach, it is not simply quadratic in terms of velocities, but contains an extra term of divergence, which is intrinsically present in its expression. Moreover, in spite of the scale-covariance statements of the present theory, we find an extra term of current in addition to the Lorentz force, within the equations of motion with electromagnetic field written in this framework. Finally, we introduce another tool - a 'symmetric product' - from the requirement of recovering the usual form of the Leibniz rule written with the operator {theta}/ds. This tool allows us to write most equations in this framework in their usual classical form; in particular the simple rules of differentiation, the equations of motion with field and also our new relativistic invariant. (author)
Singular finite-gap operators and indefinite metrics
Grinevich, Petr G.; Novikov, Sergei P.
2009-08-01
In many problems the 'real' spectral data for periodic finite-gap operators (consisting of a Riemann surface with a distingulished 'point at infinity', a local parameter near this point, and a divisor of poles) generate operators with singular real coefficients. These operators are not self-adjoint in an ordinary Hilbert space of functions of a variable x (with a positive metric). In particular, this happens for the Lamé operators with elliptic potential n(n+1)\\wp(x), whose wavefunctions were found by Hermite in the nineteenth century. However, ideas in [1]-[4] suggest that precisely such Baker-Akhiezer functions form a correct analogue of the discrete and continuous Fourier bases on Riemann surfaces. For genus g>0 these operators turn out to be symmetric with respect to an indefinite (not positive definite) inner product described in this paper. The analogue of the continuous Fourier transformation is an isometry in this inner product. A description is also given of the image of this Fourier transformation in the space of functions of x\\in R. Bibliography: 24 titles.
Metrics required for Power System Resilient Operations and Protection
Energy Technology Data Exchange (ETDEWEB)
Eshghi, K.; Johnson, B. K.; Rieger, C. G.
2016-08-01
Today’s complex grid involves many interdependent systems. Various layers of hierarchical control and communication systems are coordinated, both spatially and temporally to achieve gird reliability. As new communication network based control system technologies are being deployed, the interconnected nature of these systems is becoming more complex. Deployment of smart grid concepts promises effective integration of renewable resources, especially if combined with energy storage. However, without a philosophical focus on resilience, a smart grid will potentially lead to higher magnitude and/or duration of disruptive events. The effectiveness of a resilient infrastructure depends upon its ability to anticipate, absorb, adapt to, and/or rapidly recover from a potentially catastrophic event. Future system operations can be enhanced with a resilient philosophy through architecting the complexity with state awareness metrics that recognize changing system conditions and provide for an agile and adaptive response. The starting point for metrics lies in first understanding the attributes of performance that will be qualified. In this paper, we will overview those attributes and describe how they will be characterized by designing a distributed agent that can be applied to the power grid.
Quantum Image Encryption Algorithm Based on Quantum Image XOR Operations
Gong, Li-Hua; He, Xiang-Tao; Cheng, Shan; Hua, Tian-Xiang; Zhou, Nan-Run
2016-07-01
A novel encryption algorithm for quantum images based on quantum image XOR operations is designed. The quantum image XOR operations are designed by using the hyper-chaotic sequences generated with the Chen's hyper-chaotic system to control the control-NOT operation, which is used to encode gray-level information. The initial conditions of the Chen's hyper-chaotic system are the keys, which guarantee the security of the proposed quantum image encryption algorithm. Numerical simulations and theoretical analyses demonstrate that the proposed quantum image encryption algorithm has larger key space, higher key sensitivity, stronger resistance of statistical analysis and lower computational complexity than its classical counterparts.
Entanglement Mapping VS. Quantum Conditional Probability Operator
Chruściński, Dariusz; Kossakowski, Andrzej; Matsuoka, Takashi; Ohya, Masanori
2011-01-01
The relation between two methods which construct the density operator on composite system is shown. One of them is called an entanglement mapping and another one is called a quantum conditional probability operator. On the base of this relation we discuss the quantum correlation by means of some types of quantum entropy.
General description of discriminating quantum operations
Institute of Scientific and Technical Information of China (English)
Zhang Ke-Jia; Zhu Ping; Gao Fei; Guo Fen-Zhuo; Qin Su-Juan; Wen Qiao-Yan
2011-01-01
The discrimination of quantum operations plays a key role in quantum information and computation.Unlike discriminating quantum states,it has some special properties which can be carried out in practice.In this paper,we provide a general description of discriminating quantum operations.Concretely speaking,we describe the distinguishability between quantum operations using a measure called operator fidelity.It is shown that,employing the theory of operator fidelity,we can not only verify some previous results to discriminate unitary operations,but also exhibit a more general discrimination condition.We further apply our results to analysing the security of some quantum cryptographic protocols and discuss the realization of our method using well-developed quantum algorithms.
Atomic quantum transistor based on swapping operation
Moiseev, Sergey A; Moiseev, Eugene S
2011-01-01
We propose an atomic quantum transistor based on exchange by virtual photons between two atomic systems through the control gate-atom. The quantum transistor is realized in two QED cavities coupled in nano-optical scheme. We have found novel effect in quantum dynamics of coupled three-node atomic system which provides control-SWAP(\\theta) processes in quantum transistor operation. New possibilities of quantum entanglement in an example of bright and dark qubit states have been demonstrated for quantum transport in the atomic chain. Potentialities of the proposed nano-optical design for quantum computing and fundamental issues of multi-atomic physics are also discussed.
A quantum genetic algorithm with quantum crossover and mutation operations
SaiToh, Akira; Rahimi, Robabeh; Nakahara, Mikio
2013-11-01
In the context of evolutionary quantum computing in the literal meaning, a quantum crossover operation has not been introduced so far. Here, we introduce a novel quantum genetic algorithm that has a quantum crossover procedure performing crossovers among all chromosomes in parallel for each generation. A complexity analysis shows that a quadratic speedup is achieved over its classical counterpart in the dominant factor of the run time to handle each generation.
Difference equations of quantum current operators and quantum parafermion construction
Ding, J; Ding, Jintai; Feigin, Boris
1996-01-01
For the current realization of the affine quantum groups, a simple comultiplication for the quantum current operators was given by Drinfeld. With this comultiplication, we prove that, for the integrable modules of $U_q(\\hat x^\\pm(zq^{\\pm 2k})$ are vertex operators satisfying certain q-difference equations, and we derive the quantum parafermions of $U_q(\\hat {\\frak sl}(2))$.
Remote Operation on Quantum State Among Multiparty
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In this paper, a scheme is proposed for performing remote operation on quantum state among multiparty.We use three-particle GHZ state as quantum channels to prepare a state operator, which describes quantum correlation between states and operations. Based on the special characteristic of the state operator, observers can perform unitary operation on a system that is away from observers. Our studies show this process is deterministic. We further consider remote operation among N spatially distributed observers, and the results show the successful realization of remote operation needs collective participation of N parties, that is, there exists strong correlation among multiparty. In addition, we investigate the case in which observers share a three-particle W state as quantum channels to perform remote operation and studies find this process is probabilistic.
The operational meaning of quantum conditional information
Devetak, I; Devetak, Igor; Yard, Jon
2006-01-01
With a statistical view towards information and noise, information theory derives ultimate limitations on information processing tasks. These limits are generally expressed in terms of entropic measures of information and correlations. Here we answer the quantum information-theoretic question: ``How correlated are two quantum systems from the perspective of a third?" by solving the following `quantum state redistribution' problem. Given an arbitrary quantum state of three systems, where Alice holds two and Bob holds one, what is the cost, in terms of quantum communication and entanglement, for Alice to give one of her parts to Bob? The communication cost gives the first operational interpretation to quantum conditional mutual information. The optimal procedure is self-dual under time reversal and is perfectly composable. This generalizes known protocols such as the state merging and fully quantum Slepian-Wolf protocols, from which almost every known protocol in quantum Shannon theory can be derived.
Comparison of the Cost Metrics for Reversible and Quantum Logic Synthesis
Miller, D M; Maslov, Dmitri
2005-01-01
A breadth-first search method for determining optimal 3-line circuits composed of quantum NOT, CNOT, controlled-V and controlled-V+ (NCV) gates is introduced. Results are presented for simple gate count and for technology motivated cost metrics. The optimal NCV circuits are also compared to NCV circuits derived from optimal NOT, CNOT and Toffoli (NCT) gate circuits. The work presented here provides basic results and motivation for continued study of the direct synthesis of NCV circuits, and establishes relations between function realizations in different circuit cost metrics.
Quantum theory with bold operator tensors.
Hardy, Lucien
2015-08-06
In this paper, we present a formulation of quantum theory in terms of bold operator tensors. A circuit is built up of operations where an operation corresponds to a use of an apparatus. We associate collections of operator tensors (which together comprise a bold operator) with these apparatus uses. We give rules for combining bold operator tensors such that, for a circuit, they give a probability distribution over the possible outcomes. If we impose certain physicality constraints on the bold operator tensors, then we get exactly the quantum formalism. We provide both symbolic and diagrammatic ways to represent these calculations. This approach is manifestly covariant in that it does not require us to foliate the circuit into time steps and then evolve a state. Thus, the approach forms a natural starting point for an operational approach to quantum field theory.
The quantum phase operator a review
Barnett, Stephen M
2013-01-01
Describing the phase of an electromagnetic field mode or harmonic oscillator has been an obstacle since the early days of modern quantum theory. The quantum phase operator was even more problematic with the invention of the maser and laser in the 1950s and 1960s. This problem was not solved until the Pegg-Barnett formalism was developed in the 1980s. Edited by one of the scientists who created this key solution, The Quantum Phase Operator: A Review charts the development of phase and angle operators from their first appearance to modern theory. Bringing together vital works that have been publ
Simulation of n-qubit quantum systems. III. Quantum operations
Radtke, T.; Fritzsche, S.
2007-05-01
During the last decade, several quantum information protocols, such as quantum key distribution, teleportation or quantum computation, have attracted a lot of interest. Despite the recent success and research efforts in quantum information processing, however, we are just at the beginning of understanding the role of entanglement and the behavior of quantum systems in noisy environments, i.e. for nonideal implementations. Therefore, in order to facilitate the investigation of entanglement and decoherence in n-qubit quantum registers, here we present a revised version of the FEYNMAN program for working with quantum operations and their associated (Jamiołkowski) dual states. Based on the implementation of several popular decoherence models, we provide tools especially for the quantitative analysis of quantum operations. Apart from the implementation of different noise models, the current program extension may help investigate the fragility of many quantum states, one of the main obstacles in realizing quantum information protocols today. Program summaryTitle of program: Feynman Catalogue identifier: ADWE_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWE_v3_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: None Operating systems: Any system that supports MAPLE; tested under Microsoft Windows XP, SuSe Linux 10 Program language used:MAPLE 10 Typical time and memory requirements: Most commands that act upon quantum registers with five or less qubits take ⩽10 seconds of processor time (on a Pentium 4 processor with ⩾2 GHz or equivalent) and 5-20 MB of memory. Especially when working with symbolic expressions, however, the memory and time requirements critically depend on the number of qubits in the quantum registers, owing to the exponential dimension growth of the associated Hilbert space. For example, complex (symbolic) noise models (with several Kraus operators) for multi-qubit systems
Operator representations on quantum spaces
Energy Technology Data Exchange (ETDEWEB)
Bauer, C.; Wachter, H. [Sektion Physik, Ludwig-Maximilians-Universitaet, Theresienstr. 37, 80333, Muenchen (Germany)
2003-11-01
In this article we present explicit formulae for q-differentiation on quantum spaces which could be of particular importance in physics, i.e., q-deformed Minkowski space and q-deformed Euclidean space in three or four dimensions. The calculations are based on the covariant differential calculus of these quantum spaces. Furthermore, our formulae can be regarded as a generalization of Jackson's q-derivative to three and four dimensions. (orig.)
Operator approximant problems arising from quantum theory
Maher, Philip J
2017-01-01
This book offers an account of a number of aspects of operator theory, mainly developed since the 1980s, whose problems have their roots in quantum theory. The research presented is in non-commutative operator approximation theory or, to use Halmos' terminology, in operator approximants. Focusing on the concept of approximants, this self-contained book is suitable for graduate courses.
The operator tensor formulation of quantum theory.
Hardy, Lucien
2012-07-28
In this paper, we provide what might be regarded as a manifestly covariant presentation of discrete quantum theory. A typical quantum experiment has a bunch of apparatuses placed so that quantum systems can pass between them. We regard each use of an apparatus, along with some given outcome on the apparatus (a certain detector click or a certain meter reading for example), as an operation. An operation (e.g. B(b(2)a(3))(a(1))) can have zero or more quantum systems inputted into it and zero or more quantum systems outputted from it. The operation B(b(2)a(3))(a(1)) has one system of type a inputted, and one system of type b and one system of type a outputted. We can wire together operations to form circuits, for example, A(a(1))B(b(2)a(3))(a(1))C(b(2)a(3)). Each repeated integer label here denotes a wire connecting an output to an input of the same type. As each operation in a circuit has an outcome associated with it, a circuit represents a set of outcomes that can happen in a run of the experiment. In the operator tensor formulation of quantum theory, each operation corresponds to an operator tensor. For example, the operation B(b(2)a(3))(a(1)) corresponds to the operator tensor B(b(2)a(3))(a(1)). Further, the probability for a general circuit is given by replacing operations with corresponding operator tensors as in Prob(A(a(1))B(b(2)a(3))(a(1))C(b(2)a(3))) = Â(a(1))B(b(2)a(3))(a(1))C(b(2)a(3)). Repeated integer labels indicate that we multiply in the associated subspace and then take the partial trace over that subspace. Operator tensors must be physical (namely, they must have positive input transpose and satisfy a certain normalization condition).
Quantum remote control Teleportation of unitary operations
Huelga, S F; Chefles, A; Plenio, M B
2001-01-01
We consider the implementation of an unknown arbitrary unitary operation U upon a distant quantum system. This teleportation of U can be viewed as a quantum remote control. We investigate the protocols which achieve this using local operations, classical communication and shared entanglement (LOCCSE). Lower bounds on the necessary entanglement and classical communication are determined using causality and the linearity of quantum mechanics. We examine in particular detail the resources required if the remote control is to be implemented as a classical black box. Under these circumstances, we prove that the required resources are, necessarily, those needed for implementation by bidirectional state teleportation.
On spectral theory of quantum vertex operators
Etingof, P
1994-01-01
In this note we prove the Davies-Foda-Jimbo-Miwa-Nakayashiki conjecture on the asymptotics of the composition of n quantum vertex operators for the quantum affine algebra U_q(\\hat sl_2), as n goes to infinity. For this purpose we define and study the leading eigenvalue and eigenvector of the product of two components of the quantum vertex operator. This eigenvector and the corresponding eigenvalue were recently computed by M.Jimbo. The results of his computation are given in Section 4.
Evaluation of Standard Gear Metrics in Helicopter Flight Operation
Mosher, M.; Pryor, A. H.; Huff, E. M.
2002-01-01
Each false alarm made by a machine monitoring system carries a high price tag. The machine must be taken out of service, thoroughly inspected with possible disassembly, and then made ready for service. Loss of use of the machine and the efforts to inspect it are costly. In addition, if a monitoring system is prone to false alarms, the system will soon be turned off or ignored. For aircraft applications, one growing concern is that the dynamic flight environment differs from the laboratory environment where fault detection methods are developed and tested. Vibration measurements made in flight are less stationary than those made in a laboratory, or test facility, and thus a given fault detection method may produce more false alarms in flight than might be anticipated. In 1977. Stewart introduced several metrics, including FM0 and FM4, for evaluating the health of a gear. These metrics are single valued functions of the vibration signal that indicate if the signal deviates from an ideal model of the signal. FM0 is a measure of the ratio of the peak-to-peak level to the harmonic energy in the signal. FM4 is the kurtosis of the signal with the gear mesh harmonics and first order side bands removed. The underlying theory is that a vibration signal from a gear in good condition is expected to be dominated by a periodic signal at the gear mesh frequency. If one or a small number of gear teeth contain damage or faults, the signal will change, possibly showing increased amplitude, local phase changes or both near the damaged region of the gear. FM0 increases if a signal contains a local increase in amplitude. FM4 increases if a signal contains a local increase in amplitude or local phase change in a periodic signal. Over the years, other single value metrics were also introduced to detect the onset and growth of damage in gears. These various metrics have detected faults in several gear tests in experimental test rigs. Conditions in these tests have been steady state in the
A class of symmetric controlled quantum operations
Vaccaro, J A; Huelga, S F; Vaccaro, John A.
2001-01-01
Certain quantum gates, such as the controlled-NOT gate, are symmetric in terms of the operation of the control system upon the target system and vice versa. However, no operational criteria yet exist for establishing whether or not a given quantum gate is symmetrical in this sense. We consider a restricted, yet broad, class of two-party controlled gate operations for which the gate transforms a reference state of the target into one of an orthogonal set of states. We show that for this class of gates it is possible to establish a simple necessary and sufficient condition for the gate operation to be symmetric.
A class of symmetric controlled quantum operations
Energy Technology Data Exchange (ETDEWEB)
Vaccaro, John A.; Steuernagel, O.; Huelga, S.F. [Division of Physics and Astronomy, Department of Physical Sciences, University of Hertfordshire, Hatfield (United Kingdom)
2001-09-07
Certain quantum gates, such as the controlled-NOT gate, are symmetric in terms of the operation of the control system upon the target system and vice versa. However, no operational criteria yet exist for establishing whether or not a given quantum gate is symmetrical in this sense. We consider a restricted, yet broad, class of two-party controlled gate operations for which the gate transforms a reference state of the target into one of an orthogonal set of states. We show that for this class of gates it is possible to establish a simple necessary and sufficient condition for the gate operation to be symmetric. (author)
Comment on ``New ansatz for metric operator calculation in pseudo-Hermitian field theory''
Bender, Carl M.; Benincasa, Gregorio; Jones, H. F.
2009-12-01
In a recent Brief Report by Shalaby, a new first-order perturbative calculation of the metric operator for an iϕ3 scalar field theory is given. It is claimed that the incorporation of derivative terms in the ansatz for the metric operator results in a local solution, in contrast to the nonlocal solution previously obtained by Bender, Brody, and Jones. Unfortunately, Shalaby’s calculation is not valid because of sign errors.
Unknown Quantum States and Operations, a Bayesian View
Fuchs, C; Fuchs, Christopher A.; Schack, Ruediger
2004-01-01
The classical de Finetti theorem provides an operational definition of the concept of an unknown probability in Bayesian probability theory, where probabilities are taken to be degrees of belief instead of objective states of nature. In this paper, we motivate and review two results that generalize de Finetti's theorem to the quantum mechanical setting: Namely a de Finetti theorem for quantum states and a de Finetti theorem for quantum operations. The quantum-state theorem, in a closely analogous fashion to the original de Finetti theorem, deals with exchangeable density-operator assignments and provides an operational definition of the concept of an "unknown quantum state" in quantum-state tomography. Similarly, the quantum-operation theorem gives an operational definition of an "unknown quantum operation" in quantum-process tomography. These results are especially important for a Bayesian interpretation of quantum mechanics, where quantum states and (at least some) quantum operations are taken to be states ...
Raising and lowering operators for quantum billiards
Indian Academy of Sciences (India)
AYUSH KUMAR MANDWAL; SUDHIR R JAIN
2017-09-01
For planar integrable billiards, the eigenstates can be classified with respect to a quantity determined by the quantum numbers. Given the quantum numbers as $m$, $n$, the index which represents a class is $c = m$ mod $kn$ for a natural number, $k$. We show here that the entire tower of states can be generated from an initially given state by the application of the operators introduced here. Thus, these operators play the same role for billiards as raising and lowering operators in angular momentum algebra.
The Monge metric on the sphere and geometry of quantum states
Energy Technology Data Exchange (ETDEWEB)
Zyczkowski, Karol [Centrum Fizyki Teoretycznej, Polska Akademia Nauk, Warsaw (Poland); Instytut Fizyki im. Mariana Smoluchowskiego, Uniwersytet Jagiellonski, Cracow (Poland)). E-mail: karol@cft.edu.pl; Slomczynski, Wojciech [Instytut Matematyki, Uniwersytet Jagiellonski, Cracow (Poland)). E-mail: slomczyn@im.uj.edu.pl
2001-08-31
Topological and geometrical properties of the set of mixed quantum states in the N-dimensional Hilbert space are analysed. Assuming that the corresponding classical dynamics takes place on the sphere we use the vector SU(2) coherent states and the generalized Husimi distributions to define the Monge distance between two arbitrary density matrices. The Monge metric has a simple semiclassical interpretation and induces a non-trivial geometry. Among all pure states the distance from the maximally mixed state {rho}*, proportional to the identity matrix, admits the largest value for the coherent states, while the delocalized 'chaotic' states are close to {rho}*. This contrasts the geometry induced by the standard (trace, Hilbert-Schmidt or Bures) metrics, for which the distance from {rho}* is the same for all pure states. We discuss possible physical consequences including unitary time evolution and the process of decoherence. We introduce also a simplified Monge metric, defined in the space of pure quantum states and more suitable for numerical computation. (author)
New length operator for loop quantum gravity
Ma, Yongge; Yang, Jinsong
2010-01-01
An alternative expression for the length operator in loop quantum gravity is presented. The operator is background-independent, symmetric, positive semi-definite, and well-defined on the kinematical Hilbert space. The expression for the regularized length operator can moreover be understood both from a simple geometrical perspective as the average of a formula relating the length to area, volume and flux operators, and also consistently as the result of direct substitution of the densitized triad operator with the functional derivative operator into the regularized expression of the length. Both these derivations are discussed, and the origin of an undetermined overall factor in each case is also elucidated.
Hilbert Space Operators in Quantum Physics
Blank, Jiří; Havlíček, Miloslav
2008-01-01
The second edition of this course-tested book provides a detailed and in-depth discussion of the foundations of quantum theory as well as its applications to various systems. The exposition is self-contained; in the first part the reader finds the mathematical background in chapters about functional analysis, operators on Hilbert spaces and their spectral theory, as well as operator sets and algebras. This material is used in the second part to a systematic explanation of the foundations, in particular, states and observables, properties of canonical variables, time evolution, symmetries and various axiomatic approaches. In the third part, specific physical systems and situations are discussed. Two chapters analyze Schrödinger operators and scattering, two others added in the second edition are devoted to new important topics, quantum waveguides and quantum graphs. Some praise for the previous edition: "I really enjoyed reading this work. It is very well written, by three real experts in the field. It stands...
Entropic characterization of quantum operations
Roga, Wojciech; Zyczkowski, Karol
2011-01-01
We investigate decoherence induced by a quantum channel in terms of minimal output entropy and of map entropy. The latter is the von Neumann entropy of the Jamiolkowski state of the channel. Both quantities admit q-Renyi versions. We prove additivity of the map entropy for all q. For the case q = 2, we show that the depolarizing channel has the smallest map entropy among all channels with a given minimal output Renyi entropy of order two. This allows us to characterize pairs of channels such that the output entropy of their tensor product acting on a maximally entangled input state is larger than the sum of the minimal output entropies of the individual channels. We conjecture that for any channel {\\Phi}1 acting on a finite dimensional system there exists a class of channels {\\Phi}2 sufficiently close to a unitary map such that additivity of minimal output entropy for {\\Psi}1 x {\\Psi}2 holds.
Operational meaning of quantum measures of recovery
Cooney, Tom; Hirche, Christoph; Morgan, Ciara; Olson, Jonathan P.; Seshadreesan, Kaushik P.; Watrous, John; Wilde, Mark M.
2016-08-01
Several information measures have recently been defined that capture the notion of recoverability. In particular, the fidelity of recovery quantifies how well one can recover a system A of a tripartite quantum state, defined on systems A B C , by acting on system C alone. The relative entropy of recovery is an associated measure in which the fidelity is replaced by relative entropy. In this paper we provide concrete operational interpretations of the aforementioned recovery measures in terms of a computational decision problem and a hypothesis testing scenario. Specifically, we show that the fidelity of recovery is equal to the maximum probability with which a computationally unbounded quantum prover can convince a computationally bounded quantum verifier that a given quantum state is recoverable. The quantum interactive proof system giving this operational meaning requires four messages exchanged between the prover and verifier, but by forcing the prover to perform actions in superposition, we construct a different proof system that requires only two messages. The result is that the associated decision problem is in QIP(2) and another argument establishes it as hard for QSZK (both classes contain problems believed to be difficult to solve for a quantum computer). We finally prove that the regularized relative entropy of recovery is equal to the optimal type II error exponent when trying to distinguish many copies of a tripartite state from a recovered version of this state, such that the type I error is constrained to be no larger than a constant.
Singular Finite-Gap Operators and Indefinite Metric. I
Grinevich, P
2009-01-01
Many "real" inverse spectral data for periodic finite-gap operators (consisting of Riemann Surface with marked "infinite point", local parameter and divisors of poles) lead to operators with real but singular coefficients. These operators cannot be considered as self-adjoint in the ordinary (positive) Hilbert spaces of functions of x. In particular, it is true for the special case of Lame operators with elliptic potential $n(n+1)\\wp(x)$ where eigenfunctions were found in XIX Century by Hermit. However, such Baker-Akhiezer (BA) functions present according to the ideas of works by Krichever-Novikov (1989), Grinevich-Novikov (2001) right analog of the Discrete and Continuous Fourier Bases on Riemann Surfaces. It turns out that these operators for the nonzero genus are symmetric in some indefinite inner product, described in this work. The analog of Continuous Fourier Transform is an isometry in this inner product. In the next work with number II we will present exposition of the similar theory for Discrete Fouri...
Quantum Algorithm for K-Nearest Neighbors Classification Based on the Metric of Hamming Distance
Ruan, Yue; Xue, Xiling; Liu, Heng; Tan, Jianing; Li, Xi
2017-08-01
K-nearest neighbors (KNN) algorithm is a common algorithm used for classification, and also a sub-routine in various complicated machine learning tasks. In this paper, we presented a quantum algorithm (QKNN) for implementing this algorithm based on the metric of Hamming distance. We put forward a quantum circuit for computing Hamming distance between testing sample and each feature vector in the training set. Taking advantage of this method, we realized a good analog for classical KNN algorithm by setting a distance threshold value t to select k - n e a r e s t neighbors. As a result, QKNN achieves O(n 3) performance which is only relevant to the dimension of feature vectors and high classification accuracy, outperforms Llyod's algorithm (Lloyd et al. 2013) and Wiebe's algorithm (Wiebe et al. 2014).
Effective operator formalism for open quantum systems
DEFF Research Database (Denmark)
Reiter, Florentin; Sørensen, Anders Søndberg
2012-01-01
We present an effective operator formalism for open quantum systems. Employing perturbation theory and adiabatic elimination of excited states for a weakly driven system, we derive an effective master equation which reduces the evolution to the ground-state dynamics. The effective evolution...
Control through operators for quantum chemistry
Laurent, Philippe; Salomon, Julien; Turinici, Gabriel
2012-01-01
We consider the problem of operator identification in quantum control. The free Hamiltonian and the dipole moment are searched such that a given target state is reached at a given time. A local existence result is obtained. As a by-product, our works reveals necessary conditions on the laser field to make the identification feasible. In the last part of this work, some algorithms are proposed to compute effectively these operators.
Classical and quantum dynamics of a perfect fluid scalar-energy dependent metric cosmology
Khodadi, M.; Nozari, K.; Vakili, B.
2016-05-01
Inspired from the idea of minimally coupling of a real scalar field to geometry, we investigate the classical and quantum models of a flat energy-dependent FRW cosmology coupled to a perfect fluid in the framework of the scalar-rainbow metric gravity. We use the standard Schutz' representation for the perfect fluid and show that under a particular energy-dependent gauge fixing, it may lead to the identification of a time parameter for the corresponding dynamical system. It is shown that, under some circumstances on the minisuperspace prob energy, the classical evolution of the of the universe represents a late time expansion coming from a bounce instead of the big-bang singularity. Then we go forward by showing that this formalism gives rise to a Schrödinger-Wheeler-DeWitt equation for the quantum-mechanical description of the model under consideration, the eigenfunctions of which can be used to construct the wave function of the universe. We use the resulting wave function in order to investigate the possibility of the avoidance of classical singularities due to quantum effects by means of the many-worlds and Bohmian interpretation of quantum cosmology.
Quantum Gravity and a Time Operator in Relativistic Quantum Mechanics
Bauer, M
2016-01-01
The problem of time in the quantization of gravity arises from the fact that time in Schroedinger's equation is a parameter. This sets time apart from the spatial coordinates, represented by operators in quantum mechanics (QM). Thus "time" in QM and "time" in General Relativity (GR) are seen as mutually incompatible notions. The introduction of a dy- namical time operator in relativistic quantum mechanics (RQM), that in the Heisenberg representation is also a function of the parameter t (iden- tifed as the laboratory time), prompts to examine whether it can help to solve the disfunction referred to above. In particular, its application to the conditional interpretation of the canonical quantization approach toquantum gravity is developed. 1
Quantum operations: technical or fundamental challenge?
Mielnik, Bogdan
2013-09-01
A class of unitary operations generated by idealized, semiclassical fields is studied. The operations implemented by sharp potential kicks are revisited and the possibility of performing them by softly varying external fields is examined. The possibility of using the ion traps as ‘operation factories’ transforming quantum states is discussed. The non-perturbative algorithms indicate that the results of abstract δ-pulses of oscillator potentials can become real. Some of them, if empirically achieved, could be essential to examine certain atypical quantum ideas. In particular, simple dynamical manipulations might contribute to the Aharonov-Bohm criticism of the time-energy uncertainty principle, while some others may verify the existence of fundamental precision limits of the position measurements or the reality of ‘non-commutative geometries’.
Check-Operators and Quantum Spectral Curves
Mironov, Andrei; Morozov, Alexei
2017-06-01
We review the basic properties of effective actions of families of theories (i.e., the actions depending on additional non-perturbative moduli along with perturbative couplings), and their description in terms of operators (called check-operators), which act on the moduli space. It is this approach that led to constructing the (quantum) spectral curves and what is now nicknamed the EO/AMM topological recursion. We explain how the non-commutative algebra of check-operators is related to the modular kernels and how symplectic (special) geometry emerges from it in the classical (Seiberg-Witten) limit, where the quantum integrable structures turn into the well studied classical integrability. As time goes, these results turn applicable to more and more theories of physical importance, supporting the old idea that many universality classes of low-energy effective theories contain matrix model representatives.
Ding, J; Ding, Jintai; Feigin, Boris
1996-01-01
We construct a commutative current operator $\\bar x^+(z)$ inside $U_q(\\hat{\\frak sl}(2))$. With this operator and the condition of quantum integrability on the quantum current of $U_q(\\hat{\\frak sl}(2))$, we derive the quantization of the semi-infinite construction of integrable modules of The quantization of the functional models for $\\hat{\\frak sl}(2)$ are also given.
Operating room metrics score card-creating a prototype for individualized feedback.
Gabriel, Rodney A; Gimlich, Robert; Ehrenfeld, Jesse M; Urman, Richard D
2014-11-01
The balance between reducing costs and inefficiencies with that of patient safety is a challenging problem faced in the operating room suite. An ongoing challenge is the creation of effective strategies that reduce these inefficiencies and provide real-time personalized metrics and electronic feedback to anesthesia practitioners. We created a sample report card structure, utilizing existing informatics systems. This system allows to gather and analyze operating room metrics for each anesthesia provider and offer personalized feedback. To accomplish this task, we identified key metrics that represented time and quality parameters. We collected these data for individual anesthesiologists and compared performance to the overall group average. Data were presented as an electronic score card and made available to individual clinicians on a real-time basis in an effort to provide effective feedback. These metrics included number of cancelled cases, average turnover time, average time to operating room ready and patient in room, number of delayed first case starts, average induction time, average extubation time, average time to recovery room arrival to discharge, performance feedback from other providers, compliance to various protocols, and total anesthetic costs. The concept we propose can easily be generalized to a variety of operating room settings, types of facilities and OR health care professionals. Such a scorecard can be created using content that is important for operating room efficiency, research, and practice improvement for anesthesia providers.
Effective operator formalism for open quantum systems
DEFF Research Database (Denmark)
Reiter, Florentin; Sørensen, Anders Søndberg
2012-01-01
We present an effective operator formalism for open quantum systems. Employing perturbation theory and adiabatic elimination of excited states for a weakly driven system, we derive an effective master equation which reduces the evolution to the ground-state dynamics. The effective evolution...... involves a single effective Hamiltonian and one effective Lindblad operator for each naturally occurring decay process. Simple expressions are derived for the effective operators which can be directly applied to reach effective equations of motion for the ground states. We compare our method...
Finding of the Metric Operator for a Quasi-Hermitian Model
Directory of Open Access Journals (Sweden)
Ebru Ergun
2013-01-01
Full Text Available We consider on an appropriate Sobolev space a non-Hermitian Hamiltonian depending on the two complex parameters α and β and having real spectrum. We derive a closed formula for a family of the metric operators, which render the Hamiltonian Hermitian. In some particular cases, we calculate the Hermitian counterpart of .
Real Time Metrics and Analysis of Integrated Arrival, Departure, and Surface Operations
Sharma, Shivanjli; Fergus, John
2017-01-01
A real time dashboard was developed in order to inform and present users notifications and integrated information regarding airport surface operations. The dashboard is a supplement to capabilities and tools that incorporate arrival, departure, and surface air-traffic operations concepts in a NextGen environment. As trajectory-based departure scheduling and collaborative decision making tools are introduced in order to reduce delays and uncertainties in taxi and climb operations across the National Airspace System, users across a number of roles benefit from a real time system that enables common situational awareness. In addition to shared situational awareness the dashboard offers the ability to compute real time metrics and analysis to inform users about capacity, predictability, and efficiency of the system as a whole. This paper describes the architecture of the real time dashboard as well as an initial set of metrics computed on operational data. The potential impact of the real time dashboard is studied at the site identified for initial deployment and demonstration in 2017; Charlotte-Douglas International Airport. Analysis and metrics computed in real time illustrate the opportunity to provide common situational awareness and inform users of metrics across delay, throughput, taxi time, and airport capacity. In addition, common awareness of delays and the impact of takeoff and departure restrictions stemming from traffic flow management initiatives are explored. The potential of the real time tool to inform the predictability and efficiency of using a trajectory-based departure scheduling system is also discussed.
Pseudo-random unitary operators for quantum information processing.
Emerson, Joseph; Weinstein, Yaakov S; Saraceno, Marcos; Lloyd, Seth; Cory, David G
2003-12-19
In close analogy to the fundamental role of random numbers in classical information theory, random operators are a basic component of quantum information theory. Unfortunately, the implementation of random unitary operators on a quantum processor is exponentially hard. Here we introduce a method for generating pseudo-random unitary operators that can reproduce those statistical properties of random unitary operators most relevant to quantum information tasks. This method requires exponentially fewer resources, and hence enables the practical application of random unitary operators in quantum communication and information processing protocols. Using a nuclear magnetic resonance quantum processor, we were able to realize pseudorandom unitary operators that reproduce the expected random distribution of matrix elements.
The non-local content of quantum operations
Collins, D; Popescu, S; Collins, Daniel; Linden, Noah; Popescu, Sandu
2000-01-01
We show that quantum operations on multi-particle systems have a non-local content; this mirrors the non-local content of quantum states. We introduce a general framework for discussing the non-local content of quantum operations, and give a number of examples. Quantitative relations between quantum actions and the entanglement and classical communication resources needed to implement these actions are also described. We also show how entanglement can catalyse classical communication from a quantum action.
2016-06-01
to be used up beyond recovery or repair—and provides these items to the services when requisitioned in support of approximately 2,400 weapon...distribution functions for depot maintenance operations varies across the services . For example, the Air Force and DLA have agreed to a local recovery ...DEFENSE INVENTORY Further Analysis and Enhanced Metrics Could Improve Service Supply and Depot Operations Report
2016-07-17
2016-1896. 3.3 Physiological Measures This discussion will focus on cognitive fatigue measures that can be reasonably used during UAV operation...induced by bright points of fixation and highly predictable environments [39], such as monotonous roads. Control stations for UAV operation may be at risk...fixations; the outcome indicated by the fixation duration binning metric changed qualitatively when data qual- ity was poor. Thus, maintaining reasonable
Operational General Relativity: Possibilistic, Probabilistic, and Quantum
Hardy, Lucien
2016-01-01
In this paper we develop an operational formulation of General Relativity similar in spirit to existing operational formulations of Quantum Theory. To do this we introduce an operational space (or op-space) built out of scalar fields. A point in op-space corresponds to some nominated set of scalar fields taking some given values in coincidence. We assert that op-space is the space in which we observe the world. We introduce also a notion of agency (this corresponds to the ability to set knob settings just like in Operational Quantum Theory). The effects of agents' actions should only be felt to the future so we introduce also a time direction field. Agency and time direction can be understood as effective notions. We show how to formulate General Relativity as a possibilistic theory and as a probabilistic theory. In the possibilistic case we provide a compositional framework for calculating whether some operationally described situation is possible or not. In the probabilistic version we introduce probabiliti...
Wave operator theory of quantum dynamics
Durand, Philippe; Paidarová, Ivana
1998-09-01
An energy-dependent wave operator theory of quantum dynamics is derived for time-independent and time-dependent Hamiltonians. Relationships between Green's functions, wave operators, and effective Hamiltonians are investigated. Analytical properties of these quantities are especially relevant for studying resonances. A derivation of the relationship between the Green's functions and the (t,t') method of Peskin and Moiseyev [J. Chem. Phys. 99, 4590 (1993)] is presented. The observable quantities can be derived from the wave operators determined with the use of efficient iterative procedures. As in the theory of Bloch operators for bound states, the theory is based on a partition of the full Hilbert space into three subspaces: the model space, an intermediate space, and the outer space. On the basis of this partition an alternative definition of active spaces currently considered in large scale calculations is suggested. A numerical illustration is presented for several model systems and for the Stark effect in the hydrogen atom.
State-independent purity and fidelity of quantum operations
Kong, Fan-Zhen; Zong, Xiao-Lan; Yang, Ming; Cao, Zhuo-Liang
2016-04-01
The purity and fidelity of quantum operations are of great importance in characterizing the quality of quantum operations. The currently available definitions of the purity and fidelity of quantum operations are based on the average over all possible input pure quantum states, i.e. they are state-dependent (SD). In this paper, without resorting to quantum states, we define the state-independent (SI) purity and fidelity of a general quantum operation (evolution) in virtue of a new density matrix formalism for quantum operations, which is extended from the quantum state level to quantum operation level. The SI purity and fidelity gain more intrinsic physical properties of quantum operations than state-dependent ones, such as the purity of a one-qubit amplitude damping channel (with damping rate 1) is 1/2, which is in line with the fact that the channel is still a nonunitary operation described by two Kraus operators rather than a unitary one. But the state-dependent Haar average purity is 1 in this case. So the SI purity and fidelity proposed here can help the experimentalists to exactly quantify the implementation quality of an operation. As a byproduct, a new measure of the operator entanglement is proposed for a quantum evolution (unitary or nonunitary) in terms of the linear entropy of its density matrix on the orthonormal operator bases (OOBs) in Hilbert-Schmidt space.
Classical and quantum dynamics of a perfect fluid scalar-energy dependent metric cosmology
Khodadi, M; Vakili, B
2016-01-01
Inspired from the idea of minimally coupling of a real scalar field to geometry, we investigate the classical and quantum models of a flat energy-dependent FRW cosmology coupled to a perfect fluid in the framework of the scalar-rainbow metric gravity. We use the standard Schutz' representation for the perfect fluid and show that under a particular energy-dependent gauge fixing, it may lead to the identification of a time parameter for the corresponding dynamical system. It is shown that, under some circumstances on the minisuperspace prob energy, the classical evolution of the of the universe represents a late time expansion coming from a bounce instead of the big-bang singularity. Then we go forward by showing that this formalism gives rise to a Schr\\"{o}dinger-Wheeler-DeWitt (SWD) equation for the quantum-mechanical description of the model under consideration, the eigenfunctions of which can be used to construct the wave function of the universe. We use the resulting wave function in order to investigate t...
Dark Energy, Inflation, CMB Anisotropy and Polarization from Quantum Metric Fluctuations
Marochnik, Leonid
2014-01-01
We propose a model of cosmological evolution of the early and late Universe which is consistent with observational data and naturally explains the origin of inflation and dark energy (DE). We show that the de Sitter accelerated expansion of the FLRW space with no matter fields (hereinafter, empty space) is its natural state, and the model does not require either a scalar field or cosmological constant or any other hypotheses. Mathematically, this is due to the fact that the de Sitter state is an exact solution of the rigorous, mathematically consistent equations of one-loop quantum gravity for the empty FLRW space that are finite off the mass shell. Physically, this is due to the fact that the natural quantum metric fluctuations have the backreaction effect on the FLRW background, forming a self-polarized de Sitter graviton condensate. The energy required to maintain the accelerated expansion is drawn from the graviton vacuum. At the start and the end of cosmological evolution, the Universe is assumed to be e...
Matrix Operator Approach to Quantum Evolution Operator and Geometric Phase
Kim, Sang Pyo; Soh, Kwang Sup
2012-01-01
The Moody-Shapere-Wilczek's adiabatic effective Hamiltonian and Lagrangian method is developed further into the matrix effective Hamiltonian (MEH) and Lagrangian (MEL) approach to a parameter-dependent quantum system. The matrix operator approach formulated in the product integral (PI) provides not only a method to find wave function efficiently in the MEH approach but also higher order corrections to the effective action systematically in the MEL approach, a la the Magnus expansion and the Kubo's cumulant expansion. A coupled quantum system of a light particle of harmonic oscillator is worked out, and as a by-product a new kind of gauge potential (Berry's connection) is found even for nondegenerate case (real eigenfunctions). Moreover, in the PI formulation the holonomy of the induced gauge potential is related to the Schlesinger's exact formula for the gauge field tensor. A superadiabatic expansion is also constructed and a generalized Dykhne formula, depending on the contour integrals of homotopy class of ...
Three paths toward the quantum angle operator
Gazeau, Jean Pierre; Szafraniec, Franciszek Hugon
2016-12-01
We examine mathematical questions around angle (or phase) operator associated with a number operator through a short list of basic requirements. We implement three methods of construction of quantum angle. The first one is based on operator theory and parallels the definition of angle for the upper half-circle through its cosine and completed by a sign inversion. The two other methods are integral quantization generalizing in a certain sense the Berezin-Klauder approaches. One method pertains to Weyl-Heisenberg integral quantization of the plane viewed as the phase space of the motion on the line. It depends on a family of "weight" functions on the plane. The third method rests upon coherent state quantization of the cylinder viewed as the phase space of the motion on the circle. The construction of these coherent states depends on a family of probability distributions on the line.
Visser, M
1997-01-01
In this note I introduce the notion of the ``reliability horizon'' for semi-classical quantum gravity. This reliability horizon is an attempt to quantify the extent to which we should trust semi-classical quantum gravity, and to get a better handle on just where the Planck regime resides. I point out that the key obstruction to pushing semi-classical quantum gravity into the Planck regime is often the existence of large metric fluctuations, rather than a large back-reaction. There are many situations where the metric fluctuations become large long before the back-reaction is significant. Issues of this type are fundamental to any attempt at proving Hawking's chronology protection conjecture from first principles, since I shall prove that the onset of chronology violation is always hidden behind the reliability horizon.
An Analysis of Operating Room Performance Metrics at Reynolds Army Community Hospital
2009-06-28
the MTF does not receive any performance earnings from workload generated under the Dental inpatient and outpatient codes (CAA5 and ABFA). Also OR...increasing nursing staffing to permit completion of more cases: A case study. Anesthesia & Analgesia , 94(1), 138 - 142. Dexter, F., & Macario, A. (2002...as possible. Anesthesia & Analgesia , 94(5), 1272 - 1279. OR Metrics 54 Dexter, F., Macario, A., Traub, R.D., & Lubarsky, D.A. (2003). Operating room
The Connection Between the Metric and Generalized Projection Operators in Banach Spaces
Institute of Scientific and Technical Information of China (English)
Yakov ALBER; Jin Lu LI
2007-01-01
In this paper we study the connection between the metric projection operator PK:B→K,where B is a reflexive Banach space with dual space B* and K is a non-empty closed convex subset of B, and the generalized projection oprators Πk:B→k and πk:B*→k.We also present some results in non-reflexive Banach spaces.
Linear Transformation Theory of Quantum Field Operators and Its Applications
Institute of Scientific and Technical Information of China (English)
MA Lei
2003-01-01
We extend the linear quantum transformation theory to the case of quantum field operators. The corresponding general transformation expressions of CPT transformations and gauge field transformations are considered as its applications.
Control of Exciton Dynamics in Nanodots for Quantum Operations
Chen, Pochung; Piermarocchi, C.; Sham, L. J.
2001-08-01
We present a theory to further a new perspective of proactive control of exciton dynamics in the quantum limit. Circularly polarized optical pulses in a semiconductor nanodot are used to control the dynamics of two interacting excitons of opposite polarizations. Shaping of femtosecond laser pulses keeps the quantum operation within the decoherence time. Computation of the fidelity of the operations and application to the complete solution of a minimal quantum computing algorithm demonstrate in theory the feasibility of quantum control.
Operational metrics for the ESO Very Large Telescope: lessons learned and future steps
Primas, F.; Marteau, S.; Tacconi-Garman, L. E.; Mainieri, V.; Mysore, S.; Rejkuba, M.; Hilker, M.; Patat, F.; Sterzik, M.; Kaufer, A.; Mieske, S.
2016-07-01
When ESO's Very Large Telescope opened its first dome in April 1999 it was the first ground-based facility to offer to the scientific community access to an 8-10m class telescope with both classical and queue observing. The latter was considered to be the most promising way to ensure the observing flexibility necessary to execute the most demanding scientific programmes under the required, usually very well defined, conditions. Since then new instruments have become operational and 1st generation ones replaced, filling the 12 VLT foci and feeding the VLT Interferometer and its four Auxiliary Telescopes. Operating efficiently such a broad range of instruments installed and available every night of the year on four 8-metre telescopes offers many challenges. Although it may appear that little has changed since 1999, the underlying VLT operational model has evolved in order to accommodate different requirements from the user community and features of new instruments. Did it fulfil its original goal and, if so, how well? How did it evolve? What are the lessons learned after more than 15 years of operations? A careful analysis and monitoring of statistics and trends in Phase 1 and Phase 2 has been deployed under the DOME (Dashboard for Operational Metrics at ESO) project. The main goal of DOME is to provide robust metrics that can be followed with time in a user-friendly manner. Here, we summarize the main findings on the handling of service mode observations and present the most recent developments.
Entangled State Representation for Hamiltonian Operator of Quantum Pendulum
Institute of Scientific and Technical Information of China (English)
FANHong-Yi
2003-01-01
By virtue of the Einstein-Podolsky-Rosen entangled state, which is the common eigenvector of two panicles' relative coordinate and total momentum, we establish the bosonic operator version of the Hamiltonian for a quantum point-mass pendulum. The Hamiltonian displays the correct Schroedlnger equation in the entangled state representation.The corresponding Heisenberg operator equations which predict the angular momentum-angle uncertainty relation are derived. The quantum operator description of two quantum pendulums coupled by a spring is also derived.
Improved color metrics in solid-state lighting via utilization of on-chip quantum dots
Mangum, Benjamin D.; Landes, Tiemo S.; Theobald, Brian R.; Kurtin, Juanita N.
2017-02-01
While Quantum Dots (QDs) have found commercial success in display applications, there are currently no widely available solid state lighting products making use of QD nanotechnology. In order to have real-world success in today's lighting market, QDs must be capable of being placed in on-chip configurations, as remote phosphor configurations are typically much more expensive. Here we demonstrate solid-state lighting devices made with on-chip QDs. These devices show robust reliability under both dry and wet high stress conditions. High color quality lighting metrics can easily be achieved using these narrow, tunable QD downconverters: CRI values of Ra > 90 as well as R9 values > 80 are readily available when combining QDs with green phosphors. Furthermore, we show that QDs afford a 15% increase in overall efficiency compared to traditional phosphor downconverted SSL devices. The fundamental limit of QD linewidth is examined through single particle QD emission studies. Using standard Cd-based QD synthesis, it is found that single particle linewidths of 20 nm FWHM represent a lower limit to the narrowness of QD emission in the near term.
Birth of Dark Energy by Quantum Metric Fluctuations in Imaginary Time
Marochnik, Leonid
2012-01-01
We show that in imaginary time quantum metric fluctuations of empty space form a self-consistent De Sitter gravitational instanton that can be thought of as describing the tunneling from "nothing" into De Sitter space of real time (no cosmological constant or scalar fields are needed). The first time, this mechanism is activated to give birth to a flat inflationary Universe. The second time, it is turned on to complete cosmological evolution of the Universe after energy density of matter drops below the threshold (energy density of instantons). An accelerated expansion takes over after the scale factor exceeds this threshold, which marks the birth of dark energy at the redshift 1+z=1.44 and provides a possible solution to the "coincidence problem". The number of gravitons which tunneled into the Universe must be of the order of 10^122 to create the observational value of the Hubble constant. This number has nothing to do with vacuum energy, which is a possible solution to the "old cosmological constant proble...
Zeros and poles of quantum current operators and the condition of quantum integrability
Ding, J; Ding, Jintai; Miwa, Tetsuji
1996-01-01
For the current realization of the affine quantum groups, a simple comultiplication for the quantum current operators was given by Drinfeld. With this comultiplication, we study the zeros and poles of the quantum current operators and present a condition of integrability on the quantum current of $U_q\\left(\\hat{\\frak sl}(2)\\right)$, which is a deformation of the corresponding condition for $\\hat{\\frak sl}(2)$.
Institute of Scientific and Technical Information of China (English)
MA Zhi-Hao
2008-01-01
Metric of quantum states plays an important role in quantum information theory. In this letter, we find the deep connection between quantum logic theory and quantum information theory. Using the method of quantum logic, we can get a famous inequality in quantum information theory, and we answer a question raised by S. Gudder.
Quantum canonical ensemble: A projection operator approach
Magnus, Wim; Lemmens, Lucien; Brosens, Fons
2017-09-01
Knowing the exact number of particles N, and taking this knowledge into account, the quantum canonical ensemble imposes a constraint on the occupation number operators. The constraint particularly hampers the systematic calculation of the partition function and any relevant thermodynamic expectation value for arbitrary but fixed N. On the other hand, fixing only the average number of particles, one may remove the above constraint and simply factorize the traces in Fock space into traces over single-particle states. As is well known, that would be the strategy of the grand-canonical ensemble which, however, comes with an additional Lagrange multiplier to impose the average number of particles. The appearance of this multiplier can be avoided by invoking a projection operator that enables a constraint-free computation of the partition function and its derived quantities in the canonical ensemble, at the price of an angular or contour integration. Introduced in the recent past to handle various issues related to particle-number projected statistics, the projection operator approach proves beneficial to a wide variety of problems in condensed matter physics for which the canonical ensemble offers a natural and appropriate environment. In this light, we present a systematic treatment of the canonical ensemble that embeds the projection operator into the formalism of second quantization while explicitly fixing N, the very number of particles rather than the average. Being applicable to both bosonic and fermionic systems in arbitrary dimensions, transparent integral representations are provided for the partition function ZN and the Helmholtz free energy FN as well as for two- and four-point correlation functions. The chemical potential is not a Lagrange multiplier regulating the average particle number but can be extracted from FN+1 -FN, as illustrated for a two-dimensional fermion gas.
Minimum construction of two-qubit quantum operations
Zhang, J; Sastry, S; Whaley, K B; Zhang, Jun; Vala, Jiri; Sastry, Shankar
2003-01-01
Optimal construction of quantum operations is a fundamental problem in the realization of quantum computation. We here introduce a newly discovered quantum gate, B, that can implement any arbitrary two-qubit quantum operation with minimal number of both two- and single-qubit gates. We show this by giving an analytic circuit that implements a generic nonlocal two-qubit operation from just two applications of the B gate. We also demonstrate that for the highly scalable Josephson junction charge qubits, the B gate is also more easily and quickly generated than the CNOT gate for physically feasible parameters.
Hybrid protocol of remote implementations of quantum operations
Zhao, Ning Bo; Wang, An Min
2007-12-01
We propose a protocol of remote implementations of quantum operations by hybridizing bidirectional quantum-state teleportation (BQST) [Huelga , Phys. Rev. A 63, 042303 (2001)] and the Wang protocol [Wang, Phys. Rev. A 74, 032317 (2006)]. The protocol is available for remote implementations of quantum operations in the restricted sets specified in the paper. We also give a proof of the protocol and point out its optimization. As an extension, this hybrid protocol can be reduced to the BQST and Wang protocols.
Implementation of nonlocal quantum swap operation on two entangled pairs
Institute of Scientific and Technical Information of China (English)
郑亦庄; 顾永建; 陈立冰; 郭光灿
2002-01-01
We propose a scheme for the implementation of nonlocal quantum swap operation on two spatially separated entangled pairs and we show that the operation can swap two qubits of these entangled pairs. We discuss the resourcesof the entangled qubits and classical communication bits required for the optimal implementation of the nonlocal quantum swap operation. We also put forward a scheme for probabilistic implementation of nonlocal swap operation via a nonmaximally entangled quantum channel. The probability of a successful nonlocal swap operation is obtained by introducing a collective unitary transformation.
A Note on Dirac Operators on the Quantum Punctured Disk
Directory of Open Access Journals (Sweden)
Slawomir Klimek
2010-07-01
Full Text Available We study quantum analogs of the Dirac type operator −2z∂/∂z on the punctured disk, subject to the Atiyah-Patodi-Singer boundary conditions. We construct a parametrix of the quantum operator and show that it is bounded outside of the zero mode.
Energy Technology Data Exchange (ETDEWEB)
Salvagnini, Elena [UZ Gasthuisberg, Medical Imaging Research Center and Department of Radiology, Herestraat 49, B-3000 Leuven, Belgium and SCK-CEN, Boeretang 200, B-2400 Mol (Belgium); Bosmans, Hilde; Marshall, Nicholas W. [UZ Gasthuisberg, Medical Imaging Research Center and Department of Radiology, Herestraat 49, B-3000 Leuven (Belgium); Struelens, Lara [SCK-CEN, Boeretang 200, B-2400 Mol (Belgium)
2013-10-15
Purpose: The aim of this paper was to illustrate the value of the new metric effective detective quantum efficiency (eDQE) in relation to more established measures in the optimization process of two digital mammography systems. The following metrics were included for comparison against eDQE: detective quantum efficiency (DQE) of the detector, signal difference to noise ratio (SdNR), and detectability index (d′) calculated using a standard nonprewhitened observer with eye filter.Methods: The two systems investigated were the Siemens MAMMOMAT Inspiration and the Hologic Selenia Dimensions. The presampling modulation transfer function (MTF) required for the eDQE was measured using two geometries: a geometry containing scattered radiation and a low scatter geometry. The eDQE, SdNR, and d′ were measured for poly(methyl methacrylate) (PMMA) thicknesses of 20, 40, 60, and 70 mm, with and without the antiscatter grid and for a selection of clinically relevant target/filter (T/F) combinations. Figures of merit (FOMs) were then formed from SdNR and d′ using the mean glandular dose as the factor to express detriment. Detector DQE was measured at energies covering the range of typical clinically used spectra.Results: The MTF measured in the presence of scattered radiation showed a large drop at low spatial frequency compared to the low scatter method and led to a corresponding reduction in eDQE. The eDQE for the Siemens system at 1 mm{sup −1} ranged between 0.15 and 0.27, depending on T/F and grid setting. For the Hologic system, eDQE at 1 mm{sup −1} varied from 0.15 to 0.32, again depending on T/F and grid setting. The eDQE results for both systems showed that the grid increased the system efficiency for PMMA thicknesses of 40 mm and above but showed only small sensitivity to T/F setting. While results of the SdNR and d′ based FOMs confirmed the eDQE grid position results, they were also more specific in terms of T/F selection. For the Siemens system at 20 mm PMMA
Salvagnini, Elena; Bosmans, Hilde; Struelens, Lara; Marshall, Nicholas W
2013-10-01
The aim of this paper was to illustrate the value of the new metric effective detective quantum efficiency (eDQE) in relation to more established measures in the optimization process of two digital mammography systems. The following metrics were included for comparison against eDQE: detective quantum efficiency (DQE) of the detector, signal difference to noise ratio (SdNR), and detectability index (d') calculated using a standard nonprewhitened observer with eye filter. The two systems investigated were the Siemens MAMMOMAT Inspiration and the Hologic Selenia Dimensions. The presampling modulation transfer function (MTF) required for the eDQE was measured using two geometries: a geometry containing scattered radiation and a low scatter geometry. The eDQE, SdNR, and d' were measured for poly(methyl methacrylate) (PMMA) thicknesses of 20, 40, 60, and 70 mm, with and without the antiscatter grid and for a selection of clinically relevant target/filter (T/F) combinations. Figures of merit (FOMs) were then formed from SdNR and d' using the mean glandular dose as the factor to express detriment. Detector DQE was measured at energies covering the range of typical clinically used spectra. The MTF measured in the presence of scattered radiation showed a large drop at low spatial frequency compared to the low scatter method and led to a corresponding reduction in eDQE. The eDQE for the Siemens system at 1 mm(-1) ranged between 0.15 and 0.27, depending on T/F and grid setting. For the Hologic system, eDQE at 1 mm(-1) varied from 0.15 to 0.32, again depending on T/F and grid setting. The eDQE results for both systems showed that the grid increased the system efficiency for PMMA thicknesses of 40 mm and above but showed only small sensitivity to T/F setting. While results of the SdNR and d' based FOMs confirmed the eDQE grid position results, they were also more specific in terms of T/F selection. For the Siemens system at 20 mm PMMA, the FOMs indicated Mo/Mo (grid out) as
Software Architecture Coupling Metric for Assessing Operational Responsiveness of Trading Systems
Directory of Open Access Journals (Sweden)
Claudiu VINTE
2012-01-01
Full Text Available The empirical observation that motivates our research relies on the difficulty to assess the performance of a trading architecture beyond a few synthetic indicators like response time, system latency, availability or volume capacity. Trading systems involve complex software architectures of distributed resources. However, in the context of a large brokerage firm, which offers a global coverage from both, market and client perspectives, the term distributed gains a critical significance indeed. Offering a low latency ordering system by nowadays standards is relatively easily achievable, but integrating it in a flexible manner within the broader information system architecture of a broker/dealer requires operational aspects to be factored in. We propose a metric for measuring the coupling level within software architecture, and employ it to identify architectural designs that can offer a higher level of operational responsiveness, which ultimately would raise the overall real-world performance of a trading system.
New Hamiltonian constraint operator for loop quantum gravity
Directory of Open Access Journals (Sweden)
Jinsong Yang
2015-12-01
Full Text Available A new symmetric Hamiltonian constraint operator is proposed for loop quantum gravity, which is well defined in the Hilbert space of diffeomorphism invariant states up to non-planar vertices with valence higher than three. It inherits the advantage of the original regularization method to create new vertices to the spin networks. The quantum algebra of this Hamiltonian is anomaly-free on shell, and there is less ambiguity in its construction in comparison with the original method. The regularization procedure for this Hamiltonian constraint operator can also be applied to the symmetric model of loop quantum cosmology, which leads to a new quantum dynamics of the cosmological model.
Protected quantum computing: interleaving gate operations with dynamical decoupling sequences.
Zhang, Jingfu; Souza, Alexandre M; Brandao, Frederico Dias; Suter, Dieter
2014-02-07
Implementing precise operations on quantum systems is one of the biggest challenges for building quantum devices in a noisy environment. Dynamical decoupling attenuates the destructive effect of the environmental noise, but so far, it has been used primarily in the context of quantum memories. Here, we experimentally demonstrate a general scheme for combining dynamical decoupling with quantum logical gate operations using the example of an electron-spin qubit of a single nitrogen-vacancy center in diamond. We achieve process fidelities >98% for gate times that are 2 orders of magnitude longer than the unprotected dephasing time T2.
Energy Technology Data Exchange (ETDEWEB)
Ronald Boring; Roger Lew; Thomas Ulrich; Jeffrey Joe
2014-03-01
As control rooms are modernized with new digital systems at nuclear power plants, it is necessary to evaluate the operator performance using these systems as part of a verification and validation process. There are no standard, predefined metrics available for assessing what is satisfactory operator interaction with new systems, especially during the early design stages of a new system. This report identifies the process and metrics for evaluating human system interfaces as part of control room modernization. The report includes background information on design and evaluation, a thorough discussion of human performance measures, and a practical example of how the process and metrics have been used as part of a turbine control system upgrade during the formative stages of design. The process and metrics are geared toward generalizability to other applications and serve as a template for utilities undertaking their own control room modernization activities.
Remote implementations of partially known quantum operations of multiqubits
Wang, A M
2005-01-01
Based on our simplified HPV's scheme for one qubit, we investigate the remote implementations of the partially known quantum operations (within some restricted sets that satisfy the given conditions). After giving out the obvious forms of eight interesting restricted sets of quantum operations of two qubits, we propose the protocol of the remote implementations of them using a universal recovered operation performed by the receiver. Furthermore, we show the extension of our protocol to the case of multiqubits.
Entangled State Representation for Hamiltonian Operator of Quantum Pendulum
Institute of Scientific and Technical Information of China (English)
FAN Hong-Yi
2003-01-01
By virtue of the Einstein-Podolsky-Rosen entangled state, which is the common eigenvector of two particles'relativecoordinate and total momentum, we establish the bosonic operator version of the Hamiltonian for a quantumpoint-mass pendulum. The Hamiltonian displays the correct Schrodinger equation in the entangled state representation.The corresponding Heisenberg operator equations which predict the angular momentum-angle uncertainty relation arederived. The quantum operator description of two quantum pendulums coupled by a spring is also derived.
Lectures on algebraic quantum field theory and operator algebras
Energy Technology Data Exchange (ETDEWEB)
Schroer, Bert [Berlin Univ. (Germany). Institut fuer Theoretische Physik. E-mail: schroer@cbpf.br
2001-04-01
In this series of lectures directed towards a mainly mathematically oriented audience I try to motivate the use of operator algebra methods in quantum field theory. Therefore a title as why mathematicians are/should be interested in algebraic quantum field theory would be equally fitting. besides a presentation of the framework and the main results of local quantum physics these notes may serve as a guide to frontier research problems in mathematical. (author)
Efficient quantum circuits for dense circulant and circulant like operators
Zhou, S. S.; Wang, J. B.
2017-05-01
Circulant matrices are an important family of operators, which have a wide range of applications in science and engineering-related fields. They are, in general, non-sparse and non-unitary. In this paper, we present efficient quantum circuits to implement circulant operators using fewer resources and with lower complexity than existing methods. Moreover, our quantum circuits can be readily extended to the implementation of Toeplitz, Hankel and block circulant matrices. Efficient quantum algorithms to implement the inverses and products of circulant operators are also provided, and an example application in solving the equation of motion for cyclic systems is discussed.
Qubit-Programmable Operations on Quantum Light Fields.
Barbieri, Marco; Spagnolo, Nicolò; Ferreyrol, Franck; Blandino, Rémi; Smith, Brian J; Tualle-Brouri, Rosa
2015-10-15
Engineering quantum operations is a crucial capability needed for developing quantum technologies and designing new fundamental physics tests. Here we propose a scheme for realising a controlled operation acting on a travelling continuous-variable quantum field, whose functioning is determined by a discrete input qubit. This opens a new avenue for exploiting advantages of both information encoding approaches. Furthermore, this approach allows for the program itself to be in a superposition of operations, and as a result it can be used within a quantum processor, where coherences must be maintained. Our study can find interest not only in general quantum state engineering and information protocols, but also details an interface between different physical platforms. Potential applications can be found in linking optical qubits to optical systems for which coupling is best described in terms of their continuous variables, such as optomechanical devices.
Zhang, KeJia; Zhang, Long; Song, TingTing; Yang, YingHui
2016-06-01
In this paper, we propose certain different design ideas on a novel topic in quantum cryptography — quantum operation sharing (QOS). Following these unique ideas, three QOS schemes, the "HIEC" (The scheme whose messages are hidden in the entanglement correlation), "HIAO" (The scheme whose messages are hidden with the assistant operations) and "HIMB" (The scheme whose messages are hidden in the selected measurement basis), have been presented to share the single-qubit operations determinately on target states in a remote node. These schemes only require Bell states as quantum resources. Therefore, they can be directly applied in quantum networks, since Bell states are considered the basic quantum channels in quantum networks. Furthermore, after analyse on the security and resource consumptions, the task of QOS can be achieved securely and effectively in these schemes.
Security of Quantum Repeater Network Operation
2016-10-03
enumerating differences from classical networks. Quantum networks, of course, depend upon successful creation of high-fidelity entanglement at the link...is equivalent to the classical Internet silently corrupting data somewhere along a network path without the benefit of hop-by-hop error detection...for nodes intended to form a future Quantum Internet be required to support two classes of physically distinct qubits inside the DISTRIBUTION A
The Dirac operator and gamma matrices for quantum Minkowski spaces
1997-01-01
Gamma matrices for quantum Minkowski spaces are found. The invariance of the corresponding Dirac operator is proven. We introduce momenta for spin 1/2 particles and get (in certain cases) formal solutions of the Dirac equation.
Bolliet, B; Stahl, C; Linsefors, L; Barrau, A
2015-01-01
Loop quantum cosmology tries to capture the main ideas of loop quantum gravity and to apply them to the Universe as a whole. Two main approaches within this framework have been considered to date for the study of cosmological perturbations: the dressed metric approach and the deformed algebra approach. They both have advantages and drawbacks. In this article, we accurately compare their predictions. In particular, we compute the associated primordial tensor power spectra. We show -- numerically and analytically -- that the large scale behavior is similar for both approaches and compatible with the usual prediction of general relativity. The small scale behavior is, the other way round, drastically different. Most importantly, we show that in a range of wavenumbers explicitly calculated, both approaches do agree on predictions that, in addition, differ from standard general relativity and do not depend on unknown parameters. These features of the power spectrum at intermediate scales might constitute a univers...
New scalar constraint operator for loop quantum gravity
Assanioussi, Mehdi; Mäkinen, Ilkka
2015-01-01
We present a concrete and explicit construction of a new scalar constraint operator for loop quantum gravity. The operator is defined on the recently introduced space of partially diffeomorphism invariant states, and this space is preserved by the action of the operator. To define the Euclidean part of the scalar constraint operator, we propose a specific regularization based on the idea of so-called "special" loops. The Lorentzian part of the quantum scalar constraint is merely the curvature operator that has been introduced in an earlier work. Due to the properties of the special loops assignment, the adjoint operator of the non-symmetric constraint operator is densely defined on the partially diffeomorphism invariant Hilbert space. This fact opens up the possibility of defining a symmetric scalar constraint operator as a suitable combination of the original operator and its adjoint. We also show that the algebra of the scalar constraint operators is anomaly free, and describe the structure of the kernel of...
Junctions of surface operators and categorification of quantum groups
Chun, Sungbong; Roggenkamp, Daniel
2015-01-01
We show how networks of Wilson lines realize quantum groups U_q(sl(m)), for arbitrary m, in 3d SU(N) Chern-Simons theory. Lifting this construction to foams of surface operators in 4d theory we find that rich structure of junctions is encoded in combinatorics of planar diagrams. For a particular choice of surface operators we reproduce known mathematical constructions of categorical representations and categorified quantum groups.
Bell operator and Gaussian squeezed states in noncommutative quantum mechanics
Bastos, Catarina; Bertolami, Orfeu; Dias, Nuno Costa; Prata, João Nuno
2015-01-01
One examines putative corrections to the Bell operator due to the noncommutativity in the phase-space. Starting from a Gaussian squeezed envelop whose time evolution is driven by commutative (standard quantum mechanics) and noncommutative dynamics respectively, one concludes that, although the time evolving covariance matrix in the noncommutative case is different from the standard case, the squeezing parameter dominates and there are no noticeable noncommutative corrections to the Bell operator. This indicates that, at least for squeezed states, the privileged states to test Bell correlations, noncommutativity versions of quantum mechnics remains as non-local as quantum mechanics itself.
Bell operator and Gaussian squeezed states in noncommutative quantum mechanics
Bastos, Catarina; Bernardini, Alex E.; Bertolami, Orfeu; Dias, Nuno Costa; Prata, João Nuno
2016-05-01
We examine putative corrections to the Bell operator due to the noncommutativity in the phase space. Starting from a Gaussian squeezed envelope whose time evolution is driven by commutative (standard quantum mechanics) and noncommutative dynamics, respectively, we conclude that although the time-evolving covariance matrix in the noncommutative case is different from the standard case, the squeezing parameter dominates and there are no noticeable noncommutative corrections to the Bell operator. This indicates that, at least for squeezed states, the privileged states to test Bell correlations, noncommutativity versions of quantum mechanics remain as nonlocal as quantum mechanics itself.
Energy Technology Data Exchange (ETDEWEB)
Eto, Joseph H.; Undrill, John; Mackin, Peter; Daschmans, Ron; Williams, Ben; Haney, Brian; Hunt, Randall; Ellis, Jeff; Illian, Howard; Martinez, Carlos; O' Malley, Mark; Coughlin, Katie; LaCommare, Kristina Hamachi
2010-12-20
An interconnected electric power system is a complex system that must be operated within a safe frequency range in order to reliably maintain the instantaneous balance between generation and load. This is accomplished by ensuring that adequate resources are available to respond to expected and unexpected imbalances and restoring frequency to its scheduled value in order to ensure uninterrupted electric service to customers. Electrical systems must be flexible enough to reliably operate under a variety of"change" scenarios. System planners and operators must understand how other parts of the system change in response to the initial change, and need tools to manage such changes to ensure reliable operation within the scheduled frequency range. This report presents a systematic approach to identifying metrics that are useful for operating and planning a reliable system with increased amounts of variable renewable generation which builds on existing industry practices for frequency control after unexpected loss of a large amount of generation. The report introduces a set of metrics or tools for measuring the adequacy of frequency response within an interconnection. Based on the concept of the frequency nadir, these metrics take advantage of new information gathering and processing capabilities that system operators are developing for wide-area situational awareness. Primary frequency response is the leading metric that will be used by this report to assess the adequacy of primary frequency control reserves necessary to ensure reliable operation. It measures what is needed to arrest frequency decline (i.e., to establish frequency nadir) at a frequency higher than the highest set point for under-frequency load shedding within an interconnection. These metrics can be used to guide the reliable operation of an interconnection under changing circumstances.
Universal programmable quantum circuit schemes to emulate an operator.
Daskin, Anmer; Grama, Ananth; Kollias, Giorgos; Kais, Sabre
2012-12-21
Unlike fixed designs, programmable circuit designs support an infinite number of operators. The functionality of a programmable circuit can be altered by simply changing the angle values of the rotation gates in the circuit. Here, we present a new quantum circuit design technique resulting in two general programmable circuit schemes. The circuit schemes can be used to simulate any given operator by setting the angle values in the circuit. This provides a fixed circuit design whose angles are determined from the elements of the given matrix-which can be non-unitary-in an efficient way. We also give both the classical and quantum complexity analysis for these circuits and show that the circuits require a few classical computations. For the electronic structure simulation on a quantum computer, one has to perform the following steps: prepare the initial wave function of the system; present the evolution operator U = e(-iHt) for a given atomic and molecular Hamiltonian H in terms of quantum gates array and apply the phase estimation algorithm to find the energy eigenvalues. Thus, in the circuit model of quantum computing for quantum chemistry, a crucial step is presenting the evolution operator for the atomic and molecular Hamiltonians in terms of quantum gate arrays. Since the presented circuit designs are independent from the matrix decomposition techniques and the global optimization processes used to find quantum circuits for a given operator, high accuracy simulations can be done for the unitary propagators of molecular Hamiltonians on quantum computers. As an example, we show how to build the circuit design for the hydrogen molecule.
Why Do the Quantum Observables Form a Jordan Operator Algebra?
Niestegge, Gerd
2010-01-01
The Jordan algebra structure of the bounded real quantum observables was recognized already in the early days of quantum mechanics. While there are plausible reasons for most parts of this structure, the existence of the distributive nonassociative multiplication operation is hard to justify from a physical or statistical point of view. Considering the non-Boolean extension of classical probabilities, presented in a recent paper, it is shown in this paper that such a multiplication operation can be derived from certain properties of the conditional probabilities and the observables, i.e., from postulates with a clear statistical interpretation. The well-known close relation between Jordan operator algebras and C*-algebras then provides the connection to the quantum-mechanical Hilbert space formalism, thus resulting in a novel axiomatic approach to general quantum mechanics that includes the types II and III von Neumann algebras.
Operators versus functions: from quantum dynamical semigroups to tomographic semigroups
Aniello, Paolo
2013-11-01
Quantum mechanics can be formulated in terms of phase-space functions, according to Wigner's approach. A generalization of this approach consists in replacing the density operators of the standard formulation with suitable functions, the so-called generalized Wigner functions or (group-covariant) tomograms, obtained by means of group-theoretical methods. A typical problem arising in this context is to express the evolution of a quantum system in terms of tomograms. In the case of a (suitable) open quantum system, the dynamics can be described by means of a quantum dynamical semigroup 'in disguise', namely, by a semigroup of operators acting on tomograms rather than on density operators. We focus on a special class of quantum dynamical semigroups, the twirling semigroups, that have interesting applications, e.g., in quantum information science. The 'disguised counterparts' of the twirling semigroups, i.e., the corresponding semigroups acting on tomograms, form a class of semigroups of operators that we call tomographic semigroups. We show that the twirling semigroups and the tomographic semigroups can be encompassed in a unique theoretical framework, a class of semigroups of operators including also the probability semigroups of classical probability theory, so achieving a deeper insight into both the mathematical and the physical aspects of the problem.
Matrix Product Operator Simulations of Quantum Algorithms
2015-02-01
Communications, pages 174–188. Springer, 1999. Bibliography 145 [21] Michelangelo Grigni, Leonard Schulman, Monica Vazirani, and Umesh Vazirani...2007. [27] Andrew M Childs, Leonard J Schulman, and Umesh V Vazirani. Quan- tum algorithms for hidden nonlinear structures. In Foundations of...and quantum in- formation. Cambridge University Press, Cambridge, 2000. [86] Charles H Bennett, Ethan Bernstein, Gilles Brassard, and Umesh Vazirani
Security of Quantum Repeater Network Operation
2016-10-03
15. SUBJECT TERMS Quantum Architecture 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT SAR 18. NUMBER OF PAGES 5 19a. NAME OF...22 Rodney Van Meter Associate Professor, Faculty of Environment and Information Studies Keio University, Japan +81-90-8012-3643 rdv@sfc.keio.ac.jp
Metrics to Compare Aircraft Operating and Support Costs in the Department of Defense
2015-01-01
search costs associated with the missing Malaysia Airlines Flight 370. World Maritime News (2014), for instance, quotes Pentagon spokesman Army Col...commercial airline industry uses the metric cost per available seat mile, i.e., the cost to fly one seat one mile. This is a simple cost metric that
Hiroaki Niikuni
2015-01-01
In this paper, we consider periodic Schrödinger operators on the dumbbell-like metric graph, which is a periodic graph consisting of lines and rings. Let one line and two rings be in the basic period. We see the relationship between the structure of graph and the band-gap spectrum.
Directory of Open Access Journals (Sweden)
Hiroaki Niikuni
2015-01-01
Full Text Available In this paper, we consider periodic Schrödinger operators on the dumbbell-like metric graph, which is a periodic graph consisting of lines and rings. Let one line and two rings be in the basic period. We see the relationship between the structure of graph and the band-gap spectrum.
The thermodynamic cost of quantum operations
Bedingham, D. J.; Maroney, O. J. E.
2016-11-01
The amount of heat generated by computers is rapidly becoming one of the main problems for developing new generations of information technology. The thermodynamics of computation sets the ultimate physical bounds on heat generation. A lower bound is set by the Landauer limit, at which computation becomes thermodynamically reversible. For classical computation there is no physical principle which prevents this limit being reached, and approaches to it are already being experimentally tested. In this paper we show that for quantum computation with a set of signal states satisfying given conditions, there is an unavoidable excess heat generation that renders it inherently thermodynamically irreversible. The Landauer limit cannot, in general, be reached by quantum computers. We show the existence of a lower bound to the heat generated by quantum computing that exceeds that given by the Landauer limit, give the special conditions where this excess cost may be avoided, and provide a protocol for achieving the limiting heat cost when these conditions are met. We also show how classical computing falls within the special conditions.
A method of extracting operating parameters of a quantum circuit
Sete, Eyob A.; Block, Maxwell; Scheer, Michael; Zanoci, Cris; Vahidpour, Mehrnoosh; Thompson, Dane; Rigetti, Chad
Rigorous simulation-driven design methods are an essential component of traditional integrated circuit design. We adapt these techniques to the design and development of superconducting quantum integrated circuits by combining classical finite element analysis in the microwave domain with Brune circuit synthesis by Solgun [PhD thesis 2014] and BKD Hamiltonian analysis by Burkard et al. [Phys. Rev. B 69, 064503 (2004)]. Using the Hamiltonian of the quantum circuit, constructed using the synthesized equivalent linear circuit and the nonlinear Josephson junctions' contributions, we extract operating parameters of the quantum circuit such as resonance coupling strength, dispersive shift, qubit anharmonicitiy, and decoherence rates for single-and multi-port quantum circuits. This approach has been experimentally validated and allows the closed-loop iterative simulation-driven development of quantum information processing devices.
On Quantum Field Theories in Operator and Functional Integral Formalisms
Teleki, A; Noga, Milan; Teleki, Aba
2006-01-01
Relations and isomorphisms between quantum field theories in operator and functional integral formalisms are analyzed from the viewpoint of inequivalent representations of commutator or anticommutator rings of field operators. A functional integral in quantum field theory cannot be regarded as a Newton-Lebesgue integral but rather as a formal object to which one associates distinct numerical values for different processes of its integration. By choosing an appropriate method for the integration of a given functional integral, one can select a single representation out of infinitely many inequivalent representations for an operator whose trace is expressed by the corresponding functional integral. These properties are demonstrated with two exactly solvable examples.
GENERALIZED OPERATORS AND P(φ)2 QUANTUM FIELDS
Institute of Scientific and Technical Information of China (English)
黄志远; 让光林
2004-01-01
In this paper by Sobolev imbedding theorem and characterization theorem of generalized operators the existence of P(φ)2 quantum fields as generalized operators is obtained and a rigorous mathematical interpretation of renormalization procedure is given under white noise theory.
Modified Anti-de-Sitter Metric, Light-Front Quantized QCD, and Conformal Quantum Mechanics
Dosch, Hans Gunter; de Teramond, Guy F
2014-01-01
We briefly review the remarkable connections between light-front QCD, gravity in AdS space, and conformal quantum mechanics. We discuss, in particular, the group theoretical and geometrical aspects of the underlying one-dimensional quantum field theory. The resulting effective theory leads to a phenomenologically successful confining interaction potential in the relativistic light-front wave equation which incorporates relevant non-perturbative dynamical aspects of hadron physics.
Operating single quantum emitters with a compact Stirling cryocooler
Energy Technology Data Exchange (ETDEWEB)
Schlehahn, A.; Krüger, L.; Gschrey, M.; Schulze, J.-H.; Rodt, S.; Strittmatter, A.; Heindel, T., E-mail: tobias.heindel@tu-berlin.de; Reitzenstein, S. [Institute of Solid State Physics, Technische Universität Berlin, 10623 Berlin (Germany)
2015-01-15
The development of an easy-to-operate light source emitting single photons has become a major driving force in the emerging field of quantum information technology. Here, we report on the application of a compact and user-friendly Stirling cryocooler in the field of nanophotonics. The Stirling cryocooler is used to operate a single quantum emitter constituted of a semiconductor quantum dot (QD) at a base temperature below 30 K. Proper vibration decoupling of the cryocooler and its surrounding enables free-space micro-photoluminescence spectroscopy to identify and analyze different charge-carrier states within a single quantum dot. As an exemplary application in quantum optics, we perform a Hanbury-Brown and Twiss experiment demonstrating a strong suppression of multi-photon emission events with g{sup (2)}(0) < 0.04 from this Stirling-cooled single quantum emitter under continuous wave excitation. Comparative experiments performed on the same quantum dot in a liquid helium (LHe)-flow cryostat show almost identical values of g{sup (2)}(0) for both configurations at a given temperature. The results of this proof of principle experiment demonstrate that low-vibration Stirling cryocoolers that have so far been considered exotic to the field of nanophotonics are an attractive alternative to expensive closed-cycle cryostats or LHe-flow cryostats, which could pave the way for the development of high-quality table-top non-classical light sources.
Operating single quantum emitters with a compact Stirling cryocooler.
Schlehahn, A; Krüger, L; Gschrey, M; Schulze, J-H; Rodt, S; Strittmatter, A; Heindel, T; Reitzenstein, S
2015-01-01
The development of an easy-to-operate light source emitting single photons has become a major driving force in the emerging field of quantum information technology. Here, we report on the application of a compact and user-friendly Stirling cryocooler in the field of nanophotonics. The Stirling cryocooler is used to operate a single quantum emitter constituted of a semiconductor quantum dot (QD) at a base temperature below 30 K. Proper vibration decoupling of the cryocooler and its surrounding enables free-space micro-photoluminescence spectroscopy to identify and analyze different charge-carrier states within a single quantum dot. As an exemplary application in quantum optics, we perform a Hanbury-Brown and Twiss experiment demonstrating a strong suppression of multi-photon emission events with g((2))(0) Stirling-cooled single quantum emitter under continuous wave excitation. Comparative experiments performed on the same quantum dot in a liquid helium (LHe)-flow cryostat show almost identical values of g((2))(0) for both configurations at a given temperature. The results of this proof of principle experiment demonstrate that low-vibration Stirling cryocoolers that have so far been considered exotic to the field of nanophotonics are an attractive alternative to expensive closed-cycle cryostats or LHe-flow cryostats, which could pave the way for the development of high-quality table-top non-classical light sources.
Operating single quantum emitters with a compact Stirling cryocooler
Schlehahn, A.; Krüger, L.; Gschrey, M.; Schulze, J.-H.; Rodt, S.; Strittmatter, A.; Heindel, T.; Reitzenstein, S.
2015-01-01
The development of an easy-to-operate light source emitting single photons has become a major driving force in the emerging field of quantum information technology. Here, we report on the application of a compact and user-friendly Stirling cryocooler in the field of nanophotonics. The Stirling cryocooler is used to operate a single quantum emitter constituted of a semiconductor quantum dot (QD) at a base temperature below 30 K. Proper vibration decoupling of the cryocooler and its surrounding enables free-space micro-photoluminescence spectroscopy to identify and analyze different charge-carrier states within a single quantum dot. As an exemplary application in quantum optics, we perform a Hanbury-Brown and Twiss experiment demonstrating a strong suppression of multi-photon emission events with g(2)(0) < 0.04 from this Stirling-cooled single quantum emitter under continuous wave excitation. Comparative experiments performed on the same quantum dot in a liquid helium (LHe)-flow cryostat show almost identical values of g(2)(0) for both configurations at a given temperature. The results of this proof of principle experiment demonstrate that low-vibration Stirling cryocoolers that have so far been considered exotic to the field of nanophotonics are an attractive alternative to expensive closed-cycle cryostats or LHe-flow cryostats, which could pave the way for the development of high-quality table-top non-classical light sources.
Quantum hidden Markov models based on transition operation matrices
Cholewa, Michał; Gawron, Piotr; Głomb, Przemysław; Kurzyk, Dariusz
2017-04-01
In this work, we extend the idea of quantum Markov chains (Gudder in J Math Phys 49(7):072105 [3]) in order to propose quantum hidden Markov models (QHMMs). For that, we use the notions of transition operation matrices and vector states, which are an extension of classical stochastic matrices and probability distributions. Our main result is the Mealy QHMM formulation and proofs of algorithms needed for application of this model: Forward for general case and Vitterbi for a restricted class of QHMMs. We show the relations of the proposed model to other quantum HMM propositions and present an example of application.
Tailored jump operators for purely dissipative quantum magnetism
Weimer, Hendrik
2017-01-01
I propose an architecture for the realization of dissipative quantum many-body spin models. The dissipative processes are mediated by interactions with auxiliary particles and lead to a widely tunable class of correlated quantum jump operators. These findings enable the investigation of purely dissipative spin models, where coherent dynamics is entirely absent. I provide a detailed review of a recently introduced variational method to analyze such dissipative quantum many-body systems, and I discuss a specific example in terms of a purely dissipative Heisenberg model, for which I find an additional disordered phase that is not present in the corresponding ground state phase diagram.
Tailored jump operators for purely dissipative quantum magnetism
Weimer, Hendrik
2016-01-01
I propose an archtitecture for the realization of dissipative quantum many-body spin models. The dissipative processes are mediated by interactions with auxiliary particles and lead to a widely tunable class of correlated quantum jump operators. These findings enable the investigation of purely dissipative spin models, where coherent dynamics is entirely absent. I provide a detailed review of a recently introduced variational method to analyze such dissipative quantum many-body systems, and I discuss a specific example in terms of a purely dissipative Heisenberg model, for which I find an additional disordered phase that is not present in the corresponding ground state phase diagram.
Zhou, Nanrun; Hu, Yiqun; Gong, Lihua; Li, Guangyong
2017-06-01
A new quantum image encryption scheme is suggested by using the iterative generalized Arnold transforms and the quantum image cycle shift operations. The times of the quantum image cycle shift operations are controlled by a hyper-chaotic sequence generated by a new 4D hyper-chaotic system. The image pixels are scrambled by the iterative generalized Arnold transform, and the values of the pixels are altered by the quantum image cycle shift operations. The four initial conditions of the new 4D hyper-chaotic system are exploited to control the two parameters, the iterative rounds of the generalized Arnold transform and the times of the quantum image cycle shift operations, respectively. Thus, the main keys of the proposed quantum image encryption scheme are the four initial conditions of the new 4D hyper-chaotic system and the key space is relatively large enough. Simulation results and theoretical analyses demonstrate that the proposed quantum image encryption scheme outperforms its classical counterparts apparently.
Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle
Micho Đurđevich; Stephen Bruce Sontz
2011-01-01
A quantum principal bundle is constructed for every Coxeter group acting on a finite-dimensional Euclidean space $E$, and then a connection is also defined on this bundle. The covariant derivatives associated to this connection are the Dunkl operators, originally introduced as part of a program to generalize harmonic analysis in Euclidean spaces. This gives us a new, geometric way of viewing the Dunkl operators. In particular, we present a new proof of the commutativity of these operators amo...
Obtaining a class of Type N pure radiation metrics using invariant operators
Ramos, M P M
2004-01-01
We develop further the integration procedure in the generalised invariant formalism, and demonstrate its efficiency by obtaining a class of Petrov type N pure radiation metrics without any explicit integration, and with comparatively little detailed calculations. The method is similar to the one exploited by Edgar and Vickers when deriving the general conformally flat pure radiation metric. A major addition to the technique is the introduction of non-intrinsic elements in generalised invariant formalism, which can be exploited to keep calculations manageable.
Quantum Operator Design for Lattice Baryon Spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Lichtl, Adam [Carnegie Mellon Univ., Pittsburgh, PA (United States)
2006-09-07
A previously-proposed method of constructing spatially-extended gauge-invariant three-quark operators for use in Monte Carlo lattice QCD calculations is tested, and a methodology for using these operators to extract the energies of a large number of baryon states is developed. This work is part of a long-term project undertaken by the Lattice Hadron Physics Collaboration to carry out a first-principles calculation of the low-lying spectrum of QCD. The operators are assemblages of smeared and gauge-covariantly-displaced quark fields having a definite flavor structure. The importance of using smeared fields is dramatically demonstrated. It is found that quark field smearing greatly reduces the couplings to the unwanted high-lying short-wavelength modes, while gauge field smearing drastically reduces the statistical noise in the extended operators.
Foundations of quantum theory from classical concepts to operator algebras
Landsman, Klaas
2017-01-01
This book studies the foundations of quantum theory through its relationship to classical physics. This idea goes back to the Copenhagen Interpretation (in the original version due to Bohr and Heisenberg), which the author relates to the mathematical formalism of operator algebras originally created by von Neumann. The book therefore includes comprehensive appendices on functional analysis and C*-algebras, as well as a briefer one on logic, category theory, and topos theory. Matters of foundational as well as mathematical interest that are covered in detail include symmetry (and its "spontaneous" breaking), the measurement problem, the Kochen-Specker, Free Will, and Bell Theorems, the Kadison-Singer conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory. This book is Open Access under a CC BY licence.
Characterizing quantum phase transitions by single qubit operations
Giampaolo, S M; De Siena, S
2006-01-01
We introduce observable quantities, borrowing from concepts of quantum information theory, for the characterization of quantum phase transitions in spin systems. These observables are uniquely defined in terms of single spin unitary operations. We define the energy gap between the ground state and the state produced by the action of a single-qubit local gate. We show that this static quantity involves only single-site expectations and two-point correlation functions on the ground state. We then discuss a dynamical local observable defined as the acceleration of quantum state evolution after performing an instaneous single-qubit perturbation on the ground state. This quantity involves three-point correlations as well. We show that both the static and the dynamical observables detect and characterize completely quantum critical points in a class of spin systems.
Robust Solid State Quantum System Operating at 800 K
Kianinia, Mehran; Regan, Blake; Tran, Toan Trong; Ford, Michael J; Aharonovich, Igor; Toth, Milos
2016-01-01
Realization of Quantum information and communications technologies requires robust, stable solid state single photon sources. However, most existing sources cease to function above cryogenic or room temperature due to thermal ionization or strong phonon coupling which impede their emissive and quantum properties. Here we present an efficient single photon source based on a defect in a van der Waals crystal that is optically stable and operates at elevated temperatures of up to 800 K. The quantum nature of the source and the photon purity are maintained upon heating to 800 K and cooling back to room temperature. Our report of a robust high temperature solid state single photon source constitutes a significant step to-wards practical, integrated quantum technologies for real-world environments.
Institute of Scientific and Technical Information of China (English)
Yu Wen WANG; Jian ZHANG; Yun An CUI
2012-01-01
Let X,Y be Banach spaces and M be a linear subspace in X × Y ={{x,y}|x ∈ X,y ∈ Y}.We may view M as a multi-valued linear operator from X to Y by taking M(x) ={y|{x,y} ∈ M}.In this paper,we give several criteria for a single-valued operator from Y to X to be the metric generalized inverse of the multi-valued linear operator M.The principal tool in this paper is also the generalized orthogonal decomposition theorem in Banach spaces.
Random operators disorder effects on quantum spectra and dynamics
Aizenman, Michael
2015-01-01
This book provides an introduction to the mathematical theory of disorder effects on quantum spectra and dynamics. Topics covered range from the basic theory of spectra and dynamics of self-adjoint operators through Anderson localization-presented here via the fractional moment method, up to recent results on resonant delocalization. The subject's multifaceted presentation is organized into seventeen chapters, each focused on either a specific mathematical topic or on a demonstration of the theory's relevance to physics, e.g., its implications for the quantum Hall effect. The mathematical chapters include general relations of quantum spectra and dynamics, ergodicity and its implications, methods for establishing spectral and dynamical localization regimes, applications and properties of the Green function, its relation to the eigenfunction correlator, fractional moments of Herglotz-Pick functions, the phase diagram for tree graph operators, resonant delocalization, the spectral statistics conjecture, and rela...
Operators from mirror curves and the quantum dilogarithm
Kashaev, Rinat
2015-01-01
Mirror manifolds to toric Calabi-Yau threefolds are encoded in algebraic curves. The quantization of these curves leads naturally to quantum-mechanical operators on the real line. We show that, for a large number of local del Pezzo Calabi-Yau threefolds, these operators are of trace class. In some simple geometries, like local P2, we calculate the integral kernel of the corresponding operators in terms of Faddeev's quantum dilogarithm. Their spectral traces are expressed in terms of multi-dimensional integrals, similar to the state-integrals appearing in three-manifold topology, and we show that they can be evaluated explicitly in some cases. Our results provide further verifications of a recent conjecture which gives an explicit expression for the Fredholm determinant of these operators, in terms of enumerative invariants of the underlying Calabi-Yau threefolds.
Operators from Mirror Curves and the Quantum Dilogarithm
Kashaev, Rinat; Mariño, Marcos
2016-09-01
Mirror manifolds to toric Calabi-Yau threefolds are encoded in algebraic curves. The quantization of these curves leads naturally to quantum-mechanical operators on the real line. We show that, for a large number of local del Pezzo Calabi-Yau threefolds, these operators are of trace class. In some simple geometries, like local {{P}^2}, we calculate the integral kernel of the corresponding operators in terms of Faddeev's quantum dilogarithm. Their spectral traces are expressed in terms of multi-dimensional integrals, similar to the state-integrals appearing in three-manifold topology, and we show that they can be evaluated explicitly in some cases. Our results provide further verifications of a recent conjecture which gives an explicit expression for the Fredholm determinant of these operators, in terms of enumerative invariants of the underlying Calabi-Yau threefolds.
Influences of Gate Operation Errors in the Quantum Counting Algorithm
Institute of Scientific and Technical Information of China (English)
Qing Ai; Yan-Song Li; Gui-Lu Long
2006-01-01
In this article, the error analysis in the quantum counting algorithm is investigated. It has been found that the random error plays as important a role as the systematic error does in the phase inversion operations. Both systematic and random errors are important in the Hadamard transformation. This is quite different from the Grover algorithm and the Shor algorithm.
The Construction of Quantum Field Operators: Something of Interest
Dvoeglazov, Valeri V
2010-01-01
We draw attention to some tune problems in constructions of the quantum-field operators for spins 1/2 and 1. They are related to the existence of negative-energy and acausal solutions of relativistic wave equations. Particular attention is paid to the chiral theories, and to the method of the Lorentz boosts.
Controlled remote implementation of partially unknown quantum operation
Institute of Scientific and Technical Information of China (English)
FAN QiuBo; LIU DongDong
2008-01-01
A protocol for controlled remote implementation of a partially unknown operation on an arbitrary quantum state is proposed. In this protocol, a task can be performed using a GHZ state shared among three distant parties: Alice, Bob and the controller Charlie. This protocol is also generalized to the multi-party control system based on sharing an N-qubit GHZ state.
Directory of Open Access Journals (Sweden)
M. De la Sen
2012-01-01
Full Text Available The stabilization of dynamic switched control systems is focused on and based on an operator-based formulation. It is assumed that the controlled object and the controller are described by sequences of closed operator pairs (L,C on a Hilbert space H of the input and output spaces and it is related to the existence of the inverse of the resulting input-output operator being admissible and bounded. The technical mechanism addressed to get the results is the appropriate use of the fact that closed operators being sufficiently close to bounded operators, in terms of the gap metric, are also bounded. That philosophy is followed for the operators describing the input-output relations in switched feedback control systems so as to guarantee the closed-loop stabilization.
Ihly, Rachelle
This thesis explores the understanding of the chemistry and physics of colloidal quantum dots for practical solar energy photoconversion. Solar cell devices that make use of PbS quantum dots generally rely on constant and unchanged optical properties such that band gap energies remain tuned within the device. The design and development of unique experiments to ascertain mechanisms of optical band gap shifts occurring in PbS quantum dot thin-films exposed to air are discussed. The systematic study of the absorption properties of PbS quantum dot films exposed to air, heat, and UV illumination as a function of quantum dot size has been described. A method to improve the air-stability of films with atomic layer deposition of alumina is demonstrated. Encapsulation of quantum dot films using a protective layer of alumina results in quantum dot solids that maintain tuned absorption for 1000 hours. This thesis focuses on the use of atomic force microscopy and electrical variants thereof to study the physical and electrical characteristics of quantum dot arrays. These types of studies have broad implications in understanding charge transport mechanisms and solar cell device operation, with a particular emphasis on quantum dot transistors and solar cells. Imaging the channel potential of a PbSe quantum dot thin-film in a transistor showed a uniform distribution of charge coinciding with the transistor current voltage characteristics. In a second study, solar cell device operation of ZnO/PbS heterojunction solar cells was investigated by scanning active cross-sections with Kelvin probe microscopy as a function of applied bias, illumination and device architecture. This technique directly provides operating potential and electric field profiles to characterize drift and diffusion currents occurring in the device. SKPM established a field-free region occurring in the quantum dot layer, indicative of diffusion-limited transport. These results provide the path to optimization of
A new theorem relating quantum tomogram to the Fresnel operator
Institute of Scientific and Technical Information of China (English)
Xie Chuan-Mei; Fan Hong-Yi
2011-01-01
According to Fan-Hu's formalism (Fan Hong-Yi and Hu Li-Yun 2009 Opt. Commun. 282 3734) that the tomogram of quantum states can be considered as the module-square of the state wave function in the intermediate coordinatemomentum representation which is just the eigenvector of the Fresnel quadrature phase, we derive a new theorem for calculating quantum tomogram of density operator, i.e., the tomogram of a density operator p is equal to the marginal integration of the classical Weyl correspondence function of F+ρF, where F is the Fresnel operator. Applications of this theorem to evaluating the tomogram of optical chaotic field and squeezed chaotic optical field are presented.
Spectral Gaps of Dirac Operators Describing Graphene Quantum Dots
Benguria, Rafael D.; Fournais, Søren; Stockmeyer, Edgardo; Van Den Bosch, Hanne
2017-06-01
The two-dimensional Dirac operator describes low-energy excitations in graphene. Different choices for the boundary conditions give rise to qualitative differences in the spectrum of the resulting operator. For a family of boundary conditions, we find a lower bound to the spectral gap around zero, proportional to |Ω|-1/2, where {Ω } \\subset R2 is the bounded region where the Dirac operator acts. This family contains the so-called infinite mass and armchair cases used in the physics literature for the description of graphene quantum dots.
Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle
Durdevich, Micho; Sontz, Stephen Bruce
2013-05-01
A quantum principal bundle is constructed for every Coxeter group acting on a finite-dimensional Euclidean space E, and then a connection is also defined on this bundle. The covariant derivatives associated to this connection are the Dunkl operators, originally introduced as part of a program to generalize harmonic analysis in Euclidean spaces. This gives us a new, geometric way of viewing the Dunkl operators. In particular, we present a new proof of the commutativity of these operators among themselves as a consequence of a geometric property, namely, that the connection has curvature zero.
Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle
Directory of Open Access Journals (Sweden)
Micho Đurđevich
2013-05-01
Full Text Available A quantum principal bundle is constructed for every Coxeter group acting on a finite-dimensional Euclidean space E, and then a connection is also defined on this bundle. The covariant derivatives associated to this connection are the Dunkl operators, originally introduced as part of a program to generalize harmonic analysis in Euclidean spaces. This gives us a new, geometric way of viewing the Dunkl operators. In particular, we present a new proof of the commutativity of these operators among themselves as a consequence of a geometric property, namely, that the connection has curvature zero.
Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle
evich, Micho Đurđ
2011-01-01
A quantum principal bundle is constructed for every Coxeter group acting on a finite-dimensional Euclidean space E, and then a connection is also defined on this bundle. The covariant derivatives associated to this connection are the Dunkl operators, originally introduced as part of a program to generalize harmonic analysis in Euclidean spaces. This gives us a new, geometric way of viewing the Dunkl operators. In particular, we present a new proof of the commutivity of these operators among themselves as a consequence of a geometric property, namely, that the connection has curvature zero.
Quantum Tunneling of Massive Spin-1 Particles From Non-stationary Metrics
Sakalli, I
2016-01-01
Hawking radiation (HR) is invariant under the coordinate transformation, and it must be independent of the particle type emitting from the considered black hole (BH). From this fact, we focus on the HR of massive vector (spin-1) particles tunneling from Schwarzschild BH expressed in the Kruskal-Szekeres (KS) and dynamic Lemaitre (DL) coordinates. Using the Proca equation (PE) together with Hamilton-Jacobi (HJ) and WKB methods, we show that the tunneling rate, and its consequence Hawking temperature are well recovered by the quantum tunneling of the massive vector particles. This is the first example for the HR of the massive vector particles tunneling from a four dimensional BH expressed in non-stationary regular coordinates.
Institute of Scientific and Technical Information of China (English)
FAN HongYi
2012-01-01
In quantum mechanics theory one of the basic operator orderings is Q - P and P - Q ordering,where Q and P are the coordinate operator and the momentum operator,respectively.We derive some new fundamental operator identities about their mutual reordering.The technique of integration within Q - P ordering and P - Q ordering is introduced.The Q - P ordered and P - Q ordered formulas of the Wigner operator are also deduced which makes arranging the operators in either Q - P or P - Q ordering much more convenient.
Bengtsson, Ingemar; Zyczkowski, Karol
2007-12-01
Preface; 1. Convexity, colours and statistics; 2. Geometry of probability distributions; 3. Much ado about spheres; 4. Complex projective spaces; 5. Outline of quantum mechanics; 6. Coherent states and group actions; 7. The stellar representation; 8. The space of density matrices; 9. Purification of mixed quantum states; 10. Quantum operations; 11. Duality: maps versus states; 12. Density matrices and entropies; 13. Distinguishability measures; 14. Monotone metrics and measures; 15. Quantum entanglement; Epilogue; Appendices; References; Index.
Quantum logical operations for spin 3/2 quadrupolar nuclei monitored by quantum state tomography.
Bonk, F A; deAzevedo, E R; Sarthour, R S; Bulnes, J D; Freitas, J C C; Guimarães, A P; Oliveira, I S; Bonagamba, T J
2005-08-01
This article presents the realization of many self-reversible quantum logic gates using two-qubit quadrupolar spin 3/2 systems. Such operations are theoretically described using propagation matrices for the RF pulses that include the effect of the quadrupolar evolution during the pulses. Experimental demonstrations are performed using a generalized form of the recently developed method for quantum state tomography in spin 3/2 systems. By doing so, the possibility of controlling relative phases of superimposed pseudo-pure states is demonstrated. In addition, many aspects of the effect of the quadrupolar evolution, occurring during the RF pulses, on the quantum operations performance are discussed. Most of the procedures presented can be easily adapted to describe selective pulses of higher spin systems (>3/2) and for spin 1/2 under J couplings.
Entanglement-assisted operator codeword stabilized quantum codes
Shin, Jeonghwan; Heo, Jun; Brun, Todd A.
2016-05-01
In this paper, we introduce a unified framework to construct entanglement-assisted quantum error-correcting codes (QECCs), including additive and nonadditive codes, based on the codeword stabilized (CWS) framework on subsystems. The CWS framework is a scheme to construct QECCs, including both additive and nonadditive codes, and gives a method to construct a QECC from a classical error-correcting code in standard form. Entangled pairs of qubits (ebits) can be used to improve capacity of quantum error correction. In addition, it gives a method to overcome the dual-containing constraint. Operator quantum error correction (OQEC) gives a general framework to construct QECCs. We construct OQEC codes with ebits based on the CWS framework. This new scheme, entanglement-assisted operator codeword stabilized (EAOCWS) quantum codes, is the most general framework we know of to construct both additive and nonadditive codes from classical error-correcting codes. We describe the formalism of our scheme, demonstrate the construction with examples, and give several EAOCWS codes
Quantum entanglement of local operators in conformal field theories.
Nozaki, Masahiro; Numasawa, Tokiro; Takayanagi, Tadashi
2014-03-21
We introduce a series of quantities which characterize a given local operator in any conformal field theory from the viewpoint of quantum entanglement. It is defined by the increased amount of (Rényi) entanglement entropy at late time for an excited state defined by acting the local operator on the vacuum. We consider a conformal field theory on an infinite space and take the subsystem in the definition of the entanglement entropy to be its half. We calculate these quantities for a free massless scalar field theory in two, four and six dimensions. We find that these results are interpreted in terms of quantum entanglement of a finite number of states, including Einstein-Podolsky-Rosen states. They agree with a heuristic picture of propagations of entangled particles.
The Quantum Field Theory of the Ensemble Operator
Porter, Richard N.
2009-03-01
Quantum field theory (QFT) provides a systematic investigative tool for ensembles of molecules. The grand-canonical ensemble operator (GCEO) for an ideal gas is presented in terms of the Fock creation and annihilation operators. The ideal GCEO can be shown to obey a simple equation which facilitates calculation of quantum-statistical properties of bosonic and fermionic molecules. Examples are linked-cluster QFT derivations of the grand-canonical partition function and the Poisson distribution for non-interacting molecules. The Boltzmann limit is achieved by omitting exchange diagrams. Summations of Feynman diagrams for long- and short-range interactions to infinite order lead to a useful model of the pair-correlation function and a new avenue for the study of dynamics near the critical point for gas-liquid phase transitions.
Fundamental Entangling Operators in Quantum Mechanics and Their Properties
Dao-Ming, Lu
2016-07-01
For the first time, we introduce so-called fundamental entangling operators e^{iQ1 P2} and e^{iP1 Q2 } for composing bipartite entangled states of continuum variables, where Q i and P i ( i = 1, 2) are coordinate and momentum operator, respectively. We then analyze how these entangling operators naturally appear in the quantum image of classical quadratic coordinate transformation ( q 1, q 2) → ( A q 1 + B q 2, C q 1 + D q 2), where A D- B C = 1, which means even the basic coordinate transformation ( Q 1, Q 2) → ( A Q 1 + B Q 2, C Q 1 + D Q 2) involves entangling mechanism. We also analyse their Lie algebraic properties and use the integration technique within an ordered product of operators to show they are also one- and two- mode combinatorial squeezing operators.
Novotny, J; Jex, I
2006-01-01
The structure of all completely positive quantum operations is investigated which transform pure two-qubit input states of a given degree of entanglement in a covariant way. Special cases thereof are quantum NOT operations which transform entangled pure two-qubit input states of a given degree of entanglement into orthogonal states in an optimal way. Based on our general analysis all covariant optimal two-qubit quantum NOT operations are determined. In particular, it is demonstrated that only in the case of maximally entangled input states these quantum NOT operations can be performed perfectly.
Lind, Mats; Lee, Young Lim; Mazanowski, Janusz; Kountouriotis, Georgios K; Bingham, Geoffrey P
2014-02-01
G. P. Bingham and M. Lind (2008, Large continuous perspective transformations are necessary and sufficient for accurate perception of metric shape, Perception & Psychophysics, Vol. 70, pp. 524-540) showed that observers could perceive metric shape, given perspective changes ≥ 45° relative to a principal axis of elliptical cylinders. In this article, we tested (a) arbitrary perspective changes of 45°, (b) whether perception gradually improves with more perspective change, (c) speed of rotation, (d) whether this works with other shapes (asymmetric polyhedrons), (e) different slants, and (f) perspective changes >45°. Experiment 1 compared 45° perspective change away from, versus centered on, a principal axis. Observers adjusted an ellipse to match the cross-section of an elliptical cylinder viewed in a stereo-motion display. Experiment 2 tested whether performance would improve gradually with increases in perspective change, or suddenly with a 45° change. We also tested speed of rotation. Experiment 3 tested (a) asymmetric polyhedrons, (b) perspective change beyond 45°, and (c) the effect of slant. The results showed (a) a particular perspective was not required, (b) judgments only improved with ≥ 45° change, (c) speed was not relevant, (d) it worked with asymmetric polyhedrons, (e) slant was not relevant, and (f) judgments remained accurate beyond 45° of change. A model shows how affine operations, together with a symmetry yielded by 45° perspective change, bootstrap perception of metric shape.
The Diffeomorphism Constraint Operator in Loop Quantum Gravity
Laddha, Alok
2011-01-01
We construct the smeared diffeomorphism constraint operator at finite triangulation from the basic holonomy- flux operators of Loop Quantum Gravity, evaluate its continuum limit on the Lewandowski- Marolf habitat and show that the action of the continuum operator provides an anomaly free representation of the Lie algebra of diffeomorphisms of the 3- manifold. Key features of our analysis include: (i) finite triangulation approximants to the curvature, $F_{ab}^i$ of the Ashtekar- Barbero connection which involve not only small loop holonomies but also small surface fluxes as well as an explicit dependence on the edge labels of the spin network being acted on (ii) the dependence of the small loop underlying the holonomy on both the direction and magnitude of the shift vector field (iii) continuum constraint operators which do {\\em not} have finite action on the kinematic Hilbert space, thus implementing a key lesson from recent studies of parameterised field theory by the authors. Features (i) and (ii) provide ...
Quantum dimensions from local operator excitations in the Ising model
Caputa, Pawel
2016-01-01
We compare the time evolution of entanglement measures after local operator excitation in the critical Ising model with predictions from conformal field theory. For the spin operator and its descendants we find that Renyi entropies of a block of spins increase by a constant that matches the logarithm of the quantum dimension of the conformal family. However, for the energy operator we find a small constant contribution that differs from the conformal field theory answer equal to zero. We argue that the mismatch is caused by the subtleties in the identification between the local operators in conformal field theory and their lattice counterpart. Our results indicate that evolution of entanglement measures in locally excited states not only constraints this identification, but also can be used to extract non-trivial data about the conformal field theory that governs the critical point. We generalize our analysis to the Ising model away from the critical point, states with multiple local excitations, as well as t...
Zhang, Jingfu; Laflamme, Raymond; Suter, Dieter
2012-09-07
Large-scale universal quantum computing requires the implementation of quantum error correction (QEC). While the implementation of QEC has already been demonstrated for quantum memories, reliable quantum computing requires also the application of nontrivial logical gate operations to the encoded qubits. Here, we present examples of such operations by implementing, in addition to the identity operation, the NOT and the Hadamard gate to a logical qubit encoded in a five qubit system that allows correction of arbitrary single-qubit errors. We perform quantum process tomography of the encoded gate operations, demonstrate the successful correction of all possible single-qubit errors, and measure the fidelity of the encoded logical gate operations.
Bosonic Operator Realization of Hamiltonian for a Superconducting Quantum Interference Device
Institute of Scientific and Technical Information of China (English)
FAN Hong-Yi
2004-01-01
Based on the appropriate bosonic phase operator diagonalized in the entangled state representation we construct the Hamiltonian operator model for a superconducting quantum interference device. The current operator and voltage operator equations are derived.
Mog, Robert A.
1999-01-01
Unique and innovative graph theory, neural network, organizational modeling, and genetic algorithms are applied to the design and evolution of programmatic and organizational architectures. Graph theory representations of programs and organizations increase modeling capabilities and flexibility, while illuminating preferable programmatic/organizational design features. Treating programs and organizations as neural networks results in better system synthesis, and more robust data modeling. Organizational modeling using covariance structures enhances the determination of organizational risk factors. Genetic algorithms improve programmatic evolution characteristics, while shedding light on rulebase requirements for achieving specified technological readiness levels, given budget and schedule resources. This program of research improves the robustness and verifiability of systems synthesis tools, including the Complex Organizational Metric for Programmatic Risk Environments (COMPRE).
Composition of quantum operations and products of random matrices
Roga, Wojciech; Zyczkowski, Karol
2011-01-01
Spectral properties of evolution operators corresponding to random maps and quantized chaotic systems strongly interacting with an environment can be described by the ensemble of non-hermitian random matrices from the real Ginibre ensemble. We analyze evolution operators Psi=Psi_s...Psi_1 representing the composition of s random maps and demonstrate that their complex eigenvalues are asymptotically described by the law of Burda et al. obtained for a product of s independent random complex Ginibre matrices. Numerical data support the conjecture that the same results are applicable to characterize the distribution of eigenvalues of the s-th power of a random Ginibre matrix. Squared singular values of Psi are shown to be described by the Fuss-Catalan distribution of order s. Results obtained for products of random Ginibre matrices are also capable to describe the s-step evolution operator for a model deterministic dynamical system - a generalized quantum baker map subjected to strong interaction with an environm...
NASA science publications have used the metric system of measurement since 1970. Although NASA has maintained a metric use policy since 1979, practical constraints have restricted actual use of metric units. In 1988, an amendment to the Metric Conversion Act of 1975 required the Federal Government to adopt the metric system except where impractical. In response to Public Law 100-418 and Executive Order 12770, NASA revised its metric use policy and developed this Metric Transition Plan. NASA's goal is to use the metric system for program development and functional support activities to the greatest practical extent by the end of 1995. The introduction of the metric system into new flight programs will determine the pace of the metric transition. Transition of institutional capabilities and support functions will be phased to enable use of the metric system in flight program development and operations. Externally oriented elements of this plan will introduce and actively support use of the metric system in education, public information, and small business programs. The plan also establishes a procedure for evaluating and approving waivers and exceptions to the required use of the metric system for new programs. Coordination with other Federal agencies and departments (through the Interagency Council on Metric Policy) and industry (directly and through professional societies and interest groups) will identify sources of external support and minimize duplication of effort.
Random Quantum Circuits and Pseudo-Random Operators: Theory and Applications
Emerson, J
2003-01-01
Pseudo-random operators consist of sets of operators that exhibit many of the important statistical features of uniformly distributed random operators. Such pseudo-random sets of operators are most useful whey they may be parameterized and generated on a quantum processor in a way that requires exponentially fewer resources than direct implementation of the uniformly random set. Efficient pseudo-random operators can overcome the exponential cost of random operators required for quantum communication tasks such as super-dense coding of quantum states and approximately secure quantum data-hiding, and enable efficient stochastic methods for noise estimation on prototype quantum processors. This paper summarizes some recently published work demonstrating a random circuit method for the implementation of pseudo-random unitary operators on a quantum processor [Emerson et al., Science 302:2098 (Dec.~19, 2003)], and further elaborates the theory and applications of pseudo-random states and operators.
Operational dynamic modeling transcending quantum and classical mechanics.
Bondar, Denys I; Cabrera, Renan; Lompay, Robert R; Ivanov, Misha Yu; Rabitz, Herschel A
2012-11-09
We introduce a general and systematic theoretical framework for operational dynamic modeling (ODM) by combining a kinematic description of a model with the evolution of the dynamical average values. The kinematics includes the algebra of the observables and their defined averages. The evolution of the average values is drawn in the form of Ehrenfest-like theorems. We show that ODM is capable of encompassing wide-ranging dynamics from classical non-relativistic mechanics to quantum field theory. The generality of ODM should provide a basis for formulating novel theories.
Irreducible Tensor Operators and Multiple-Quantum NMR.
Hutchison, Wayne Douglas
The aim of the work detailed in this thesis, is to provide a concise, and illuminating, mathematical description of multiple quantum nuclear magnetic resonance (MQNMR) experiments, on essentially isolated (non-coupled) nuclei. The treatment used is based on irreducible tensor operators, which form an orthonormal basis set. Such operators can be used to detail the state of the nuclear ensemble (density matrix) during every stage, preparation, evolution and detection, of a MQNMR experiment. Moreover, such operators can be also used to provide a rigorous analysis of pulsed NMR experiments, on oriented nuclei at low temperatures, where the initial density matrix is far from trivial. The specific topics dealt with in this thesis are as follows. In the first place the properties of irreducible tensor operators are discussed in some detail. In particular, symmetric and anti-symmetric combinations of tensor operators are introduced, to reflect the Hermitian nature of the nuclear Hamiltonian and density matrix. Secondly, the creation of multipolar nuclear states using hard, non-selective rf pulses, is detailed for spin I = 1, 3/2, 2 and 5/2 nuclei, subject to an axially symmetric quadrupole interaction. Results are also given for general I. Thirdly, some experimental results, verifying the production of a triple quantum NMR state, for the I = 3/2 ^{23}Na nuclei in a single crystal of NaIO_4 are presented and discussed. Fourthly, the treatment of MQNMR experiments is extended to the low temperature regime where the initial density matrix includes Fano statistical tensors other than rank one. In particular, it is argued that MQNMR techniques could be used to enhance the anisotropy of gamma-ray emission from oriented nuclei at low temperatures. Fifthly, the effect of a more general quadrupole Hamiltonian (including an asymmetry term) on MQNMR experiments is considered for spins I = 1 and 3/2. In particular, it is shown that double quantum states evolve to give longitudinal NMR
Molecular machines operating on the nanoscale: from classical to quantum
Directory of Open Access Journals (Sweden)
Igor Goychuk
2016-03-01
Full Text Available The main physical features and operating principles of isothermal nanomachines in the microworld, common to both classical and quantum machines, are reviewed. Special attention is paid to the dual, constructive role of dissipation and thermal fluctuations, the fluctuation–dissipation theorem, heat losses and free energy transduction, thermodynamic efficiency, and thermodynamic efficiency at maximum power. Several basic models are considered and discussed to highlight generic physical features. This work examines some common fallacies that continue to plague the literature. In particular, the erroneous beliefs that one should minimize friction and lower the temperature for high performance of Brownian machines, and that the thermodynamic efficiency at maximum power cannot exceed one-half are discussed. The emerging topic of anomalous molecular motors operating subdiffusively but very efficiently in the viscoelastic environment of living cells is also discussed.
Induced Ginibre ensemble of random matrices and quantum operations
Fischmann, J; Khoruzhenko, B A; Sommers, H -J; Zyczkowski, K
2011-01-01
A generalisation of the Ginibre ensemble of non-Hermitian random square matrices is introduced. The corresponding probability measure is induced by the ensemble of rectangular Gaussian matrices via a quadratisation procedure. We derive the joint probability density of eigenvalues for such induced Ginibre ensemble and study various spectral correlation functions for complex and real matrices, and analyse universal behaviour in the limit of large dimensions. In this limit the eigenvalues of the induced Ginibre ensemble cover uniformly a ring in the complex plane. The real induced Ginibre ensemble is shown to be useful to describe statistical properties of evolution operators associated with random quantum operations, for which the dimensions of the input state and the output state do differ.
Quantum dimensions from local operator excitations in the Ising model
Caputa, Paweł; Rams, Marek M.
2017-02-01
We compare the time evolution of entanglement measures after local operator excitation in the critical Ising model with predictions from conformal field theory. For the spin operator and its descendants we find that Rényi entropies of a block of spins increase by a constant that matches the logarithm of the quantum dimension of the conformal family. However, for the energy operator we find a small constant contribution that differs from the conformal field theory answer equal to zero. We argue that the mismatch is caused by the subtleties in the identification between the local operators in conformal field theory and their lattice counterpart. Our results indicate that evolution of entanglement measures in locally excited states not only constraints this identification, but also can be used to extract non-trivial data about the conformal field theory that governs the critical point. We generalize our analysis to the Ising model away from the critical point, states with multiple local excitations, as well as the evolution of the relative entropy after local operator excitation and discuss universal features that emerge from numerics.
Blecher, David P
2012-01-01
The present paper is a sequel to our paper "Metric characterization of isometries and of unital operator spaces and systems". We characterize certain common objects in the theory of operator spaces (unitaries, unital operator spaces, operator systems, operator algebras, and so on), in terms which are purely linear-metric, by which we mean that they only use the vector space structure of the space and its matrix norms. In the last part we give some characterizations of operator algebras (which are not linear-metric in our strict sense described in the paper).
Codes in W*-Metric Spaces: Theory and Examples
Bumgardner, Christopher J.
2011-01-01
We introduce a "W*"-metric space, which is a particular approach to non-commutative metric spaces where a "quantum metric" is defined on a von Neumann algebra. We generalize the notion of a quantum code and quantum error correction to the setting of finite dimensional "W*"-metric spaces, which includes codes and error correction for classical…
Kroon, Cindy D.
2007-01-01
Created for a Metric Day activity, Metric Madness is a board game for two to four players. Students review and practice metric vocabulary, measurement, and calculations by playing the game. Playing time is approximately twenty to thirty minutes.
Semiclassical genetic algorithm with quantum crossover and mutation operations
SaiToh, Akira; Nakahara, Mikio
2012-01-01
In order for finding a good individual for a given fitness function in the context of evolutionary computing, we introduce a novel semiclassical quantum genetic algorithm. It has both of quantum crossover and quantum mutation procedures unlike conventional quantum genetic algorithms. A complexity analysis shows a certain improvement over its classical counterpart.
Jorgensen, PET
1987-01-01
Historically, operator theory and representation theory both originated with the advent of quantum mechanics. The interplay between the subjects has been and still is active in a variety of areas.This volume focuses on representations of the universal enveloping algebra, covariant representations in general, and infinite-dimensional Lie algebras in particular. It also provides new applications of recent results on integrability of finite-dimensional Lie algebras. As a central theme, it is shown that a number of recent developments in operator algebras may be handled in a particularly e
Measures of coherence-generating power for quantum unital operations
Zanardi, Paolo; Styliaris, Georgios; Campos Venuti, Lorenzo
2017-05-01
Given an orthonormal basis B in a d -dimensional Hilbert space and a unital quantum operation E acting on it, one can define a nonlinear mapping that associates with E a d ×d real-valued matrix that we call the coherence matrix of E with respect to B . This is the Gram matrix of the coherent part of the basis projections of B under E . We show that one can use this coherence matrix to define vast families of measures of the coherence-generating power (CGP) of the operation. These measures have a natural geometrical interpretation as separation of E from the set of incoherent unital operations. The probabilistic approach to CGP discussed in P. Zanardi et al. [Phys. Rev. A 95, 052306 (2017)., 10.1103/PhysRevA.95.052306] can be reformulated and generalized, introducing, alongside the coherence matrix, another d ×d real-valued matrix, the simplex correlation matrix. This matrix describes the relevant statistical correlations in the input ensemble of incoherent states. Contracting these two matrices, one finds CGP measures associated with the process of preparing the given incoherent ensemble and processing it with the chosen unital operation. Finally, in the unitary case, we discuss how these concepts can be made compatible with an underlying tensor product structure by defining families of CGP measures that are additive.
Quantum Encoding and Entanglement in Terms of Phase Operators Associated with Harmonic Oscillator
Singh, Manu Pratap; Rajput, B. S.
2016-10-01
Realization of qudit quantum computation has been presented in terms of number operator and phase operators associated with one-dimensional harmonic oscillator and it has been demonstrated that the representations of generalized Pauli group, viewed in harmonic oscillator operators, allow the qudits to be explicitly encoded in such systems. The non-Hermitian quantum phase operators contained in decomposition of the annihilation and creation operators associated with harmonic oscillator have been analysed in terms of semi unitary transformations (SUT) and it has been shown that the non-vanishing analytic index for harmonic oscillator leads to an alternative class of quantum anomalies. Choosing unitary transformation and the Hermitian phase operator free from quantum anomalies, the truncated annihilation and creation operators have been obtained for harmonic oscillator and it has been demonstrated that any attempt of removal of quantum anomalies leads to absence of minimum uncertainty.
Robustness of coherence: An operational and observable measure of quantum coherence
Napoli, Carmine; Cianciaruso, Marco; Piani, Marco; Johnston, Nathaniel; Adesso, Gerardo
2016-01-01
Quantifying coherence is an essential endeavour for both quantum foundations and quantum technologies. Here the robustness of coherence is defined and proven a full monotone in the context of the recently introduced resource theories of quantum coherence. The measure is shown to be observable, as it can be recast as the expectation value of a coherence witness operator for any quantum state. The robustness of coherence is evaluated analytically on relevant classes of states, and an efficient semidefinite program that computes it on general states is given. An operational interpretation is finally provided: the robustness of coherence quantifies the advantage enabled by a quantum state in a phase-discrimination task.
Entanglement Entropy of Local Operators in Quantum Lifshitz Theory
Zhou, Tianci
2016-01-01
We study the growth of entanglement entropy(EE) of local operator excitation in the quantum Lifshitz model which has dynamic exponent z = 2. Specifically, we act a local vertex operator on the groundstate at a distance $l$ to the entanglement cut and calculate the EE as a function of time for the state's subsequent time evolution. We find that the excess EE compared with the groundstate is a monotonically increasing function which is vanishingly small before the onset at $t \\sim l^2$ and eventually saturates to a constant proportional to the scaling dimension of the vertex operator. The quasi-particle picture can interpret the final saturation as the exhaustion of the quasi-particle pairs, while the diffusive nature of the time scale $t \\sim l^2$ replaces the common causality constraint in CFT calculation. To further understand this property, we compute the excess EE of a small disk probe far from the excitation point and find chromatography pattern in EE generated by quasi-particles of different propagation ...
Yao, Xing-Can; Fiurásek, Jaromír; Lu, He; Gao, Wei-Bo; Chen, Yu-Ao; Chen, Zeng-Bing; Pan, Jian-Wei
2010-09-17
We experimentally demonstrate an advanced linear-optical programmable quantum processor that combines two elementary single-qubit programmable quantum gates. We show that this scheme enables direct experimental probing of quantum commutation relations for Pauli operators acting on polarization states of single photons. Depending on a state of two-qubit program register, we can probe either commutation or anticommutation relations. Very good agreement between theory and experiment is observed, indicating high-quality performance of the implemented quantum processor.
2015-02-16
Microwave-driven coherent operation of a semiconductor quantum dot charge qubit Dohun Kim,1 D. R. Ward,1 C. B. Simmons,1 John King Gamble,2 Robin...Fig.4a. Coherent microwave ac-gating of a semiconductor quantum dot charge qubit offers fast ( >GHz) manip- ulation rates for all elementary rotation...2014). [12] Kim, D. et al. Quantum control and process tomography of a semiconductor quantum dot hybrid qubit. Nature 511, 70–74 (2014). [13] Vion, D
Quantum walk through lattice with temporal, spatial, and fluctuating disordered operations
Chandrashekar, C M
2011-01-01
Quantum walks and its dynamic properties have provided a framework to various applications ranging from quantum computing to simulation of physical processes in nature. We present a discrete-time quantum walk model with the evolution operator for each step in the form of the Hamiltonian operator. The Hamiltonian form of the evolution operator is extended to define the discrete-time quantum walk using two-state particle on a two-dimensional lattice structure such as, triangular, kagome and honeycomb lattice. We also study the walk dynamics using temporal, spatially static, and fluctuating disordered unitary evolution operators and show that the localization is possible only with a spatially static disordered operations. This approach provides a general framework for using a two-state particle discrete-time quantum walk to simulate, control, and study the dynamics in form of ordered and disordered Hamiltonian operations in various one- and two-dimensional physical systems.
Sarkar, Sarben
2010-01-01
The role of Finsler-like metrics in situations where Lorentz symmetry breaking and also CPT violation are discussed. Various physical instances of such metrics both in quantum gravity and analogue systems are discussed. Both differences and similarities between the cases will be emphasised. In particular the medium of D-particles that arise in string theory will be examined. In this case the breaking of Lorentz invariance, at the level of quantum fluctuations, together with concomitant CPT in certain situations will be analysed. In particular it will be shown correlations for neutral meson pairs will be modified and a new contribution to baryogenesis will appear.
Metric-adjusted skew information
DEFF Research Database (Denmark)
Liang, Cai; Hansen, Frank
2010-01-01
We give a truly elementary proof of the convexity of metric-adjusted skew information following an idea of Effros. We extend earlier results of weak forms of superadditivity to general metric-adjusted skew information. Recently, Luo and Zhang introduced the notion of semi-quantum states on a bipa......We give a truly elementary proof of the convexity of metric-adjusted skew information following an idea of Effros. We extend earlier results of weak forms of superadditivity to general metric-adjusted skew information. Recently, Luo and Zhang introduced the notion of semi-quantum states...
Lin, Jun-You; He, Jun-Gang; Gao, Yan-Chun; Li, Xue-Mei; Zhou, Ping
2017-04-01
We present a scheme for controlled remote implementation of an arbitrary single-qubit operation by using partially entangled states as the quantum channel. The sender can remote implement an arbitrary single-qubit operation on the remote receiver's quantum system via partially entangled states under the controller's control. The success probability for controlled remote implementation of quantum operation can achieve 1 if the sender and the controller perform proper projective measurements on their entangled particles. Moreover, we also discuss the scheme for remote sharing the partially unknown operations via partially entangled quantum channel. It is shown that the quantum entanglement cost and classical communication can be reduced if the implemented operation belongs to the restrict sets.
About the velocity operator for spinning particles in quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Salesi, Giovanni [Universita Statale di Catania (Italy). Dipt. di Fisica]|[Istituto Nazionale di Fisica Nucleare, Catania (Italy); Recami, Erasmo; Rodrigues Junior, Waldyr A. [Universidade Estadual de Campinas, SP (Brazil). Dept. de Matematica Aplicada
1995-12-01
Starting from the formal expressions of the hydrodynamical (or local) quantities employed in the applications of Clifford Algebras to quantum mechanics, we introduce - in terms of the ordinary tensorial framework - a new definition for the field of a generic quantity. By translating from Clifford into sensor algebra, we also propose a new (non-relativistic) velocity operator for a spin 1/2 particle. This operator is the sum of the ordinary part p/m describing the mean motion (the motion of the center-of-mass), and of a second part associated with the so-called Zitterbewegung, which is the spin internal motion observed in the center-of-mass frame. This spin component of the velocity operator is non-zero not only in the Pauli theoretical framework in presence of external magnetic fields and spin precession, but also in the Schroedinger case, when the wave-function is a spin eigenstate. In the latter case, one gets a decomposition of the velocity field for the Madelueng fluid into two distinct parts: which constitutes the non-relativistic analogue of the Gordon decomposition for the Dirac current. We find furthermore that the Zitterbewegung motion involves a velocity field which is solenoidal, and that the local angular velocity is parallel to the spin vector. In presence of a non-constant spin vector (Pauli case) we have, besides the component normal to spin present even in the Schroedinger theory, also a component of the local velocity which is parallel to the rotor of the spin vector. (author). 19 refs.
The Conal representation of Quantum States and Non Trace-Preserving Quantum Operations
Arrighi, P; Arrighi, Pablo; Patricot, Christophe
2003-01-01
We represent generalized density matrices of a $d$-complex dimensional quantum system as a subcone of a real pointed cone of revolution in $\\mathbb{R}^{d^2}$, or indeed a Minkowskian cone in $\\mathbb{E}^{1,d^2-1}$. Generalized pure states correspond to certain future-directed light-like vectors of $\\mathbb{E}^{1,d^2-1}$. This extension of the Generalized Bloch Sphere enables us to cater for non-trace-preserving quantum operations, and in particluar to view the per-outcome effects of generalized measurements. We show that these consist of the product of an orthogonal transform about the axis of the cone of revolution and a positive real linear transform. We give detailed formulae for the one qubit case and express the post-measurement states in terms of the initial state vectors and measurement vectors. We apply these results in order to find the information gain versus disturbance tradeoff in the case of two equiprobable pure states. Thus we recover Fuch's formula in an elegant manner.
On the maximum speed of operation of a quantum "black box"
Dugic, M
2001-01-01
We investigate the minimum time needed for (i.e. the maximum speed of) a quantum "black box" ("oracle") operation which employs "quantum parallelism" to be executed. We emphasize that the operation considered employs the quantum-measurement-like establishing of entanglement in the composite system "input register + output register" of a quantum computer's hardware, and we show that the speed of the operation can be increased by increasing the coupling (strength of interaction) in the composite system, as well as by some local operations (e.g., a proper state preparation) performed on the output register. It also proves that the operation employing a macroscopic (or at least a mesoscopic) system to mediate the registers' interaction should be much faster than the operation performed through direct registers' interaction. Finally, we show that adding energy to the composite system needs not to speed up the operation considered. Rather, e.g., in the case of mutually directly interacting registers, the requiremen...
Some remarks on quasi-Hermitian operators
Energy Technology Data Exchange (ETDEWEB)
Antoine, Jean-Pierre, E-mail: jean-pierre.antoine@uclouvain.be [Institut de Recherche en Mathématique et Physique, Université Catholique de Louvain, B-1348 Louvain-la-Neuve (Belgium); Trapani, Camillo, E-mail: camillo.trapani@unipa.it [Dipartimento di Matematica e Informatica, Università di Palermo, I-90123, Palermo (Italy)
2014-01-15
A quasi-Hermitian operator is an operator that is similar to its adjoint in some sense, via a metric operator, i.e., a strictly positive self-adjoint operator. Whereas those metric operators are in general assumed to be bounded, we analyze the structure generated by unbounded metric operators in a Hilbert space. Following our previous work, we introduce several generalizations of the notion of similarity between operators. Then we explore systematically the various types of quasi-Hermitian operators, bounded or not. Finally, we discuss their application in the so-called pseudo-Hermitian quantum mechanics.
Chistyakov, Vyacheslav
2015-01-01
Aimed toward researchers and graduate students familiar with elements of functional analysis, linear algebra, and general topology; this book contains a general study of modulars, modular spaces, and metric modular spaces. Modulars may be thought of as generalized velocity fields and serve two important purposes: generate metric spaces in a unified manner and provide a weaker convergence, the modular convergence, whose topology is non-metrizable in general. Metric modular spaces are extensions of metric spaces, metric linear spaces, and classical modular linear spaces. The topics covered include the classification of modulars, metrizability of modular spaces, modular transforms and duality between modular spaces, metric and modular topologies. Applications illustrated in this book include: the description of superposition operators acting in modular spaces, the existence of regular selections of set-valued mappings, new interpretations of spaces of Lipschitzian and absolutely continuous mappings, the existe...
Fraunhofer regime of operation for superconducting quantum interference filters
DEFF Research Database (Denmark)
Shadrin, A.V.; Constantinian, K.Y.; Ovsyannikov, G.A.;
2008-01-01
Series arrays of superconducting quantum interference devices (SQUIDs) with incommensurate loop areas, so-called superconducting quantum interference filters (SQIFs), are investigated in the kilohertz and the gigahertz frequency range. In SQIFs made of high-T-c bicrystal junctions the flux-to-vol...
Scaling dimensions of manifestly generally covariant operators in two-dimensional quantum gravity
Nishimura, J; Tsuchiya, A; Jun Nishimura; Shinya Tamura; Asato Tsuchiya
1994-01-01
Using (2+$\\epsilon$)-dimensional quantum gravity recently formulated by Kawai, Kitazawa and Ninomiya, we calculate the scaling dimensions of manifestly generally covariant operators in two-dimensional quantum gravity coupled to $(p,q)$ minimal conformal matter. In the spectrum appear all the scaling dimensions of the scaling operators in the matrix model except the boundary operators, while there are also many others which have no corresponding scaling dimensions in the matrix model.
Institute of Scientific and Technical Information of China (English)
Ananya Ghatak; Bhabani Prasad Mandal
2013-01-01
To develop a unitary quantum theory with probabilistic description for pseudo-Hermitian systems one needs to consider the theories in a different Hilbert space endowed with a positive definite metric operator.There are different approaches to find such metric operators.We compare the different approaches of calculating positive definite metric operators in pseudo-Hermitian theories with the help of several explicit examples in non-relativistic as well as in relativistic situations.Exceptional points and spontaneous symmetry breaking are also discussed in these models.
An Operator-Based Exact Treatment of Open Quantum Systems
Nicolosi, S
2005-01-01
"Quantum mechanics must be regarded as open systems. On one hand, this is due to the fact that, like in classical physics, any realistic system is subjected to a coupling to an uncontrollable environment which influences it in a non-negligible way. The theory of open quantum systems thus plays a major role in many applications of quantum physics since perfect isolation of quantum system is not possible and since a complete microscopic description or control of the environment degrees of freedom is not feasible or only partially so" [1]. Practical considerations therefore force one to seek for a simpler, effectively probabilistic description in terms of an open system. There is a close physical and mathematical connection between the evolution of an open system, the state changes induced by quantum measurements, and the classical notion of a stochastic process. The paper provides a bibliographic review of this interrelations, it shows the mathematical equivalence between markovian master equation and generaliz...
Rotta, Davide; Sebastiano, Fabio; Charbon, Edoardo; Prati, Enrico
2017-06-01
Even the quantum simulation of an apparently simple molecule such as Fe2S2 requires a considerable number of qubits of the order of 106, while more complex molecules such as alanine (C3H7NO2) require about a hundred times more. In order to assess such a multimillion scale of identical qubits and control lines, the silicon platform seems to be one of the most indicated routes as it naturally provides, together with qubit functionalities, the capability of nanometric, serial, and industrial-quality fabrication. The scaling trend of microelectronic devices predicting that computing power would double every 2 years, known as Moore's law, according to the new slope set after the 32-nm node of 2009, suggests that the technology roadmap will achieve the 3-nm manufacturability limit proposed by Kelly around 2020. Today, circuital quantum information processing architectures are predicted to take advantage from the scalability ensured by silicon technology. However, the maximum amount of quantum information per unit surface that can be stored in silicon-based qubits and the consequent space constraints on qubit operations have never been addressed so far. This represents one of the key parameters toward the implementation of quantum error correction for fault-tolerant quantum information processing and its dependence on the features of the technology node. The maximum quantum information per unit surface virtually storable and controllable in the compact exchange-only silicon double quantum dot qubit architecture is expressed as a function of the complementary metal-oxide-semiconductor technology node, so the size scale optimizing both physical qubit operation time and quantum error correction requirements is assessed by reviewing the physical and technological constraints. According to the requirements imposed by the quantum error correction method and the constraints given by the typical strength of the exchange coupling, we determine the workable operation frequency
2016-12-02
Networking with QUantum operationally-Secure Technology for Maritime Deployment (CONQUEST) Contract Period of Performance: 2 September 2016 – 1 September...potential of using advanced photonic integrated circuits to enable high- speed quantum-secure communications. Task 5: QKD network via un-trusted quantum...has a practical advantage in its imple- mentation since it can use conventional optical telecom components, and does not require cryostats to support
Lorentz covariant reduced-density-operator theory for relativistic quantum information processing
Ahn, D; Hwang, S W; Ahn, Doyeol; Lee, Hyuk-jae; Hwang, Sung Woo
2003-01-01
In this paper, we derived Lorentz covariant quantum Liouville equation for the density operator which describes the relativistic quantum information processing from Tomonaga-Schwinger equation and an exact formal solution for the reduced-density-operator is obtained using the projector operator technique and the functional calculus. When all the members of the family of the hypersurfaces become flat hyperplanes, it is shown that our results agree with those of non-relativistic case which is valid only in some specified reference frame. The formulation presented in this work is general and might be applied to related fields such as quantum electrodynamics and relativistic statistical mechanics.
Directory of Open Access Journals (Sweden)
Masanao Ozawa
2017-01-01
Full Text Available In quantum logic there is well-known arbitrariness in choosing a binary operation for conditional. Currently, we have at least three candidates, called the Sasaki conditional, the contrapositive Sasaki conditional, and the relevance conditional. A fundamental problem is to show how the form of the conditional follows from an analysis of operational concepts in quantum theory. Here, we attempt such an analysis through quantum set theory (QST. In this paper, we develop quantum set theory based on quantum logics with those three conditionals, each of which defines different quantum logical truth value assignment. We show that those three models satisfy the transfer principle of the same form to determine the quantum logical truth values of theorems of the ZFC set theory. We also show that the reals in the model and the truth values of their equality are the same for those models. Interestingly, however, the order relation between quantum reals significantly depends on the underlying conditionals. We characterize the operational meanings of those order relations in terms of joint probability obtained by the successive projective measurements of arbitrary two observables. Those characterizations clearly show their individual features and will play a fundamental role in future applications to quantum physics.
Metric measure space as a framework for gravitation
Rahmanpour, Nafiseh; Shojaie, Hossein
2016-10-01
In this manuscript, we show how conformal invariance can be incorporated in a classical theory of gravitation, in the context of metric measure space. Metric measure space involves a geometrical scalar f, dubbed as density function, which here appears as a conformal degree of freedom. In this framework, we present conformally invariant field equations, the relevant identities and geodesic equations. In metric measure space, the volume element and accordingly the operators with integral based definitions are modified. For instance, the divergence operator in this space differs from the Riemannian one. As a result, a gravitational theory formulated in this space has a generalized second Bianchi identity and a generalized conservation of energy-momentum tensor. It is shown how, by using the generalized identity for conservation of energy-momentum tensor, one can obtain a conformally invariant geodesic equation. By comparison of the geodesic equations in metric measure space with the Bohmian trajectories, in both relativistic and non-relativistic regimes, a relation between density function f and the quantum potential is proposed. This suggests metric measure space to be considered as a suitable framework for geometric description of Bohm's quantum mechanics. On the other hand, as it is known, Weyl geometry is one of the main approaches to construct conformally invariant gravitational models. Regarding the fact that the connection in the integrable Weyl space is modified and in metric measure space remains the same as it is in the Riemann space, the mathematical analogy between these two spaces is also discussed.
Metric adjusted skew information
DEFF Research Database (Denmark)
Hansen, Frank
2008-01-01
establish a connection between the geometrical formulation of quantum statistics as proposed by Chentsov and Morozova and measures of quantum information as introduced by Wigner and Yanase and extended in this article. We show that the set of normalized Morozova-Chentsov functions describing the possible...... quantum statistics is a Bauer simplex and determine its extreme points. We determine a particularly simple skew information, the "¿-skew information," parametrized by a ¿ ¿ (0, 1], and show that the convex cone this family generates coincides with the set of all metric adjusted skew informations.......We extend the concept of Wigner-Yanase-Dyson skew information to something we call "metric adjusted skew information" (of a state with respect to a conserved observable). This "skew information" is intended to be a non-negative quantity bounded by the variance (of an observable in a state...
Inequalities for quantum skew information
DEFF Research Database (Denmark)
Audenaert, Koenraad; Cai, Liang; Hansen, Frank
2008-01-01
We study quantum information inequalities and show that the basic inequality between the quantum variance and the metric adjusted skew information generates all the multi-operator matrix inequalities or Robertson type determinant inequalities studied by a number of authors. We introduce an order...... relation on the set of functions representing quantum Fisher information that renders the set into a lattice with an involution. This order structure generates new inequalities for the metric adjusted skew informations. In particular, the Wigner-Yanase skew information is the maximal skew information...... with respect to this order structure in the set of Wigner-Yanase-Dyson skew informations....
Ihly, Rachelle
2014-01-01
This thesis explores the understanding of the chemistry and physics of colloidal quantum dots for practical solar energy photoconversion. Solar cell devices that make use of PbS quantum dots generally rely on constant and unchanged optical properties such that band gap energies remain tuned within the device. The design and development of unique experiments to ascertain mechanisms of optical band gap shifts occurring in PbS quantum dot thin-films exposed to air are discussed. The systematic s...
Lee, Kai-Yan; Fung, Chi-Hang Fred; Chau, H. F.
2013-05-01
We investigate the necessary and sufficient condition for a convex cone of positive semidefinite operators to be fixed by a unital quantum operation ϕ acting on finite-dimensional quantum states. By reducing this problem to the problem of simultaneous diagonalization of the Kraus operators associated with ϕ, we can completely characterize the kinds of quantum states that are fixed by ϕ. Our work has several applications. It gives a simple proof of the structural characterization of a unital quantum operation that acts on finite-dimensional quantum states—a result not explicitly mentioned in earlier studies. It also provides a necessary and sufficient condition for determining what kind of measurement statistics is preserved by a unital quantum operation. Finally, our result clarifies and extends the work of Størmer by giving a proof of a reduction theorem on the unassisted and entanglement-assisted classical capacities, coherent information, and minimal output Renyi entropy of a unital channel acting on a finite-dimensional quantum state.
Battle of the sexes game analysis using Yang-Baxter operator as quantum gate
López R., Juan M.
2012-06-01
The Battle of the Sexes game is analyzed from quantum game theory using quantum initial states as possible strategies for two players. Quantum circuits are presented as schemes of development proposing also the use of Yang-Baxter operators as quantum gates in the circuits. This formalism is implemented using a Computer Algebra Software (CAS) due to its complex and long mathematical treatment. Payoff matrices of the players are given as the results for each case shown. Biology and finances applications are also proposed.
A quantum switching architecture on the basis of limited nonlocal operation
Institute of Scientific and Technical Information of China (English)
JIANG Min; ZHANG Zeng-ke; DONG Dao-yi
2006-01-01
Quantum information system is fragile to be disturbed by the external environment. Quantum switching architecture is one of the promising schemes for transferring input quantum data to its destination port substituted for fully connected quantum networks. Since at present, interactions between the qubits are limited to a small number of neighboring qubits, one novel approach was extended, and the improved architecture was further demonstrated under limited nonlocal operation. The performance evaluation shows that the whole architecture with improved control module can achieve a time complexity of O(n2) and will be more feasible for physical realization.
Area metric gravity and accelerating cosmology
Punzi, R; Wohlfarth, M N R; Punzi, Raffaele; Schuller, Frederic P.; Wohlfarth, Mattias N.R.
2007-01-01
Area metric manifolds emerge as effective classical backgrounds in quantum string theory and quantum gauge theory, and present a true generalization of metric geometry. Here, we consider area metric manifolds in their own right, and develop in detail the foundations of area metric differential geometry. Based on the construction of an area metric curvature scalar, which reduces in the metric-induced case to the Ricci scalar, we re-interpret the Einstein-Hilbert action as dynamics for an area metric spacetime. In contrast to modifications of general relativity based on metric geometry, no continuous deformation scale needs to be introduced; the extension to area geometry is purely structural and thus rigid. We present an intriguing prediction of area metric gravity: without dark energy or fine-tuning, the late universe exhibits a small acceleration.
More on effective composite metrics
Heisenberg, Lavinia
2015-07-01
In this work we study different classes of effective composite metrics proposed in the context of one-loop quantum corrections in bimetric gravity. For this purpose we consider contributions of the matter loops in the form of cosmological constants and potential terms yielding two types of effective composite metrics. This guarantees a nice behavior at the quantum level. However, the theoretical consistency at the classical level needs to be ensured additionally. It turns out that among all these possible couplings, only one unique effective metric survives these criteria at the classical level.
More on effective composite metrics
Heisenberg, Lavinia
2015-01-01
In this work we study different classes of effective composite metrics proposed in the context of one-loop quantum corrections in bimetric gravity. For this purpose we consider contributions of the matter loops in form of cosmological constants and potential terms yielding two types of effective composite metrics. This guarantees a nice behaviour at the quantum level. However, the theoretical consistency at the classical level needs to be ensured additionally. It turns out that among all these possible couplings only one unique effective metric survives this criteria at the classical level.
A Quantum Computational Semantics for Epistemic Logical Operators. Part I: Epistemic Structures
Beltrametti, Enrico; Dalla Chiara, Maria Luisa; Giuntini, Roberto; Leporini, Roberto; Sergioli, Giuseppe
2014-10-01
Some critical open problems of epistemic logics can be investigated in the framework of a quantum computational approach. The basic idea is to interpret sentences like "Alice knows that Bob does not understand that π is irrational" as pieces of quantum information (generally represented by density operators of convenient Hilbert spaces). Logical epistemic operators ( to understand, to know…) are dealt with as (generally irreversible) quantum operations, which are, in a sense, similar to measurement-procedures. This approach permits us to model some characteristic epistemic processes, that concern both human and artificial intelligence. For instance, the operation of "memorizing and retrieving information" can be formally represented, in this framework, by using a quantum teleportation phenomenon.
Non-adiabatic holonomy operators in classical and quantum completely integrable systems
Giachetta, G; Sardanashvily, G
2002-01-01
Given a completely integrable system, we associate to any connection on its invariant tori fibred over a parameter manifold the classical and quantum holonomy operator (generalized Berry's phase factor), without any adiabatic approximation.
Das, Ashok
2016-01-01
We develop an operator description, much like thermofield dynamics, for quantum field theories on a real time path with an arbitrary parameter $\\sigma\\,(0\\leq\\sigma\\leq\\beta)$. We point out new features which arise when $\\sigma\
Modified SQUID Operator Equation for a Single-Qubit Structure Coupled to a Quantum Resonator
Institute of Scientific and Technical Information of China (English)
LIANG Bao-Long; WANG Ji-Suo; FAN Hong-Yi; MENG Xiang-Guo
2008-01-01
Role of self-inductance in superconducting quantum interference device (SQUID) charge qubit is considered. It is found that when an SQUID charge qubit is coupled to a quantum LC resonator, the SQUID voltage operator equation is modified in accompanying with the modification of operator Faraday equation describing the inductance. It is shown that when the extra energy is applied to the junction, the mean phase will be squeezed according to a damping factor.
Unified Theory of Annihilation-Creation Operators for Solvable (`Discrete') Quantum Mechanics
Odake, Satoru; Sasaki, Ryu
2006-01-01
The annihilation-creation operators $a^{(\\pm)}$ are defined as the positive/negative frequency parts of the exact Heisenberg operator solution for the `sinusoidal coordinate'. Thus $a^{(\\pm)}$ are hermitian conjugate to each other and the relative weights of various terms in them are solely determined by the energy spectrum. This unified method applies to most of the solvable quantum mechanics of single degree of freedom including those belonging to the `discrete' quantum mechanics.
Noon, Abbas; Kadry, Seifedine
2011-01-01
Round Robin, considered as the most widely adopted CPU scheduling algorithm, undergoes severe problems directly related to quantum size. If time quantum chosen is too large, the response time of the processes is considered too high. On the other hand, if this quantum is too small, it increases the overhead of the CPU. In this paper, we propose a new algorithm, called AN, based on a new approach called dynamic-time-quantum; the idea of this approach is to make the operating systems adjusts the time quantum according to the burst time of the set of waiting processes in the ready queue. Based on the simulations and experiments, we show that the new proposed algorithm solves the fixed time quantum problem and increases the performance of Round Robin.
Quantum Field Theory: From Operators to Path Integrals
Huang, Kerson
1998-07-01
A unique approach to quantum field theory, with emphasis on the principles of renormalization Quantum field theory is frequently approached from the perspective of particle physics. This book adopts a more general point of view and includes applications of condensed matter physics. Written by a highly respected writer and researcher, it first develops traditional concepts, including Feynman graphs, before moving on to key topics such as functional integrals, statistical mechanics, and Wilson's renormalization group. The connection between the latter and conventional perturbative renormalization is explained. Quantum Field Theory is an exceptional textbook for graduate students familiar with advanced quantum mechanics as well as physicists with an interest in theoretical physics. It features: * Coverage of quantum electrodynamics with practical calculations and a discussion of perturbative renormalization * A discussion of the Feynman path integrals and a host of current subjects, including the physical approach to renormalization, spontaneous symmetry breaking and superfluidity, and topological excitations * Nineteen self-contained chapters with exercises, supplemented with graphs and charts
Spectra of quantum KdV Hamiltonians, Langlands duality, and affine opers
Frenkel, Edward
2016-01-01
We prove a system of relations in the Grothendieck ring of the category O of representations of the Borel subalgebra of an untwisted quantum affine algebra U_q(g^) introduced in [HJ]. This system was discovered in [MRV1, MRV2], where it was shown that solutions of this system can be attached to certain affine opers for the Langlands dual affine Kac-Moody algebra of g^, introduced in [FF5]. Together with the results of [BLZ3, BHK], which enable one to associate quantum g^-KdV Hamiltonians to representations from the category O, this provides strong evidence for the conjecture of [FF5] linking the spectra of quantum g^-KdV Hamiltonians and affine opers for the Langlands dual affine algebra. As a bonus, we obtain a direct and uniform proof of the Bethe Ansatz equations for a large class of quantum integrable models associated to arbitrary untwisted quantum affine algebras, under a mild genericity condition.
Quantum Mechanical Version of z-Transform Related to Eigenkets of Boson Creation Operator
Institute of Scientific and Technical Information of China (English)
FANHong-Yi; FULiang; A.Wiinsche
2004-01-01
Using the completeness relation composed of the coherent state and of the eigenket of bosonic creation operator, we establish a one-to-one correspondence between the z-transform and the quantum-mechanical transform from the representation by number states |n) to the representation by coherent states |(z)) (Bargmann representation).In this way, the quantum-mechanical version of the various properties of z-transform are obtained and the operators for embodying these properties in the Fock space are derived, which may find applications in quantum states engineering.
Quantum field theory from operators to path integrals
Huang, Kerson
1998-01-01
A unique approach to quantum field theory, with emphasis on the principles of renormalization Quantum field theory is frequently approached from the perspective of particle physics. This book adopts a more general point of view and includes applications of condensed matter physics. Written by a highly respected writer and researcher, it first develops traditional concepts, including Feynman graphs, before moving on to key topics such as functional integrals, statistical mechanics, and Wilson's renormalization group. The connection between the latter and conventional perturbative renormalization is explained
Actively Secure Two-Party Evaluation of Any Quantum Operation
DEFF Research Database (Denmark)
Dupuis, Frédéric; Nielsen, Jesper Buus; Salvail, Louis
2012-01-01
We provide the first two-party protocol allowing Alice and Bob to evaluate privately even against active adversaries any completely positive, trace-preserving map , given as a quantum circuit, upon their joint quantum input state . Our protocol leaks no more to any active adversary than an ideal ...... functionality for provided Alice and Bob have the cryptographic resources for active secure two-party classical computation. Our protocol is constructed from the protocol for the same task secure against specious adversaries presented in [4]....
Manifestly scale-invariant regularization and quantum effective operators
Ghilencea, D.M.
2016-01-01
Scale invariant theories are often used to address the hierarchy problem, however the regularization of their quantum corrections introduces a dimensionful coupling (dimensional regularization) or scale (Pauli-Villars, etc) which break this symmetry explicitly. We show how to avoid this problem and study the implications of a manifestly scale invariant regularization in (classical) scale invariant theories. We use a dilaton-dependent subtraction function $\\mu(\\sigma)$ which after spontaneous breaking of scale symmetry generates the usual DR subtraction scale $\\mu(\\langle\\sigma\\rangle)$. One consequence is that "evanescent" interactions generated by scale invariance of the action in $d=4-2\\epsilon$ (but vanishing in $d=4$), give rise to new, finite quantum corrections. We find a (finite) correction $\\Delta U(\\phi,\\sigma)$ to the one-loop scalar potential for $\\phi$ and $\\sigma$, beyond the Coleman-Weinberg term. $\\Delta U$ is due to an evanescent correction ($\\propto\\epsilon$) to the field-dependent masses (of...
Nanopatterned Quantum Dot Lasers for High Speed, High Efficiency, Operation
2015-04-27
SUBTITLE 13. SUPPLEMENTARY NOTES 12. DISTRIBUTION AVAILIBILITY STATEMENT 6. AUTHORS 7. PERFORMING ORGANIZATION NAMES AND ADDRESSES 15. SUBJECT TERMS ...growth using metalorganic chemical vapor deposition (MOCVD). These methods allowed us to realize quantum dot active regions in which the injected carriers...temperature sensitivity , commonly observed in self-assembled QD lasers2. An alternate approach to SK QD formation is the use of nanopatterning with
High-fidelity gate operations for quantum computing beyond dephasing time limits
Souza, Alexandre M.; Sarthour, Roberto S.; Oliveira, Ivan S.; Suter, Dieter
2015-12-01
The implementation of quantum gates with fidelities that exceed the threshold for reliable quantum computing requires robust gates whose performance is not limited by the precision of the available control fields. The performance of these gates also should not be affected by the noisy environment of the quantum register. Here we use randomized benchmarking of quantum gate operations to compare the performance of different families of gates that compensate errors in the control field amplitudes and decouple the system from the environmental noise. We obtain average fidelities of up to 99.8%, which exceeds the threshold value for some quantum error correction schemes as well as the expected limit from the dephasing induced by the environment.
Fermionic quantum operations: a computational framework I. Basic invariance properties
Lakos, Gyula
2015-01-01
The objective of this series of papers is to recover information regarding the behaviour of FQ operations in the case $n=2$, and FQ conform-operations in the case $n=3$. In this first part we study how the basic invariance properties of FQ operations ($n=2$) are reflected in their formal power series expansions.
Note: A hand-held high-Tc superconducting quantum interference device operating without shielding.
He, D F
2011-02-01
By improving the compensation circuit, a hand-held high-Tc rf superconducting quantum interference devices (SQUID) system was developed. It could operate well when moving in unshielded environment. To check the operation, it was used to do eddy-current testing by hand moving the SQUID, and the artificial defect under 6 mm aluminum plate could be successfully detected in shielded environment.
2012-11-01
As the old 'publish or perish' adage is brought into question, additional research-impact indices, known as altmetrics, are offering new evaluation alternatives. But such metrics may need to adjust to the evolution of science publishing.
Photonic quantum digital signatures operating over kilometer ranges in installed optical fiber
Collins, Robert J.; Fujiwara, Mikio; Amiri, Ryan; Honjo, Toshimori; Shimizu, Kaoru; Tamaki, Kiyoshi; Takeoka, Masahiro; Andersson, Erika; Buller, Gerald S.; Sasaki, Masahide
2016-10-01
The security of electronic communications is a topic that has gained noteworthy public interest in recent years. As a result, there is an increasing public recognition of the existence and importance of mathematically based approaches to digital security. Many of these implement digital signatures to ensure that a malicious party has not tampered with the message in transit, that a legitimate receiver can validate the identity of the signer and that messages are transferable. The security of most digital signature schemes relies on the assumed computational difficulty of solving certain mathematical problems. However, reports in the media have shown that certain implementations of such signature schemes are vulnerable to algorithmic breakthroughs and emerging quantum processing technologies. Indeed, even without quantum processors, the possibility remains that classical algorithmic breakthroughs will render these schemes insecure. There is ongoing research into information-theoretically secure signature schemes, where the security is guaranteed against an attacker with arbitrary computational resources. One such approach is quantum digital signatures. Quantum signature schemes can be made information-theoretically secure based on the laws of quantum mechanics while comparable classical protocols require additional resources such as anonymous broadcast and/or a trusted authority. Previously, most early demonstrations of quantum digital signatures required dedicated single-purpose hardware and operated over restricted ranges in a laboratory environment. Here, for the first time, we present a demonstration of quantum digital signatures conducted over several kilometers of installed optical fiber. The system reported here operates at a higher signature generation rate than previous fiber systems.
Secure Quantum Key Distribution Network with Bell States and Local Unitary Operations
Institute of Scientific and Technical Information of China (English)
LI Chun-Yan; ZHOU Hong-Yu; WANG Yan; DENG Fu-Guo
2005-01-01
@@ We propose a theoretical scheme for secure quantum key distribution network following the ideas in quantum dense coding. In this scheme, the server of the network provides the service for preparing and measuring the Bell states,and the users encode the states with local unitary operations. For preventing the server from eavesdropping, we design a decoy when the particle is transmitted between the users. The scheme has high capacity as one particle carries two bits of information and its efficiency for qubits approaches 100%. Moreover, it is unnecessary for the users to store the quantum states, which makes this scheme more convenient in applications than others.
An arbitrated quantum signature protocol based on the chained CNOT operations encryption
Li, Feng-Guang; Shi, Jian-Hong
2015-06-01
At present, the encryption scheme used by most arbitrated quantum signature (AQS) protocols is quantum one-time pad (QOTP) which encrypts data qubit by qubit. Though QOTP can achieve high security for data encryption, it is not suitable for AQS. There are many attacks on AQS using QOTP. In this paper, we propose an AQS protocol based on another encryption scheme called the chained CNOT operations, which encrypts quantum message ensemble. Our protocol preserves all merits in the similar AQS schemes and has better security. Security analysis shows that our protocol cannot be forged and disavowed under the existing attacks.
q-differential operator representation of the quantum superalgebra Uq(sl(M+1|N+1))
Kimura, K
1996-01-01
A representation of the quantum superalgebra Uq(sl(M+1|N+1)) is constructed based on the q-differential operators acting on the coherent states parameterized by coordinates. These coordinates correspond to the local ones of the flag manifold. This realization provides us with a guide to construct the free field realization for the quantum affine superalgebra Uq^(sl(M+1|N+1)) at arbitrary level.
Characteristic operator functions for quantum input-plant-output models and coherent control
Gough, John E.
2015-01-01
We introduce the characteristic operator as the generalization of the usual concept of a transfer function of linear input-plant-output systems to arbitrary quantum nonlinear Markovian input-output models. This is intended as a tool in the characterization of quantum feedback control systems that fits in with the general theory of networks. The definition exploits the linearity of noise differentials in both the plant Heisenberg equations of motion and the differential form of the input-output relations. Mathematically, the characteristic operator is a matrix of dimension equal to the number of outputs times the number of inputs (which must coincide), but with entries that are operators of the plant system. In this sense, the characteristic operator retains details of the effective plant dynamical structure and is an essentially quantum object. We illustrate the relevance to model reduction and simplification definition by showing that the convergence of the characteristic operator in adiabatic elimination limit models requires the same conditions and assumptions appearing in the work on limit quantum stochastic differential theorems of Bouten and Silberfarb [Commun. Math. Phys. 283, 491-505 (2008)]. This approach also shows in a natural way that the limit coefficients of the quantum stochastic differential equations in adiabatic elimination problems arise algebraically as Schur complements and amounts to a model reduction where the fast degrees of freedom are decoupled from the slow ones and eliminated.
Quantum dynamics for classical systems with applications of the number operator
Bagarello, Fabio
2013-01-01
Mathematics is increasingly applied to classical problems in finance, biology, economics, and elsewhere. Quantum Dynamics for Classical Systems describes how quantum tools—the number operator in particular—can be used to create dynamical systems in which the variables are operator-valued functions and whose results explain the presented model. The book presents mathematical results and their applications to concrete systems and discusses the methods used, results obtained, and techniques developed for the proofs of the results. The central ideas of number operators are illuminated while avoiding excessive technicalities that are unnecessary for understanding and learning the various mathematical applications. The presented dynamical systems address a variety of contexts and offer clear analyses and explanations of concluded results. Additional features in Quantum Dynamics for Classical Systems include: Applications across diverse fields including stock markets and population migration as well as a uniqu...
An efficient matrix product operator representation of the quantum chemical Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
Keller, Sebastian, E-mail: sebastian.keller@phys.chem.ethz.ch; Reiher, Markus, E-mail: markus.reiher@phys.chem.ethz.ch [ETH Zürich, Laboratory of Physical Chemistry, Vladimir-Prelog-Weg 2, 8093 Zürich (Switzerland); Dolfi, Michele, E-mail: dolfim@phys.ethz.ch; Troyer, Matthias, E-mail: troyer@phys.ethz.ch [ETH Zürich, Institute of Theoretical Physics, Wolfgang-Pauli-Strasse 27, 8093 Zürich (Switzerland)
2015-12-28
We describe how to efficiently construct the quantum chemical Hamiltonian operator in matrix product form. We present its implementation as a density matrix renormalization group (DMRG) algorithm for quantum chemical applications. Existing implementations of DMRG for quantum chemistry are based on the traditional formulation of the method, which was developed from the point of view of Hilbert space decimation and attained higher performance compared to straightforward implementations of matrix product based DMRG. The latter variationally optimizes a class of ansatz states known as matrix product states, where operators are correspondingly represented as matrix product operators (MPOs). The MPO construction scheme presented here eliminates the previous performance disadvantages while retaining the additional flexibility provided by a matrix product approach, for example, the specification of expectation values becomes an input parameter. In this way, MPOs for different symmetries — abelian and non-abelian — and different relativistic and non-relativistic models may be solved by an otherwise unmodified program.
Designing reversible arithmetic, logic circuit to implement micro-operation in quantum computation
Kalita, Gunajit; Saikia, Navajit
2016-10-01
The futuristic computing is desired to be more power full with low-power consumption. That is why quantum computing has been a key area of research for quite some time and is getting more and more attention. Quantum logic being reversible, a significant amount of contributions has been reported on reversible logic in recent times. Reversible circuits are essential parts of quantum computers, and hence their designs are of great importance. In this paper, designs of reversible circuits are proposed using a recently proposed reversible gate for arithmetic and logic operations to implement various micro-operations (simple add and subtract, add with carry, subtract with borrow, transfer, incrementing, decrementing etc., and logic operations like XOR, XNOR, complementing etc.) in a reversible computer like quantum computer. The two new reversible designs proposed here for half adder and full adders are also used in the presented reversible circuits to implement various microoperations. The quantum costs of these designs are comparable. Many of the implemented micro-operations are not seen in previous literatures. The performances of the proposed circuits are compared with existing designs wherever available.
Explicit expressions of quantum mechanical rotation operators for spins 1 to 2
Kocakoç, Mehpeyker; Tapramaz, Recep
2016-03-01
Quantum mechanical rotation operators are the subject of quantum mechanics, mathematics and pulsed magnetic resonance spectroscopies, namely NMR, EPR and ENDOR. They are also necessary for spin based quantum information systems. The rotation operators of spin 1/2 are well known and can be found in related textbooks. But rotation operators of other spins greater than 1/2 can be found numerically by evaluating the series expansions of exponential operator obtained from Schrödinger equation, or by evaluating Wigner-d formula or by evaluating recently established expressions in polynomial forms discussed in the text. In this work, explicit symbolic expressions of x, y and z components of rotation operators for spins 1 to 2 are worked out by evaluating series expansion of exponential operator for each element of operators and utilizing linear curve fitting process. The procedures gave out exact expressions of each element of the rotation operators. The operators of spins greater than 2 are under study and will be published in a separate paper.
Bunao, Joseph
2016-01-01
This study considers the operator $\\hat{T}$ corresponding to the classical spacetime four-volume $T$ of a finite patch of spacetime in the context of Unimodular Loop Quantum Cosmology for the homogeneous and isotropic model with flat spatial sections and without matter sources. Since $T$ is canonically conjugate to the cosmological "constant" $\\Lambda$, the operator $\\hat{T}$ is constructed by solving its canonical commutation relation with $\\hat{\\Lambda}$ - the operator corresponding to $\\Lambda$. %This is done by expanding $\\hat{T}$ in terms of Bender-Dunne-like basis operators $\\hat{T}_{m,n}$ and solving for the expansion coefficients. This conjugacy, along with the action of $\\hat{T}$ on definite volume states reducing to $T$, allows us to interpret that $\\hat{T}$ is indeed a quantum spacetime four-volume operator. The eigenstates $\\Phi_{\\tau}$ are calculated and, considering $\\tau\\in\\mathbb{R}$, we find that the $\\Phi_{\\tau}$'s are normalizable suggesting that the real line $\\mathbb{R}$ is in the discret...
Marinelli, Dimitri; Aquilanti, Vincenzo; Anderson, Roger W; Bitencourt, Ana Carla P; Ragni, Mirco
2014-01-01
A unified vision of the symmetric coupling of angular momenta and of the quantum mechanical volume operator is illustrated. The focus is on the quantum mechanical angular momentum theory of Wigner's 6j symbols and on the volume operator of the symmetric coupling in spin network approaches: here, crucial to our presentation are an appreciation of the role of the Racah sum rule and the simplification arising from the use of Regge symmetry. The projective geometry approach permits the introduction of a symmetric representation of a network of seven spins or angular momenta. Results of extensive computational investigations are summarized, presented and briefly discussed.
An operational approach to spacetime symmetries: Lorentz transformations from quantum communication
Höhn, Philipp A.; Müller, Markus P.
2016-06-01
In most approaches to fundamental physics, spacetime symmetries are postulated a priori and then explicitly implemented in the theory. This includes Lorentz covariance in quantum field theory and diffeomorphism invariance in quantum gravity, which are seen as fundamental principles to which the final theory has to be adjusted. In this paper, we suggest, within a much simpler setting, that this kind of reasoning can actually be reversed, by taking an operational approach inspired by quantum information theory. We consider observers in distinct laboratories, with local physics described by the laws of abstract quantum theory, and without presupposing a particular spacetime structure. We ask what information-theoretic effort the observers have to spend to synchronize their descriptions of local physics. If there are ‘enough’ observables that can be measured universally on several different quantum systems, we show that the observers’ descriptions are related by an element of the orthochronous Lorentz group {{{O}}}+(3,1), together with a global scaling factor. Not only does this operational approach predict the Lorentz transformations, but it also accurately describes the behavior of relativistic Stern-Gerlach devices in the WKB approximation, and it correctly predicts that quantum systems carry Lorentz group representations of different spin. This result thus hints at a novel information-theoretic perspective on spacetime.
Fast universal quantum gates on microwave photons with all-resonance operations in circuit QED.
Hua, Ming; Tao, Ming-Jie; Deng, Fu-Guo
2015-03-19
Stark shift on a superconducting qubit in circuit quantum electrodynamics (QED) has been used to construct universal quantum entangling gates on superconducting resonators in previous works. It is a second-order coupling effect between the resonator and the qubit in the dispersive regime, which leads to a slow state-selective rotation on the qubit. Here, we present two proposals to construct the fast universal quantum gates on superconducting resonators in a microwave-photon quantum processor composed of multiple superconducting resonators coupled to a superconducting transmon qutrit, that is, the controlled-phase (c-phase) gate on two microwave-photon resonators and the controlled-controlled phase (cc-phase) gates on three resonators, resorting to quantum resonance operations, without any drive field. Compared with previous works, our universal quantum gates have the higher fidelities and shorter operation times in theory. The numerical simulation shows that the fidelity of our c-phase gate is 99.57% within about 38.1 ns and that of our cc-phase gate is 99.25% within about 73.3 ns.
Application of generalized operator representation in the time evolution of quantum systems
He, Rui; Liu, Xiangyuan; Song, Jun
2016-10-01
We have systematically explored the application of generalized operator representation including P-, W-, and Husimi representation in the time evolution of quantum systems. In particular, by using the method of differentiation within an ordered product of operators, we give the normally and antinormally ordered forms of the integral kernels of Husimi operator representations and its corresponding formulations. By making use of the generalized operator representation, we transform exponentially complex operator equations into tractable phase-space equations. As a simple application, the time evolution equation of Husimi function in the amplitude dissipative channel is clearly obtained.
Roga, W.; Spehner, D.; Illuminati, F.
2016-06-01
We investigate and compare three distinguished geometric measures of bipartite quantum correlations that have been recently introduced in the literature: the geometric discord, the measurement-induced geometric discord, and the discord of response, each one defined according to three contractive distances on the set of quantum states, namely the trace, Bures, and Hellinger distances. We establish a set of exact algebraic relations and inequalities between the different measures. In particular, we show that the geometric discord and the discord of response based on the Hellinger distance are easy to compute analytically for all quantum states whenever the reference subsystem is a qubit. These two measures thus provide the first instance of discords that are simultaneously fully computable, reliable (since they satisfy all the basic Axioms that must be obeyed by a proper measure of quantum correlations), and operationally viable (in terms of state distinguishability). We apply the general mathematical structure to determine the closest classical-quantum state of a given state and the maximally quantum-correlated states at fixed global state purity according to the different distances, as well as a necessary condition for a channel to be quantumness breaking.
Graphical calculus of volume, inverse volume and Hamiltonian operators in loop quantum gravity
Yang, Jinsong; Ma, Yongge
2017-04-01
To adopt a practical method to calculate the action of geometrical operators on quantum states is a crucial task in loop quantum gravity. In this paper, the graphical calculus based on the original Brink graphical method is applied to loop quantum gravity along the line of previous work. The graphical method provides a very powerful technique for simplifying complicated calculations. The closed formula of the volume operator and the actions of the Euclidean Hamiltonian constraint operator and the so-called inverse volume operator on spin-network states with trivalent vertices are derived via the graphical method. By employing suitable and non-ambiguous graphs to represent the action of operators as well as the spin-network states, we use the simple rules of transforming graphs to obtain the resulting formula. Comparing with the complicated algebraic derivation in some literature, our procedure is more concise, intuitive and visual. The resulting matrix elements of the volume operator is compact and uniform, fitting for both gauge-invariant and gauge-variant spin-network states. Our results indicate some corrections to the existing results for the Hamiltonian operator and inverse volume operator in the literature.
Graphical calculus of volume, inverse volume and Hamiltonian operators in loop quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Yang, Jinsong [Guizhou University, Department of Physics, Guiyang (China); Academia Sinica, Institute of Physics, Taipei (China); Ma, Yongge [Beijing Normal University, Department of Physics, Beijing (China)
2017-04-15
To adopt a practical method to calculate the action of geometrical operators on quantum states is a crucial task in loop quantum gravity. In this paper, the graphical calculus based on the original Brink graphical method is applied to loop quantum gravity along the line of previous work. The graphical method provides a very powerful technique for simplifying complicated calculations. The closed formula of the volume operator and the actions of the Euclidean Hamiltonian constraint operator and the so-called inverse volume operator on spin-network states with trivalent vertices are derived via the graphical method. By employing suitable and non-ambiguous graphs to represent the action of operators as well as the spin-network states, we use the simple rules of transforming graphs to obtain the resulting formula. Comparing with the complicated algebraic derivation in some literature, our procedure is more concise, intuitive and visual. The resulting matrix elements of the volume operator is compact and uniform, fitting for both gauge-invariant and gauge-variant spin-network states. Our results indicate some corrections to the existing results for the Hamiltonian operator and inverse volume operator in the literature. (orig.)
An operational approach to spacetime symmetries: Lorentz transformations from quantum communication
Hoehn, Philipp A
2015-01-01
In most approaches to fundamental physics, spacetime symmetries are postulated a priori and then explicitly implemented in the theory. This includes Lorentz covariance in quantum field theory and diffeomorphism invariance in quantum gravity, which are seen as fundamental principles to which the final theory has to be adjusted. In this paper, we suggest within a much simpler setting that this kind of reasoning can actually be reversed, by taking an operational approach inspired by quantum information theory. We consider observers in distant laboratories, with local physics described by the laws of abstract quantum theory, and without presupposing a particular spacetime structure. We ask what information-theoretic effort the observers have to spend to synchronize their descriptions of local physics. If there are "enough" observables that can be measured jointly on different types of systems, we show that the observers' descriptions are related by an element of the Lorentz group O^+(3,1), together with a global ...
Ou, Congjie; Chamberlin, Ralph V.; Abe, Sumiyoshi
2017-01-01
The Lindblad equation is widely employed in studies of Markovian quantum open systems. Here, the following question is posed: in a quantum open system with a time-dependent Hamiltonian such as a subsystem in contact with the heat bath, what is the corresponding Lindblad equation for the quantum state that keeps the internal energy of the subsystem constant in time? This issue is of importance in realizing quasi-stationary states of open systems such as quantum circuits and batteries. As an illustrative example, the time-dependent harmonic oscillator is analyzed. It is shown that the Lindbladian operator is uniquely determined with the help of a Lie-algebraic structure, and the time derivative of the von Neumann entropy is shown to be nonnegative if the curvature of the harmonic potential monotonically decreases in time.
Bellet, Aurelien; Sebban, Marc
2015-01-01
Similarity between objects plays an important role in both human cognitive processes and artificial systems for recognition and categorization. How to appropriately measure such similarities for a given task is crucial to the performance of many machine learning, pattern recognition and data mining methods. This book is devoted to metric learning, a set of techniques to automatically learn similarity and distance functions from data that has attracted a lot of interest in machine learning and related fields in the past ten years. In this book, we provide a thorough review of the metric learnin
Generalized space and linear momentum operators in quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Costa, Bruno G. da, E-mail: bruno.costa@ifsertao-pe.edu.br [Instituto Federal de Educação, Ciência e Tecnologia do Sertão Pernambucano, Campus Petrolina, BR 407, km 08, 56314-520 Petrolina, Pernambuco (Brazil); Instituto de Física, Universidade Federal da Bahia, R. Barão de Jeremoabo s/n, 40170-115 Salvador, Bahia (Brazil); Borges, Ernesto P., E-mail: ernesto@ufba.br [Instituto de Física, Universidade Federal da Bahia, R. Barão de Jeremoabo s/n, 40170-115 Salvador, Bahia (Brazil)
2014-06-15
We propose a modification of a recently introduced generalized translation operator, by including a q-exponential factor, which implies in the definition of a Hermitian deformed linear momentum operator p{sup ^}{sub q}, and its canonically conjugate deformed position operator x{sup ^}{sub q}. A canonical transformation leads the Hamiltonian of a position-dependent mass particle to another Hamiltonian of a particle with constant mass in a conservative force field of a deformed phase space. The equation of motion for the classical phase space may be expressed in terms of the generalized dual q-derivative. A position-dependent mass confined in an infinite square potential well is shown as an instance. Uncertainty and correspondence principles are analyzed.
Renormalizing the Kinetic Energy Operator in Elementary Quantum Mechanics
Coutinho, F. A. B.; Amaku, M.
2009-01-01
In this paper, we consider solutions to the three-dimensional Schrodinger equation of the form [psi](r) = u(r)/r, where u(0) [is not equal to] 0. The expectation value of the kinetic energy operator for such wavefunctions diverges. We show that it is possible to introduce a potential energy with an expectation value that also diverges, exactly…
Renormalizing the Kinetic Energy Operator in Elementary Quantum Mechanics
Coutinho, F. A. B.; Amaku, M.
2009-01-01
In this paper, we consider solutions to the three-dimensional Schrodinger equation of the form [psi](r) = u(r)/r, where u(0) [is not equal to] 0. The expectation value of the kinetic energy operator for such wavefunctions diverges. We show that it is possible to introduce a potential energy with an expectation value that also diverges, exactly…
On $q$-normal operators and quantum complex plane
Cimpri\\vc, Jaka; Schmüdgen, Konrad
2011-01-01
For $q>0$ let $\\cA$ denote the unital $\\ast$-algebra with generator $x$ and defining relation $xx^\\ast=qxx^\\ast$. Based on this algebra we study $q$-normal operators, the complex $q$-moment problem, positive elements and sums of squares.
Are the spectra of geometrical operators in Loop Quantum Gravity really discrete?
Dittrich, Bianca
2007-01-01
One of the celebrated results of Loop Quantum Gravity (LQG) is the discreteness of the spectrum of geometrical operators such as length, area and volume operators. This is an indication that Planck scale geometry in LQG is discontinuous rather than smooth. However, there is no rigorous proof thereof at present, because the afore mentioned operators are not gauge invariant, they do not commute with the quantum constraints. The relational formalism in the incarnation of Rovelli's partial and complete observables provides a possible mechanism for turning a non gauge invariant operator into a gauge invariant one. In this paper we investigate whether the spectrum of such a physical, that is gauge invariant, observable can be predicted from the spectrum of the corresponding gauge variant observables. We will not do this in full LQG but rather consider much simpler examples where field theoretical complications are absent. We find, even in those simpler cases, that kinematical discreteness of the spectrum does not n...
Far-infrared quantum cascade lasers operating in AlAs phonon Reststrahlen band
Ohtani, K; Süess, M J; Faist, J; Andrews, A M; Zederbauer, T; Detz, H; Schrenk, W; Strasser, G
2016-01-01
We report on the operation of a double metal waveguide far-infrared quantum cascade laser emitting at 28 $\\mu$m, corresponding to the AlAs-like phonon Reststrahlen band. To avoid absorption by AlAs-like optical phonons, the Al-free group-V alloy GaAs$_{0.51}$Sb$_{0.49}$ is used as a barrier layer in the bound-to-continuum based active region. Lasing occurs at a wavelength of 28.3 $\\mu$m, which is the longest wavelength among the quantum cascade lasers operating from mid-infrared to far-infrared. The threshold current density at 50 K is 5.5 kA/cm$^{2}$ and maximum operation temperature is 175 K. We also discuss the feasibility that operation wavelength cover the whole spectral range bridging between mid-infrared and terahertz by choosing suited group III-V materials.
Room Temperature Operation of a Buried Heterostructure Photonic Crystal Quantum Cascade Laser
Peretti, R; Wolf, J M; Bonzon, C; Süess, M J; Lourdudoss, S; Metaferia, W; Beck, M; Faist, J
2015-01-01
We demonstrated room temperature operation of deep etched photonic crystal quantum cascade laser emitting around 8.5 micron. We fabricated buried heterostructure photonic crystals, resulting in single mode laser emission on a high order slow Bloch modes of the photonic crystal, between high symmetry points of the Brillouin.
Construction of some Quantum Stochastic Operator Cocycles by the Semigroup Method
Indian Academy of Sciences (India)
J Martin Lindsay; Stephen J Wills
2006-11-01
A new method for the construction of Fock-adapted quantum stochastic operator cocycles is outlined, and its use is illustrated by application to a number of examples arising in physics and probability. The construction uses the Trotter–Kato theorem and a recent characterisation of such cocycles in terms of an associated family of contraction semigroups.
The Fermionic Signature Operator and Quantum States in Rindler Space-Time
Finster, Felix; Röken, Christian
2016-01-01
The fermionic signature operator is constructed in Rindler space-time. It is shown to be an unbounded self-adjoint operator on the Hilbert space of solutions of the massive Dirac equation. In two-dimensional Rindler space-time, we prove that the resulting fermionic projector state coincides with the Fulling-Rindler vacuum. Moreover, the fermionic signature operator gives a covariant construction of general thermal states, in particular of the Unruh state. The fermionic signature operator is shown to be well-defined in asymptotically Rindler space-times. In four-dimensional Rindler space-time, our construction gives rise to new quantum states.
Stewart, Terrence C; Eliasmith, Chris
2013-06-01
Quantum probability (QP) theory can be seen as a type of vector symbolic architecture (VSA): mental states are vectors storing structured information and manipulated using algebraic operations. Furthermore, the operations needed by QP match those in other VSAs. This allows existing biologically realistic neural models to be adapted to provide a mechanistic explanation of the cognitive phenomena described in the target article by Pothos & Busemeyer (P&B).
A Scheme for Atomic Entangled States and Quantum Gate Operations in Cavity QED
Institute of Scientific and Technical Information of China (English)
LI Peng-Bo; GU Ying; GONG Qi-Huang; GUO Guang-Can
2009-01-01
We propose a scheme for controllably entangling the ground states of five-state W-type atoms confined in a cavity and realizing swap gate and phase gate operations.In this scheme the cavity is only virtually excited and the atomic excited states are almost not occupied,so the produced entangled states and quantum logic operations are very robust against the cavity decay and atomic spontaneous emission.
Study of a self-adjoint operator indicating the direction of time within standard quantum mechanics
Strauss, Y; Machnes, S; Horwitz, L P
2011-01-01
In [J. Math. Phys. 51 (2010) 022104] a self-adjoint operator was introduced that has the property that it indicates the direction of time within the framework of standard quantum mechanics, in the sense that as a function of time its expectation value decreases monotonically for any initial state. In this paper we study some of this operator's properties. In particular, we derive its spectrum and generalized eigenstates, and treat the example of the free particle.
Scheme for Remote Implementation of Partially Unknown Quantum Operation of Two Qubits in Cavity QED
Institute of Scientific and Technical Information of China (English)
QIU Liang; WANG An-Min
2008-01-01
By constructing the recovery operations of the protocol of remote implementation of partially unknown quantum operation of two qubits [An-Min Wang: Phys. Rev. A 74 (2006) 032317] with two-qubit Cnot gate and single qubit logic gates, we present a scheme to implement it in cavity QED. Long-lived Rydberg atoms are used as qubits, and the interaction between the atoms and the field of cavity is a nonresonant one. Finally, we analyze the experimental feasibility of this scheme.
Fan, Hong-yi; Lu, Hai-liang; Fan, Yue
2006-02-01
Newton-Leibniz integration rule only applies to commuting functions of continuum variables, while operators made of Dirac's symbols (ket versus bra, e.g., | q>mechanics are usually not commutative. Therefore, integrations over the operators of type |>mathematical gap between classical mechanics and quantum mechanics, and further reveals the beauty and elegance of Dirac's symbolic method and transformation theory. Various applications of the IWOP technique, including constructing the entangled state representations and their applications, are presented.
BRST and anti-BRST operators for quantum linear algebra U{sub q}(gl(N))
Energy Technology Data Exchange (ETDEWEB)
Isaev, A.P. E-mail: isaevap@thsun1.jinr.ru; Ogievetsky, O.V. E-mail: isaevap@thsun1.jinr.ru
2001-09-01
For a quantum Lie algebra U{sub q}(gl(N)) we construct BRST, anti-BRST and Laplace operators. The (anti)commutator with the BRST operator defines the differential on the de Rham complex over the quantum group GL{sub q}(N). The Hodge decomposition theorem for this complex is formulated.
Renormalizing the kinetic energy operator in elementary quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Coutinho, F A B [Faculdade de Medicina, Universidade de Sao Paulo e LIM 01-HCFMUSP, 05405-000 Sao Paulo (Brazil); Amaku, M [Faculdade de Medicina Veterinaria e Zootecnia, Universidade de Sao Paulo, 05508-970 Sao Paulo (Brazil)], E-mail: coutinho@dim.fm.usp.br
2009-09-15
In this paper, we consider solutions to the three-dimensional Schroedinger equation of the form {psi}(r) = u(r)/r, where u(0) {ne} 0. The expectation value of the kinetic energy operator for such wavefunctions diverges. We show that it is possible to introduce a potential energy with an expectation value that also diverges, exactly cancelling the kinetic energy divergence. This renormalization procedure produces a self-adjoint Hamiltonian. We solve some problems with this new Hamiltonian to illustrate its usefulness.
Bunao, J.
2017-02-01
This study considers the operator \\hat{T} corresponding to the classical spacetime four-volume \\tilde{T} (on-shell) of a finite patch of spacetime in the context of unimodular loop quantum cosmology for the homogeneous and isotropic model with flat spatial sections and without matter sources. Since the spacetime four-volume is canonically conjugate to the cosmological ‘constant’, the operator \\hat{T} is constructed by solving its canonical commutation relation with {\\hat Λ } —the operator corresponding to the classical cosmological constant on-shell {\\tilde Λ } . This conjugacy, along with the action of \\hat{T} on definite volume states reducing to \\tilde{T} , allows us to interpret that \\hat{T} is indeed a quantum spacetime four-volume operator. The discrete spectrum of \\hat{T} is calculated by considering the set of all τ’s where the eigenvalue equation has a solution {{ Φ }τ} in the domain of \\hat{T} . It turns out that, upon assigning the maximal domain D≤ft(\\hat{T}\\right) to \\hat{T} , we have {{ Φ }τ}\\in D≤ft(\\hat{T}\\right) for all τ \\in {C} so that the spectrum of \\hat{T} is purely discrete and is the entire complex plane. A family of operators {{\\hat{T}}≤ft({{b0},{φ0}\\right)}} was also considered as possible self-adjoint versions of \\hat{T} . They represent the restrictions of \\hat{T} on their respective domains D≤ft({{\\hat{T}}≤ft({{b0},{φ0}\\right)}}\\right) which are just the maximal domain with additional quasi-periodic conditions. Their possible self-adjointness is motivated by their discrete spectra only containing real and discrete numbers {τm} for m=0,+/- 1,+/- 2,... .
Chitambar, Eric; Gour, Gilad
2016-07-01
Considerable work has recently been directed toward developing resource theories of quantum coherence. In this Letter, we establish a criterion of physical consistency for any resource theory. This criterion requires that all free operations in a given resource theory be implementable by a unitary evolution and projective measurement that are both free operations in an extended resource theory. We show that all currently proposed basis-dependent theories of coherence fail to satisfy this criterion. We further characterize the physically consistent resource theory of coherence and find its operational power to be quite limited. After relaxing the condition of physical consistency, we introduce the class of dephasing-covariant incoherent operations as a natural generalization of the physically consistent operations. Necessary and sufficient conditions are derived for the convertibility of qubit states using dephasing-covariant operations, and we show that these conditions also hold for other well-known classes of incoherent operations.
Chitambar, Eric; Gour, Gilad
2016-07-15
Considerable work has recently been directed toward developing resource theories of quantum coherence. In this Letter, we establish a criterion of physical consistency for any resource theory. This criterion requires that all free operations in a given resource theory be implementable by a unitary evolution and projective measurement that are both free operations in an extended resource theory. We show that all currently proposed basis-dependent theories of coherence fail to satisfy this criterion. We further characterize the physically consistent resource theory of coherence and find its operational power to be quite limited. After relaxing the condition of physical consistency, we introduce the class of dephasing-covariant incoherent operations as a natural generalization of the physically consistent operations. Necessary and sufficient conditions are derived for the convertibility of qubit states using dephasing-covariant operations, and we show that these conditions also hold for other well-known classes of incoherent operations.
Jackson, John David
2006-01-01
Advanced undergraduates and graduate students studying quantum mechanics will find this text a valuable guide to mathematical methods. Emphasizing the unity of a variety of different techniques, it is enduringly relevant to many physical systems outside the domain of quantum theory.Concise in its presentation, this text covers eigenvalue problems in classical physics, orthogonal functions and expansions, the Sturm-Liouville theory and linear operators on functions, and linear vector spaces. Appendixes offer useful information on Bessel functions and Legendre functions and spherical harmonics.
Quevedo, Hernando
2016-01-01
We review the problem of describing the gravitational field of compact stars in general relativity. We focus on the deviations from spherical symmetry which are expected to be due to rotation and to the natural deformations of mass distributions. We assume that the relativistic quadrupole moment takes into account these deviations, and consider the class of axisymmetric static and stationary quadrupolar metrics which satisfy Einstein's equations in empty space and in the presence of matter represented by a perfect fluid. We formulate the physical conditions that must be satisfied for a particular spacetime metric to describe the gravitational field of compact stars. We present a brief review of the main static and axisymmetric exact solutions of Einstein's vacuum equations, satisfying all the physical conditions. We discuss how to derive particular stationary and axisymmetric solutions with quadrupolar properties by using the solution generating techniques which correspond either to Lie symmetries and B\\"acku...
Active mode locking of quantum cascade lasers operating in external ring cavity
Revin, D G; Wang, Y; Cockburn, J W; Belyanin, A
2015-01-01
Stable ultrashort light pulses and frequency combs generated by mode-locked lasers have many important applications including high-resolution spectroscopy, fast chemical detection and identification, studies of ultrafast processes, and laser metrology. While compact mode-locked lasers emitting in the visible and near infrared range have revolutionized photonic technologies, the systems operating in the mid-infrared range where most gases have their strong absorption lines, are bulky and expensive and rely on nonlinear frequency down-conversion. Quantum cascade lasers are the most powerful and versatile compact light sources in the mid-infrared range, yet achieving their mode locked operation remains a challenge despite dedicated effort. Here we report the first demonstration of active mode locking of an external-cavity quantum cascade laser. The laser operates in the mode-locked regime at room temperature and over the full dynamic range of injection currents of a standard commercial laser chip.
Uzdin, Raam
2016-08-01
Collective behavior, where a set of elements interact and generate effects that are beyond the reach of the individual noninteracting elements, is always of great interest in physics. Quantum collective effects that have no classical analog are even more intriguing. In this work, we show how to construct collective quantum heat machines and explore their performance boosts with respect to regular machines. Without interactions between the machines, the individual units operate in a stochastic, nonquantum manner. The construction of the collective machine becomes possible by introducing two simple quantum operations: coherence extraction and coherence injection. Together, these operations can harvest coherence from one engine and use it to boost the performance of a slightly different engine. For weakly driven engines, we show that the collective work output scales quadratically with the number of engines rather than linearly. Eventually, the boost saturates and then becomes linear. Nevertheless, even in saturation, work is still significantly boosted compared to individual operation. To study the reversibility of the collective machine, we introduce the "entropy-pollution" measure. It is shown that there is a regime where the collective machine is N times more reversible while producing N times more work, compared to the individual operation of N units. Moreover, the collective machine can even be more reversible than the most reversible unit in the collective. This high level of reversibility becomes possible due to a special symbiotic mechanism between engine pairs.
On the discrete spectrum of the Dirac operator on bent chain quantum graph
Directory of Open Access Journals (Sweden)
Belov Michail
2017-01-01
Full Text Available We study Dirac operators on an infinite quantum graph of a bent chain form which consists of identical rings connected at the touching points by δ-couplings with a parameter α ∈ ℝ. We are interested in the discrete spectrum of the corresponding Hamiltonian. It can be non-empty due to a local (geometrical perturbation of the corresponding infinite chain of rings. The quantum graph of analogous geometry with the Schrodinger operator on the edges was considered by Duclos, Exner and Turek in 2008. They showed that the absence of δ-couplings at vertices (i.e. the Kirchhoff condition at the vertices lead to the absence of eigenvalues. We consider the relativistic particle (the Dirac operator instead of the Schrodinger one but the result is analogous. Quantum graphs of such type are suitable for description of grapheme-based nanostructures. It is established that the negativity of α is the necessary and sufficient condition for the existence of eigenvalues of the Dirac operator (i.e. the discrete spectrum of the Hamiltonian in this case is not empty. The continuous spectrum of the Hamiltonian for bent chain graph coincides with that for the corresponding straight infinite chain. Conditions for appearance of more than one eigenvalue are obtained. It is related to the bending angle. The investigation is based on the transfer-matrix approach. It allows one to reduce the problem to an algebraic task. δ-couplings was introduced by the operator extensions theory method.
Energy Technology Data Exchange (ETDEWEB)
Frye, Jason Neal; Veitch, Cynthia K.; Mateski, Mark Elliot; Michalski, John T.; Harris, James Mark; Trevino, Cassandra M.; Maruoka, Scott
2012-03-01
Threats are generally much easier to list than to describe, and much easier to describe than to measure. As a result, many organizations list threats. Fewer describe them in useful terms, and still fewer measure them in meaningful ways. This is particularly true in the dynamic and nebulous domain of cyber threats - a domain that tends to resist easy measurement and, in some cases, appears to defy any measurement. We believe the problem is tractable. In this report we describe threat metrics and models for characterizing threats consistently and unambiguously. The purpose of this report is to support the Operational Threat Assessment (OTA) phase of risk and vulnerability assessment. To this end, we focus on the task of characterizing cyber threats using consistent threat metrics and models. In particular, we address threat metrics and models for describing malicious cyber threats to US FCEB agencies and systems.
Roberts, Mark D
2016-01-01
Scalar-tensor theory has arbitrary functions of the scalar field in front of the geometric and scalar terms in the Lagrangain. The extent to which these arbitrary functions appear in the Wheeler-deWitt wavefunction of mini-super Robertson-Walker spacetimes is discussed. The function of the scalar field in front of the Einstein-Hilbert action allows a current to be constructed which suggests transfer from matter to geometry of aspects of the wavefunction.
From Smooth Curves to Universal Metrics
Gurses, Metin; Tekin, Bayram
2016-01-01
A special class of metrics, called universal metrics, solve all gravity theories defined by covariant field equations purely based on the metric tensor. Since we currently lack the knowledge of what the full of quantum corrected field equations of gravity are at a given microscopic length scale, these metrics are particularly important in understanding quantum fields in curved backgrounds in a consistent way. But, finding explicit universal metrics has been a hard problem as there does not seem to be a procedure for it. In this work, we overcome this difficulty and give a construction of universal metrics of d dimensional spacetime from curves constrained to live in a d-1 dimensional Minkowski spacetime or a Euclidean space.
From smooth curves to universal metrics
Gürses, Metin; Şişman, Tahsin ćaǧrı; Tekin, Bayram
2016-08-01
A special class of metrics, called universal metrics, solves all gravity theories defined by covariant field equations purely based on the metric tensor. Since we currently lack the knowledge of what the full quantum-corrected field equations of gravity are at a given microscopic length scale, these metrics are particularly important in understanding quantum fields in curved backgrounds in a consistent way. However, finding explicit universal metrics has been a difficult problem as there does not seem to be a procedure for it. In this work, we overcome this difficulty and give a construction of universal metrics of d -dimensional spacetime from curves constrained to live in a (d -1 )-dimensional Minkowski spacetime or a Euclidean space.
Khrennikov, Andrei
2016-09-01
We represent Born's rule as an analog of the formula of total probability (FTP): the classical formula is perturbed by an additive interference term. In this note we consider practically the most general case: generalized quantum observables given by positive operator valued measures and measurement feedback on states described by atomic instruments. This representation of Born's rule clarifies the probabilistic structure of quantum mechanics (QM). The probabilistic counterpart of QM can be treated as the probability update machinery based on the special generalization of classical FTP. This is the essence of the Växjö interpretation of QM: statistical realist contextual and local interpretation. We analyze the origin of the additional interference term in quantum FTP by considering the contextual structure of the two slit experiment which was emphasized by R. Feynman.
Reveal non-Markovianity of open quantum systems via local operations
Yang, Huan; Chen, Yanbei
2011-01-01
Non-Markovianity, as an important feature of general open quantum systems, is usually difficult to quantify with limited knowledge of how the plant that we are interested in interacts with its environment-the bath. It often happens that the reduced dynamics of the plant attached to a non-Markovian bath becomes indistinguishable from the one with a Markovian bath, if we left the entire system freely evolve. Here we show that non-Markovianity can be revealed via applying local unitary operations on the plant-they will influence the plant evolution at later times due to memory of the bath. This not only provides a new criterion for non-Markovianity, but also sheds light on protecting and recovering quantum coherence in non-Markovian systems, which will be useful for quantum-information processing.
Memristive operation mode of a site-controlled quantum dot floating gate transistor
Energy Technology Data Exchange (ETDEWEB)
Maier, P., E-mail: patrick.maier@physik.uni-wuerzburg.de; Hartmann, F.; Mauder, T.; Emmerling, M.; Schneider, C.; Kamp, M.; Worschech, L. [Technische Physik, Physikalisches Institut, Wilhelm Conrad Röntgen Research Center for Complex Material Systems, Universität Würzburg, Am Hubland, D-97074 Würzburg (Germany); Höfling, S. [Technische Physik, Physikalisches Institut, Wilhelm Conrad Röntgen Research Center for Complex Material Systems, Universität Würzburg, Am Hubland, D-97074 Würzburg (Germany); SUPA, School of Physics and Astronomy, University of St Andrews, St Andrews KY16 9SS (United Kingdom)
2015-05-18
We have realized a floating gate transistor based on a GaAs/AlGaAs heterostructure with site-controlled InAs quantum dots. By short-circuiting the source contact with the lateral gates and performing closed voltage sweep cycles, we observe a memristive operation mode with pinched hysteresis loops and two clearly distinguishable conductive states. The conductance depends on the quantum dot charge which can be altered in a controllable manner by the voltage value and time interval spent in the charging region. The quantum dot memristor has the potential to realize artificial synapses in a state-of-the-art opto-electronic semiconductor platform by charge localization and Coulomb coupling.
Quantum dynamics of a macroscopic magnet operating as an environment of a mechanical oscillator
Foti, C.; Cuccoli, A.; Verrucchi, P.
2016-12-01
We study the dynamics of a bipartite quantum system in a way such that its formal description keeps holding even if one of its parts becomes macroscopic; the problem is related to the analysis of the quantum-to-classical crossover, but our approach implies that the whole system stays genuinely quantum. The aim of the work is to understand (1) if, (2) to what extent, and possibly (3) how the evolution of a macroscopic environment testifies to the coupling with its microscopic quantum companion. To this purpose we consider a magnetic environment made of a large number of spin-1/2 particles, coupled with a quantum mechanical oscillator, possibly in the presence of an external magnetic field. We take the value of the total environmental spin S constant and large, which allows us to consider the environment as one single macroscopic system, and further deal with the hurdles of the spin-algebra via approximations that are valid in the large-S limit. We find an insightful expression for the propagator of the whole system, where we identify an effective "back-action" term, i.e., an operator acting on the magnetic environment only, and yet missing in the absence of the quantum principal system. This operator emerges as a time-dependent magnetic anisotropy whose character, whether uniaxial or planar, also depends on the detuning between the frequency of the oscillator and the level splitting in the spectrum of the free magnetic system, induced by the possible presence of the external field. The time dependence of the anisotropy is analyzed, and its effects on the dynamics of the magnet, as well as its relation to the entangling evolution of the overall system, are discussed.
Directory of Open Access Journals (Sweden)
Sarah N. Steigerwald
2015-12-01
Full Text Available Background: Considerable resources have been invested in both low- and high-fidelity simulators in surgical training. The purpose of this study was to investigate if the Fundamentals of Laparoscopic Surgery (FLS, low-fidelity box trainer and LapVR (high-fidelity virtual reality training systems correlate with operative performance on the Global Operative Assessment of Laparoscopic Skills (GOALS global rating scale using a porcine cholecystectomy model in a novice surgical group with minimal laparoscopic experience. Methods: Fourteen postgraduate year 1 surgical residents with minimal laparoscopic experience performed tasks from the FLS program and the LapVR simulator as well as a live porcine laparoscopic cholecystectomy. Performance was evaluated using standardized FLS metrics, automatic computer evaluations, and a validated global rating scale. Results: Overall, FLS score did not show an association with GOALS global rating scale score on the porcine cholecystectomy. None of the five LapVR task scores were significantly associated with GOALS score on the porcine cholecystectomy. Conclusions: Neither the low-fidelity box trainer or the high-fidelity virtual simulator demonstrated significant correlation with GOALS operative scores. These findings offer caution against the use of these modalities for brief assessments of novice surgical trainees, especially for predictive or selection purposes.
Quantum-optical description of losses in ring resonators based on field-operator transformations
Alsing, Paul M.; Hach, Edwin E.; Tison, Christopher C.; Smith, A. Matthew
2017-05-01
In this work we examine loss in ring resonator networks from an operator valued phasor addition approach which considers the multiple transmission and cross coupling paths of a quantum field traversing a ring resonator coupled to one or two external waveguide buses. We demonstrate the consistency of our approach by the preservation of the operator commutation relation of the out-coupled bus mode. We compare our results to those obtained from the conventional quantum Langevin approach which introduces noise operators in addition to the quantum Heisenberg equations in order to preserve commutation relations in the presence of loss. It is shown that the two expressions agree in the neighborhood of a cavity resonance where the Langevin approach is applicable, whereas the operator valued phasor addition expression we derive is more general, remaining valid far from resonances. In addition, we examine the effects of internal and coupling losses on the Hong-Ou-Mandel manifold discussed in Hach et al. [Phys. Rev. A 89, 043805 (2014), 10.1103/PhysRevA.89.043805] that generalizes the destructive interference of two incident photons interfering on a 50:50 beam splitter (HOM effect) to the case of an add-drop double bus ring resonator.
Energy Technology Data Exchange (ETDEWEB)
Reinhardt, Hugo [Tuebingen Univ. (Germany). Inst. fuer Theoretische Physik
2012-11-01
The first volume of this two-volume textbook gives a modern introduction to the quantum theory, which connects Feynman's path-integral formulation with the traditional operator formalism. In easily understandable form starting from the double-slit experiment the characteristic features and foundations of quantum theory are made accessible by means of the functional-integral approach. Just this approach makes a ''derivation'' of the Schroedinger equation from the principle of the interfering alternatives possible. In the following the author developes the traditional operator formulation of quantum mechanics, which is better suited for practical solution of elementary problems. However he then refers to the functional-integral approach, when this contributes to a better understanding. A further advance of this concept: The functional-integral approach facilitates essentially the later access to quantum field theory. The work is in like manner suited for the self-study as for the deepening accompanying of the course.
Jackson, Brian A; Faith, Kay Sullivan
2013-02-01
Although significant progress has been made in measuring public health emergency preparedness, system-level performance measures are lacking. This report examines a potential approach to such measures for Strategic National Stockpile (SNS) operations. We adapted an engineering analytic technique used to assess the reliability of technological systems-failure mode and effects analysis-to assess preparedness. That technique, which includes systematic mapping of the response system and identification of possible breakdowns that affect performance, provides a path to use data from existing SNS assessment tools to estimate likely future performance of the system overall. Systems models of SNS operations were constructed and failure mode analyses were performed for each component. Linking data from existing assessments, including the technical assistance review and functional drills, to reliability assessment was demonstrated using publicly available information. The use of failure mode and effects estimates to assess overall response system reliability was demonstrated with a simple simulation example. Reliability analysis appears an attractive way to integrate information from the substantial investment in detailed assessments for stockpile delivery and dispensing to provide a view of likely future response performance.
Quantum Exchange Algebra and Exact Operator Solution of $A_{2}$-Toda Field Theory
Takimoto, Y; Kurokawa, H; Fujiwara, T
1999-01-01
Locality is analyzed for Toda field theories by noting novel chiral description in the conventional nonchiral formalism. It is shown that the canonicity of the interacting to free field mapping described by the classical solution is automatically guaranteed by the locality. Quantum Toda theories are investigated by applying the method of free field quantization. We give Toda exponential operators associated with fundamental weight vectors as bilinear forms of chiral fields satisfying characteristic quantum exchange algebra. It is shown that the locality leads to nontrivial relations among the ${\\cal R}$-matrix and the expansion coefficients of the exponential operators. The Toda exponentials are obtained for $A_2$-system by extending the algebraic method developed for Liouville theory. The canonical commutation relations and the operatorial field equations are also examined.
Institute of Scientific and Technical Information of China (English)
HAN Lian-Fang; CHEN Yue-Ming; YUAN Hao
2009-01-01
We propose a deterministic quantum secure direct communication protocol by using dense coding.The two check photon sequences are used to check the securities of the channels between the message sender and the receiver.The continuous variable operations instead of the usual discrete unitary operations are performed on the travel photons so that the security of the present protocol can be enhanced.Therefore some specific attacks such as denial-of-service attack, intercept-measure-resend attack and invisible photon attack can be prevented in ideal quantum channel.In addition, the scheme is still secure in noise channel.Furthurmore, this protocol has the advantage of high capacity and can be realized in the experiment.
Rapid single-flux-quantum circuits for low noise mK operation
Intiso, Samuel; Pekola, Jukka; Savin, Alexander; Devyatov, Ygor; Kidiyarova-Shevchenko, Anna
2006-05-01
Rapid single-flux-quantum (RSFQ) technology has been proposed as control electronics for superconducting quantum bits because of the material and working temperature compatibility. In this work, we consider practical aspects of RSFQ circuit design for low noise low power operation. At the working temperature of 20 mK and operational frequency of 2 GHz, dissipated power per junction is reduced to 25 pW by using 6 µA critical current junctions available at the Hypres and VTT low Jc fabrication process. To limit phonon temperature to 30 mK, a maximum of 40 junctions can be placed on a 5 mm × 5 mm chip. Electron temperature in resistive shunts of Josephson junctions is minimized by use of cooling fins, giving minimum electron temperatures of about 150 mK for the Hypres process and 70 mK for the VTT process.
A gravitational wave observatory operating beyond the quantum shot-noise limit
Ligo Scientific Collaboration; Abadie, J.; Abbott, B. P.; Abbott, R.; Abbott, T. D.; Abernathy, M.; Adams, C.; Adhikari, R.; Affeldt, C.; Allen, B.; Allen, G. S.; Amador Ceron, E.; Amariutei, D.; Amin, R. S.; Anderson, S. B.; Anderson, W. G.; Arai, K.; Arain, M. A.; Araya, M. C.; Aston, S. M.; Atkinson, D.; Aufmuth, P.; Aulbert, C.; Aylott, B. E.; Babak, S.; Baker, P.; Ballmer, S.; Barker, D.; Barr, B.; Barriga, P.; Barsotti, L.; Barton, M. A.; Bartos, I.; Bassiri, R.; Bastarrika, M.; Batch, J.; Bauchrowitz, J.; Behnke, B.; Bell, A. S.; Belopolski, I.; Benacquista, M.; Berliner, J. M.; Bertolini, A.; Betzwieser, J.; Beveridge, N.; Beyersdorf, P. T.; Bilenko, I. A.; Billingsley, G.; Birch, J.; Biswas, R.; Black, E.; Blackburn, J. K.; Blackburn, L.; Blair, D.; Bland, B.; Bock, O.; Bodiya, T. P.; Bogan, C.; Bondarescu, R.; Bork, R.; Born, M.; Bose, S.; Brady, P. R.; Braginsky, V. B.; Brau, J. E.; Breyer, J.; Bridges, D. O.; Brinkmann, M.; Britzger, M.; Brooks, A. F.; Brown, D. A.; Brummitt, A.; Buonanno, A.; Burguet-Castell, J.; Burmeister, O.; Byer, R. L.; Cadonati, L.; Camp, J. B.; Campsie, P.; Cannizzo, J.; Cannon, K.; Cao, J.; Capano, C. D.; Caride, S.; Caudill, S.; Cavagliá, M.; Cepeda, C.; Chalermsongsak, T.; Chalkley, E.; Charlton, P.; Chelkowski, S.; Chen, Y.; Christensen, N.; Cho, H.; Chua, S. S. Y.; Chung, S.; Chung, C. T. Y.; Ciani, G.; Clara, F.; Clark, D. E.; Clark, J.; Clayton, J. H.; Conte, R.; Cook, D.; Corbitt, T. R.; Cordier, M.; Cornish, N.; Corsi, A.; Costa, C. A.; Coughlin, M.; Couvares, P.; Coward, D. M.; Coyne, D. C.; Creighton, J. D. E.; Creighton, T. D.; Cruise, A. M.; Cumming, A.; Cunningham, L.; Cutler, R. M.; Dahl, K.; Danilishin, S. L.; Dannenberg, R.; Danzmann, K.; Daudert, B.; Daveloza, H.; Davies, G.; Daw, E. J.; Dayanga, T.; Debra, D.; Degallaix, J.; Dent, T.; Dergachev, V.; Derosa, R.; Desalvo, R.; Dhurandhar, S.; Diguglielmo, J.; di Palma, I.; Díaz, M.; Donovan, F.; Dooley, K. L.; Dorsher, S.; Drever, R. W. P.; Driggers, J. C.; Du, Z.; Dumas, J.-C.; Dwyer, S.; Eberle, T.; Edgar, M.; Edwards, M.; Effler, A.; Ehrens, P.; Engel, R.; Etzel, T.; Evans, K.; Evans, M.; Evans, T.; Factourovich, M.; Fairhurst, S.; Fan, Y.; Farr, B. F.; Farr, W.; Fazi, D.; Fehrmann, H.; Feldbaum, D.; Finn, L. S.; Fisher, R. P.; Flanigan, M.; Foley, S.; Forsi, E.; Fotopoulos, N.; Frede, M.; Frei, M.; Frei, Z.; Freise, A.; Frey, R.; Fricke, T. T.; Friedrich, D.; Fritschel, P.; Frolov, V. V.; Fulda, P. J.; Fyffe, M.; Ganija, M. R.; Garcia, J.; Garofoli, J. A.; Geng, R.; Gergely, L. Á.; Gholami, I.; Ghosh, S.; Giaime, J. A.; Giampanis, S.; Giardina, K. D.; Gill, C.; Goetz, E.; Goggin, L. M.; González, G.; Gorodetsky, M. L.; Goßler, S.; Graef, C.; Grant, A.; Gras, S.; Gray, C.; Gray, N.; Greenhalgh, R. J. S.; Gretarsson, A. M.; Grosso, R.; Grote, H.; Grunewald, S.; Guido, C.; Gupta, R.; Gustafson, E. K.; Gustafson, R.; Ha, T.; Hage, B.; Hallam, J. M.; Hammer, D.; Hammond, G.; Hanks, J.; Hanna, C.; Hanson, J.; Harms, J.; Harry, G. M.; Harry, I. W.; Harstad, E. D.; Hartman, M. T.; Haughian, K.; Hayama, K.; Heefner, J.; Heintze, M. C.; Hendry, M. A.; Heng, I. S.; Heptonstall, A. W.; Herrera, V.; Hewitson, M.; Hild, S.; Hoak, D.; Hodge, K. A.; Holt, K.; Hong, T.; Hooper, S.; Hosken, D. J.; Hough, J.; Howell, E. J.; Hughey, B.; Huynh-Dinh, T.; Husa, S.; Huttner, S. H.; Ingram, D. R.; Inta, R.; Isogai, T.; Ivanov, A.; Izumi, K.; Jacobson, M.; Jang, H.; Johnson, W. W.; Jones, D. I.; Jones, G.; Jones, R.; Ju, L.; Kalmus, P.; Kalogera, V.; Kamaretsos, I.; Kandhasamy, S.; Kang, G.; Kanner, J. B.; Katsavounidis, E.; Katzman, W.; Kaufer, H.; Kawabe, K.; Kawamura, S.; Kawazoe, F.; Kells, W.; Keppel, D. G.; Keresztes, Z.; Khalaidovski, A.; Khalili, F. Y.; Khazanov, E. A.; Kim, B.; Kim, C.; Kim, D.; Kim, H.; Kim, K.; Kim, N.; Kim, Y.-M.; King, P. J.; Kinsey, M.; Kinzel, D. L.; Kissel, J. S.; Klimenko, S.; Kokeyama, K.; Kondrashov, V.; Kopparapu, R.; Koranda, S.; Korth, W. Z.; Kozak, D.; Kringel, V.; Krishnamurthy, S.; Krishnan, B.; Kuehn, G.; Kumar, R.; Kwee, P.; Lam, P. K.; Landry, M.; Lang, M.; Lantz, B.; Lastzka, N.; Lawrie, C.; Lazzarini, A.; Leaci, P.; Lee, C. H.; Lee, H. M.; Leindecker, N.; Leong, J. R.; Leonor, I.; Li, J.; Lindquist, P. E.; Lockerbie, N. A.; Lodhia, D.; Lormand, M.; Luan, J.; Lubinski, M.; Lück, H.; Lundgren, A. P.; MacDonald, E.; Machenschalk, B.; Macinnis, M.; MacLeod, D. M.; Mageswaran, M.; Mailand, K.; Mandel, I.; Mandic, V.; Marandi, A.; Márka, S.; Márka, Z.; Markosyan, A.; Maros, E.; Martin, I. W.; Martin, R. M.; Marx, J. N.; Mason, K.; Matichard, F.; Matone, L.; Matzner, R. A.; Mavalvala, N.; Mazzolo, G.; McCarthy, R.; McClelland, D. E.; McGuire, S. C.; McIntyre, G.; McIver, J.; McKechan, D. J. A.; Meadors, G. D.; Mehmet, M.; Meier, T.; Melatos, A.; Melissinos, A. C.; Mendell, G.; Menendez, D.
2011-12-01
Around the globe several observatories are seeking the first direct detection of gravitational waves (GWs). These waves are predicted by Einstein's general theory of relativity and are generated, for example, by black-hole binary systems. Present GW detectors are Michelson-type kilometre-scale laser interferometers measuring the distance changes between mirrors suspended in vacuum. The sensitivity of these detectors at frequencies above several hundred hertz is limited by the vacuum (zero-point) fluctuations of the electromagnetic field. A quantum technology--the injection of squeezed light--offers a solution to this problem. Here we demonstrate the squeezed-light enhancement of GEO600, which will be the GW observatory operated by the LIGO Scientific Collaboration in its search for GWs for the next 3-4 years. GEO600 now operates with its best ever sensitivity, which proves the usefulness of quantum entanglement and the qualification of squeezed light as a key technology for future GW astronomy.
ABC of ladder operators for rationally extended quantum harmonic oscillator systems
Cariñena, José F.; Plyushchay, Mikhail S.
2017-07-01
The problem of construction of ladder operators for rationally extended quantum harmonic oscillator (REQHO) systems of a general form is investigated in the light of existence of different schemes of the Darboux-Crum-Krein-Adler transformations by which such systems can be generated from the quantum harmonic oscillator. Any REQHO system is characterized by the number of separated states in its spectrum, the number of ‘valence bands’ in which the separated states are organized, and by the total number of the missing energy levels and their position. All these peculiarities of a REQHO system are shown to be detected and reflected by a trinity (A^+/- , B^+/- , C^+/-) of the basic (primary) lowering and raising ladder operators related between themselves by certain algebraic identities with coefficients polynomially-dependent on the Hamiltonian. We show that all the secondary, higher-order ladder operators are obtainable by a composition of the basic ladder operators of the trinity which form the set of the spectrum-generating operators. Each trinity, in turn, can be constructed from the intertwining operators of the two complementary minimal schemes of the Darboux-Crum-Krein-Adler transformations.
Institute of Scientific and Technical Information of China (English)
刘当婷; 田野; 赵士平; 任育峰; 陈赓华
2015-01-01
We discuss a simple relation between the input and output signals of a superconducting quantum interference device magnetometer operating in flux locked mode in a cosine curve approximation. According to this relation, an original fast input signal can be easily retrieved from its distorted output response. This technique can be used in some areas such as sensitive and fast detection of magnetic or metallic grains in medicine and food security checking.
2008-01-01
We discuss approximations of vertex couplings of quantum graphs using families of thin branched manifolds. We show that if a Neumann type Laplacian on such manifolds is amended by suitable potentials, the resulting Schr\\"odinger operators can approximate non-trivial vertex couplings. The latter include not only the delta-couplings but also those with wavefunctions discontinuous at the vertex. We work out the example of the symmetric delta'-couplings and conjecture that the same method can be ...
Coherent chemical kinetics as quantum walks. I. Reaction operators for radical pairs.
Chia, A; Tan, K C; Pawela, Ł; Kurzyński, P; Paterek, T; Kaszlikowski, D
2016-03-01
Classical chemical kinetics uses rate-equation models to describe how a reaction proceeds in time. Such models are sufficient for describing state transitions in a reaction where coherences between different states do not arise, in other words, a reaction that contains only incoherent transitions. A prominent example of a reaction containing coherent transitions is the radical-pair model. The kinetics of such reactions is defined by the so-called reaction operator that determines the radical-pair state as a function of intermediate transition rates. We argue that the well-known concept of quantum walks from quantum information theory is a natural and apt framework for describing multisite chemical reactions. By composing Kraus maps that act only on two sites at a time, we show how the quantum-walk formalism can be applied to derive a reaction operator for the standard avian radical-pair reaction. Our reaction operator predicts the same recombination dephasing rate as the conventional Haberkorn model, which is consistent with recent experiments [K. Maeda et al., J. Chem. Phys. 139, 234309 (2013)], in contrast to previous work by Jones and Hore [J. A. Jones and P. J. Hore, Chem. Phys. Lett. 488, 90 (2010)]. The standard radical-pair reaction has conventionally been described by either a normalized density operator incorporating both the radical pair and reaction products or a trace-decreasing density operator that considers only the radical pair. We demonstrate a density operator that is both normalized and refers only to radical-pair states. Generalizations to include additional dephasing processes and an arbitrary number of sites are also discussed.
Propagation of light in area metric backgrounds
Energy Technology Data Exchange (ETDEWEB)
Punzi, Raffaele; Wohlfarth, Mattias N R [Zentrum fuer Mathematische Physik und II. Institut fuer Theoretische Physik, Universitaet Hamburg, Luruper Chaussee 149, 22761 Hamburg (Germany); Schuller, Frederic P, E-mail: raffaele.punzi@desy.d, E-mail: fps@aei.mpg.d, E-mail: mattias.wohlfarth@desy.d [Max Planck Institut fuer Gravitationsphysik, Albert Einstein Institut, Am Muehlenberg 1, 14467 Potsdam (Germany)
2009-02-07
The propagation of light in area metric spacetimes, which naturally emerge as refined backgrounds in quantum electrodynamics and quantum gravity, is studied from first principles. In the geometric-optical limit, light rays are found to follow geodesics in a Finslerian geometry, with the Finsler norm being determined by the area metric tensor. Based on this result, and an understanding of the nonlinear relation between ray vectors and wave covectors in such refined backgrounds, we study light deflection in spherically symmetric situations and obtain experimental bounds on the non-metricity of spacetime in the solar system.
Room-temperature operation of mid-infrared surface-plasmon quantum cascade lasers
Bahriz, M.; Moreau, V.; Palomo, J.; Krysa, A. B.; Austin, D.; Cockburn, J. W.; Roberts, J. S.; Wilson, L. R.; Julien, F.; Colombelli, R.
2007-04-01
We report the pulsed, room-temperature operation of an InGaAs/AllnAs quantum cascade laser at an operating wavelength of ≈ 7.5 μm in which the optical mode is a surface-plasmon polariton excitation. The use of a silver-based electrical contact with reduced optical losses at the laser emission wavelength allows for a reduction of the laser threshold current by a factor of two relative to samples with a gold-based contact layer.
High Temperature Operation of 5.5μm Strain-Compensated Quantum Cascaded Lasers
Institute of Scientific and Technical Information of China (English)
LU Xiu-Zhen; LIU Feng-Qi; LIU Jun-Qi; JIN Peng; WANG Zhan-Guo
2005-01-01
@@ We develop 5.5-μm Inx Ga1-xAs/InyAl1-yAs strain-compensated quantum cascade lasers with InP and InGaAs cladding layers by using solid-source molecular-beam epitaxy. Pulse operation has been achieved up to 323K (50℃) for uncoated 20-μm-wide and 2-mm-long devices. These devices display an output power of 36mW with a duty cycle of 1% at room temperature. In continuous wave operation a record peak optical power of 10mW per facet has been measured at 83 K.
Continuous wave operation of quantum cascade lasers with frequency-shifted feedback
Energy Technology Data Exchange (ETDEWEB)
Lyakh, A., E-mail: arkadiy.lyakh@ucf.edu [Pranalytica, Inc., 1101 Colorado Ave., Santa Monica, CA 90401 (United States); NanoScience Technology Center, University of Central Florida, 12424 Research Pkwy, Orlando, FL 32826 (United States); College of Optics and Photonics, University of Central Florida, 304 Scorpius St, Orlando, FL 32826 (United States); Barron-Jimenez, R.; Dunayevskiy, I.; Go, R.; Tsvid, G.; Patel, C. Kumar N., E-mail: patel@pranalytica.com [Pranalytica, Inc., 1101 Colorado Ave., Santa Monica, CA 90401 (United States)
2016-01-15
Operation of continuous wave quantum cascade lasers with a frequency-shifted feedback provided by an acousto-optic modulator is reported. Measured linewidth of 1.7 cm{sup −1} for these devices, under CW operating conditions, was in a good agreement with predictions of a model based on frequency-shifted feedback seeded by spontaneous emission. Linewidth broadening was observed for short sweep times, consistent with sound wave grating period variation across the illuminated area on the acousto-optic modulator. Standoff detection capability of the AOM-based QCL setup was demonstrated for several solid materials.
Realization of the N(odd)-Dimensional Quantum Euclidean Space by Differential Operators
Institute of Scientific and Technical Information of China (English)
LI Yun; JING Si-Cong
2004-01-01
The quantum Euclidean space RNq is a kind of noncommutative space that is obtained from ordinary Euclidean space RN by deformation with parameter q. When N is odd, the structure of this space is similar to R3q.Motivated by realization ofR3q by differential operators in R3, we give such realization for R5q and R7q cases and generalize our results to RNq (N odd) in this paper, that is, we show that the algebra of RNq can be realized by differential operators acting on C∞ functions on undeformed space RN.
Institute of Scientific and Technical Information of China (English)
WANG Yi-Min; ZHOU Yan-Li; LIANG Lin-Mei; LI Cheng-Zu
2009-01-01
We propose a feasible scheme to achieve universal quantum gate operations in decoherence-free subspace with superconducting charge qubits placed in a microwave cavity.Single-logic-qubit gates can be realized with cavity assisted interaction, which possesses the advantages of unconventional geometric gate operation.The two-logic-qubit controlled-phase gate between subsystems can be constructed with the help of a variable electrostatic transformer, The collective decoherence can be successfully avoided in our well-designed system.Moreover, GHZ state for logical qubits can also be easily produced in this system.
Directory of Open Access Journals (Sweden)
Schnabel Roman
2013-08-01
Full Text Available This contribution reviews our recent progress on the generation of squeezed light [1], and also the recent squeezed-light enhancement of the gravitational wave detector GEO 600 [2]. GEO 600 is currently the only GW observatory operated by the LIGO Scientific Collaboration in its search for gravitational waves. With the help of squeezed states of light it now operates with its best ever sensitivity, which not only proves the qualification of squeezed light as a key technology for future gravitational wave astronomy but also the usefulness of quantum entanglement.
Energy Technology Data Exchange (ETDEWEB)
Dattoli, Giuseppe; Torre, Amalia [ENEA, Centro Ricerche Frascati, Rome (Italy). Dipt. Innovazione; Ottaviani, Pier Luigi [ENEA, Centro Ricerche Bologna (Italy); Vasquez, Luis [Madris, Univ. Complutense (Spain). Dept. de Matemateca Aplicado
1997-10-01
The finite-difference based integration method for evolution-line equations is discussed in detail and framed within the general context of the evolution operator picture. Exact analytical methods are described to solve evolution-like equations in a quite general physical context. The numerical technique based on the factorization formulae of exponential operator is then illustrated and applied to the evolution-operator in both classical and quantum framework. Finally, the general view to the finite differencing schemes is provided, displaying the wide range of applications from the classical Newton equation of motion to the quantum field theory.
Learning Sequence Neighbourhood Metrics
Bayer, Justin; van der Smagt, Patrick
2011-01-01
Recurrent neural networks (RNNs) in combination with a pooling operator and the neighbourhood components analysis (NCA) objective function are able to detect the characterizing dynamics of sequences and embed them into a fixed-length vector space of arbitrary dimensionality. Subsequently, the resulting features are meaningful and can be used for visualization or nearest neighbour classification in linear time. This kind of metric learning for sequential data enables the use of algorithms tailored towards fixed length vector spaces such as R^n.
On the existence of certain axisymmetric interior metrics
Santacruz, C Angulo; Nowakowski, M
2010-01-01
One of the effects of noncommutative coordinate operators is that the delta-function connected to the quantum mechanical amplitude between states sharp to the position operator gets smeared by a Gaussian distribution. Although this is not the full account of effects of noncommutativity, this effect is in particular important, as it removes the point singularities of Schwarzschild and Reissner-Nordstr\\"{o}m solutions. In this context, it seems to be of some importance to probe also into ring-like singularities which appear in the Kerr case. In particular, starting with an anisotropic energy-momentum tensor and a general axisymmetric ansatz of the metric together with an arbitrary mass distribution (e.g. Gaussian) we derive the full set of Einstein equations that the Noncommutative Geometry inspired Kerr solution should satisfy. Using these equations we prove two theorems regarding the existence of certain Kerr metrics inspired by Noncommutative Geometry.
New approach for anti-normally and normally ordering bosonic-operator functions in quantum optics
Xu, Shi-Min; Zhang, Yun-Hai; Xu, Xing-Lei; Li, Hong-Qi; Wang, Ji-Suo
2016-12-01
In this paper, we provide a new kind of operator formula for anti-normally and normally ordering bosonic-operator functions in quantum optics, which can help us arrange a bosonic-operator function f(λQ̂ + νP̂) in its anti-normal and normal ordering conveniently. Furthermore, mutual transformation formulas between anti-normal ordering and normal ordering, which have good universality, are derived too. Based on these operator formulas, some new differential relations and some useful mathematical integral formulas are easily derived without really performing these integrations. Project supported by the Natural Science Foundation of Shandong Province, China (Grant No. ZR2015AM025) and the Natural Science Foundation of Heze University, China (Grant No. XY14PY02).
Directory of Open Access Journals (Sweden)
D. H. Wu
2017-03-01
Full Text Available We demonstrate a surface grating coupled substrate emitting quantum cascade ring laser with high power room temperature continuous wave operation at 4.64 μm. A second order surface metal/semiconductor distributed-feedback grating is used for in-plane feedback and vertical out-coupling. A device with 400 μm radius ring cavity exhibits an output power of 202 mW in room temperature continuous wave operation. Single mode operation with a side mode suppression ratio of 25 dB is obtained along with a good linear tuning with temperature. The far field measurement exhibits a low divergent concentric ring beam pattern with a lobe separation of ∼0.34°, which indicates that the device operates in fundamental mode (n = 1.
Directory of Open Access Journals (Sweden)
Abbas Noon
2011-05-01
Full Text Available Round Robin, considered as the most widely adopted CPU scheduling algorithm, undergoes severe problems directly related to quantum size. If time quantum chosen is too large, the response time of the processes is considered too high. On the other hand, if this quantum is too small, it increases the overhead of the CPU. In this paper, we propose a new algorithm, called AN, based on a new approach called dynamic-time-quantum; the idea of this approach is to make the operating systems adjusts the time quantum according to the burst time of the set of waiting processes in the ready queue. Based on the simulations and experiments, we show that the new proposed algorithm solves the fixed time quantum problem and increases the performance of Round Robin.
Two-loop scale-invariant scalar potential and quantum effective operators
Energy Technology Data Exchange (ETDEWEB)
Ghilencea, D.M. [National Institute of Physics and Nuclear Engineering (IFIN-HH), Theoretical Physics Department, Bucharest (Romania); CERN, Theory Division, Geneva 23 (Switzerland); Lalak, Z.; Olszewski, P. [University of Warsaw, Faculty of Physics, Institute of Theoretical Physics, Warsaw (Poland)
2016-12-15
Spontaneous breaking of quantum scale invariance may provide a solution to the hierarchy and cosmological constant problems. In a scale-invariant regularization, we compute the two-loop potential of a Higgs-like scalar φ in theories in which scale symmetry is broken only spontaneously by the dilaton (σ). Its VEV left angle σ right angle generates the DR subtraction scale (μ ∝ left angle σ right angle), which avoids the explicit scale symmetry breaking by traditional regularizations (where μ = fixed scale). The two-loop potential contains effective operators of non-polynomial nature as well as new corrections, beyond those obtained with explicit breaking (μ = fixed scale). These operators have the form φ{sup 6}/σ{sup 2}, φ{sup 8}/σ{sup 4}, etc., which generate an infinite series of higher dimensional polynomial operators upon expansion about left angle σ right angle >> left angle φ right angle, where such hierarchy is arranged by one initial, classical tuning. These operators emerge at the quantum level from evanescent interactions (∝ ε) between σ and φ that vanish in d = 4 but are required by classical scale invariance in d = 4 - 2ε. The Callan-Symanzik equation of the two-loop potential is respected and the two-loop beta functions of the couplings differ from those of the same theory regularized with μ = fixed scale. Therefore the running of the couplings enables one to distinguish between spontaneous and explicit scale symmetry breaking. (orig.)
Optimization of quantum Hamiltonian evolution: From two projection operators to local Hamiltonians
Patel, Apoorva; Priyadarsini, Anjani
Given a quantum Hamiltonian and its evolution time, the corresponding unitary evolution operator can be constructed in many different ways, corresponding to different trajectories between the desired end-points and different series expansions. A choice among these possibilities can then be made to obtain the best computational complexity and control over errors. It is shown how a construction based on Grover's algorithm scales linearly in time and logarithmically in the error bound, and is exponentially superior in error complexity to the scheme based on the straightforward application of the Lie-Trotter formula. The strategy is then extended first to simulation of any Hamiltonian that is a linear combination of two projection operators, and then to any local efficiently computable Hamiltonian. The key feature is to construct an evolution in terms of the largest possible steps instead of taking small time steps. Reflection operations and Chebyshev expansions are used to efficiently control the total error on the overall evolution, without worrying about discretization errors for individual steps. We also use a digital implementation of quantum states that makes linear algebra operations rather simple to perform.
Two-loop scale-invariant scalar potential and quantum effective operators
Ghilencea, D.M.
2016-01-01
Spontaneous breaking of quantum scale invariance may provide a solution to the hierarchy and cosmological constant problems. In a scale-invariant regularization, we compute the two-loop potential of a higgs-like scalar $\\phi$ in theories in which scale symmetry is broken only spontaneously by the dilaton ($\\sigma$). Its vev $\\langle\\sigma\\rangle$ generates the DR subtraction scale ($\\mu\\sim\\langle\\sigma\\rangle$), which avoids the explicit scale symmetry breaking by traditional regularizations (where $\\mu$=fixed scale). The two-loop potential contains effective operators of non-polynomial nature as well as new corrections, beyond those obtained with explicit breaking ($\\mu$=fixed scale). These operators have the form: $\\phi^6/\\sigma^2$, $\\phi^8/\\sigma^4$, etc, which generate an infinite series of higher dimensional polynomial operators upon expansion about $\\langle\\sigma\\rangle\\gg \\langle\\phi\\rangle$, where such hierarchy is arranged by {\\it one} initial, classical tuning. These operators emerge at the quantum...
Institute of Scientific and Technical Information of China (English)
WU Tao; LIU Jian-She; LI Zheng
2006-01-01
@@ Superconducting flux qubits with three Josephson junctions are promising candidates for the building blocks of a quantum computer. We have applied the imaginary time evolution method to study the model of this qubit accurately by calculating its wavefunctions and eigenenergies. Because such qubits are manipulated with magnetic lux microwave pulses, they might be irradiated into non-computational states, which is called the leakage effect.By the evolution of the density matrix of the qubit under either hard-shaped π-pulse or Gaussian-shaped π-pulse to carry out quantum NOT operation, it has been demonstrated that the leakage effect for a flux qubit is very small even for hard-shaped microwave pulses while Gaussian-shaped pulses may suppress the leakage effect to a negligible level.
Linear optics only allows every possible quantum operation for one photon or one port
Moyano-Fernández, Julio José; Garcia-Escartin, Juan Carlos
2017-01-01
We study the evolution of the quantum state of n photons in m different modes when they go through a lossless linear optical system. We show that there are quantum evolution operators U that cannot be built with linear optics alone unless the number of photons or the number of modes is equal to one. The evolution for single photons can be controlled with the known realization of any unitary proved by Reck, Zeilinger, Bernstein and Bertani. The evolution for a single mode corresponds to the trivial evolution in a phase shifter. We analyze these two cases and prove that any other combination of the number of photons and modes produces a Hilbert state too large for the linear optics system to give any desired evolution.
Infinitely many commuting operators for the elliptic quantum group $U_{q,p}(\\hat{sl_N})$
Kojima, Takeo
2011-01-01
We construct two classes of infinitely many commuting operators associated with the elliptic quantum group $U_{q,p}(\\hat{sl_N})$. We call one of them the integral of motion ${\\cal G}_m$, $(m \\in {\\mathbb N})$ and the other the boundary transfer matrix $T_B(z)$, $(z \\in {\\mathbb C})$. The integral of motion ${\\cal G}_m$ is related to elliptic deformation of the $N$-th KdV theory. The boundary transfer matrix $T_B(z)$ is related to the boundary $U_{q,p}(\\hat{sl_N})$ face model. We diagonalize the boundary transfer matrix $T_B(z)$ by using the free field realization of the elliptic quantum group, however diagonalization of the integral of motion ${\\cal G}_m$ is open problem even for the simplest case $U_{q,p}(\\hat{sl_2})$.
Blanchard, Philippe
2015-01-01
The second edition of this textbook presents the basic mathematical knowledge and skills that are needed for courses on modern theoretical physics, such as those on quantum mechanics, classical and quantum field theory, and related areas. The authors stress that learning mathematical physics is not a passive process and include numerous detailed proofs, examples, and over 200 exercises, as well as hints linking mathematical concepts and results to the relevant physical concepts and theories. All of the material from the first edition has been updated, and five new chapters have been added on such topics as distributions, Hilbert space operators, and variational methods. The text is divided into three main parts. Part I is a brief introduction to distribution theory, in which elements from the theories of ultradistributions and hyperfunctions are considered in addition to some deeper results for Schwartz distributions, thus providing a comprehensive introduction to the theory of generalized functions. P...
Clawson, Savannah Ellen
2017-01-01
The quantum efficiency of a Burle 8850 photomultiplier tube with a potassium-caesium-antimony (bialkali) photocathode was determined by attenuating a 1 mW HeNe laser emitting at 633 nm and measuring the signal frequency when the laser was incident on the photomultiplier. A temperature range of 5 $^{\\circ}$C $-$ 20 $^{\\circ}$C was investigated and it was found that the quantum efficiency decreases with temperature, with the signal frequency decreasing at a faster rate than the dark current frequency. Therefore, it was concluded that it would not be beneficial to cool photomultiplier tubes operating in the visible spectrum for use in collinear laser spectroscopy due to a decreasing signal-to-noise ratio. The signal pulse height distribution was also analysed and found to be independent of temperature within the range investigated.
Modified gravity from the nonperturbative quantization of a metric
Energy Technology Data Exchange (ETDEWEB)
Dzhunushaliev, Vladimir [Al-Farabi Kazakh National University, Department of Theoretical and Nuclear Physics, Almaty (Kazakhstan); IETP, Al-Farabi Kazakh National University, Almaty (Kazakhstan); Institute of Physicotechnical Problems and Material Science, NAS of the Kyrgyz Republic, Bishkek (Kyrgyzstan); Universitaet Oldenburg, Institut fuer Physik, Oldenburg (Germany); Eurasian National University, Institute for Basic Research, Astana (Kazakhstan); Folomeev, Vladimir [IETP, Al-Farabi Kazakh National University, Almaty (Kazakhstan); Institute of Physicotechnical Problems and Material Science, NAS of the Kyrgyz Republic, Bishkek (Kyrgyzstan); Universitaet Oldenburg, Institut fuer Physik, Oldenburg (Germany); Kleihaus, Burkhard; Kunz, Jutta [Universitaet Oldenburg, Institut fuer Physik, Oldenburg (Germany)
2015-04-01
Based on certain assumptions for the expectation value of a product of the quantum fluctuating metric at two points, the gravitational and scalar field Lagrangians are evaluated. Assuming a vanishing expectation value of the first-order terms of the metric, the calculations are performed with an accuracy of second order. It is shown that such quantum corrections give rise to modified gravity. (orig.)
Quantum singularity of Levi-Civita spacetimes
Konkowski, D A; Wieland, C
2004-01-01
Quantum singularities in general relativistic spacetimes are determined by the behavior of quantum test particles. A static spacetime is quantum mechanically singular if the spatial portion of the wave operator is not essentially self-adjoint. Here Weyl's limit point-limit circle criterion is used to determine whether a wave operator is essentially self-adjoint. This test is then applied to scalar wave packets in Levi-Civita spacetimes to help elucidate the physical properties of the spacetimes in terms of their metric parameters.
High-temperature operation of broadband bidirectional terahertz quantum-cascade lasers
Khanal, Sudeep; Gao, Liang; Zhao, Le; Reno, John L.; Kumar, Sushil
2016-09-01
Terahertz quantum cascade lasers (QCLs) with a broadband gain medium could play an important role for sensing and spectroscopy since then distributed-feedback schemes could be utilized to produce laser arrays on a single semiconductor chip with wide spectral coverage. QCLs can be designed to emit at two different frequencies when biased with opposing electrical polarities. Here, terahertz QCLs with bidirectional operation are developed to achieve broadband lasing from the same semiconductor chip. A three-well design scheme with shallow-well GaAs/Al0.10Ga0.90As superlattices is developed to achieve high-temperature operation for bidirectional QCLs. It is shown that shallow-well heterostructures lead to optimal quantum-transport in the superlattice for bidirectional operation compared to the prevalent GaAs/Al0.15Ga0.85As material system. Broadband lasing in the frequency range of 3.1-3.7 THz is demonstrated for one QCL design, which achieves maximum operating temperatures of 147 K and 128 K respectively in opposing polarities. Dual-color lasing with large frequency separation is demonstrated for a second QCL, that emits at ~3.7 THz and operates up to 121 K in one polarity, and at ~2.7 THz up to 105 K in the opposing polarity. These are the highest operating temperatures achieved for broadband terahertz QCLs at the respective emission frequencies, and could lead to commercial development of broadband terahertz laser arrays.
Non-compact groups, tensor operators and applications to quantum gravity
Sellaroli, Giuseppe
2016-01-01
This work focuses on non-compact groups and their applications to quantum gravity, mainly through the use of tensor operators. First, the mathematical theory of tensor operators for a Lie group is recast in a new way which is used to generalise the Wigner-Eckart theorem to non-compact groups. The result relies on the knowledge of the recoupling theory between finite-dimensional and infinite-dimensional irreducible representations of the group; here the previously unconsidered cases of the 3D and 4D Lorentz groups are investigated in detail. As an application, the Wigner-Eckart theorem is used to generalise the Jordan-Schwinger representation of SU(2) to both groups, for all representation classes. Next, the results obtained for the 3D Lorentz group are applied to (2+1) Lorentzian loop quantum gravity to develop an analogue of the well-known spinorial approach used in the Euclidean case. Tensor operators are used to construct observables and to generalise the Hamiltonian constraint introduced by Bonzom and Liv...
Particle number conservation in quantum many-body simulations with matrix product operators
Muth, Dominik
2011-01-01
Incorporating conservation laws explicitly into Matrix product states (MPS) has proven to make numerical simulations of quantum many-body systems much less resources consuming. We will discuss here, to what extent this concept can be used in matrix product operators (MPO). Quite counter-intuitively the expectation of gaining in speed by sacrificing information about all but a single symmetry sector is not in all cases fulfilled. It turns out that often the entanglement imposed by the global constraint of fixed particle number is the limiting factor in the canonical ensemble.
Tunable single and dual mode operation of an external cavity quantum-dot injection laser
Energy Technology Data Exchange (ETDEWEB)
Biebersdorf, A [Photonics and Optoelectronics Group, Physics Department and CeNS, Ludwig-Maximilians-Universitaet, Amalienstrasse 54, D-80799 Munich (Germany); Lingk, C [Photonics and Optoelectronics Group, Physics Department and CeNS, Ludwig-Maximilians-Universitaet, Amalienstrasse 54, D-80799 Munich (Germany); De Giorgi, M [Photonics and Optoelectronics Group, Physics Department and CeNS, Ludwig-Maximilians-Universitaet, Amalienstrasse 54, D-80799 Munich (Germany); Feldmann, J [Photonics and Optoelectronics Group, Physics Department and CeNS, Ludwig-Maximilians-Universitaet, Amalienstrasse 54, D-80799 Munich (Germany); Sacher, J [Sacher Lasertechnik GmbH, Hannah Arendt Strasse 3-7, D-35037 Marburg (Germany); Arzberger, M [Walter Schottky Institut, Technische Universitaet Muenchen, Am Coulombwall, D-85748 Garching (Germany); Ulbrich, C [Walter Schottky Institut, Technische Universitaet Muenchen, Am Coulombwall, D-85748 Garching (Germany); Boehm, G [Walter Schottky Institut, Technische Universitaet Muenchen, Am Coulombwall, D-85748 Garching (Germany); Amann, M-C [Walter Schottky Institut, Technische Universitaet Muenchen, Am Coulombwall, D-85748 Garching (Germany); Abstreiter, G [Walter Schottky Institut, Technische Universitaet Muenchen, Am Coulombwall, D-85748 Garching (Germany)
2003-08-21
We investigate quantum-dot (QD) lasers in an external cavity using Littrow and Littman configurations. Here, we report on a continuously tunable QD laser with a broad tuning range from 1047 to 1130 nm with high stability and efficient side mode suppression. The full-width at half-maximum of the laser line is 0.85 nm determined mainly by the quality of the external grating. This laser can be operated in a dual-mode modus, where the mode-spacing can be tuned continuously between 1.1 and 34 nm. Simultaneous emission of the two laser modes is shown by sum frequency generation experiments.
Extracting fundamental transverse mode operation in broad area quantum cascade lasers
Kaspi, R.; Luong, S.; Yang, C.; Lu, C.; Newell, T. C.; Bate, T.
2016-11-01
Power scaling in broad area quantum cascade lasers results in the operation of high order transverse modes with a far-field profile consisting of two lobes propagating at large angles relative to the optical axis. We report a method of suppressing the high order transverse modes that can extract the fundamental mode and provide emission along the optical axis. By generating a lateral constriction in the waveguide in the form of short trenches defined by the focused ion beam milling technique, we report broad area devices in which most of the power is contained in a near diffraction-limited beam that provides high brightness.
General Approach to Quantum Channel Impossibility by Local Operations and Classical Communication
Cohen, Scott M.
2017-01-01
We describe a general approach to proving the impossibility of implementing a quantum channel by local operations and classical communication (LOCC), even with an infinite number of rounds, and find that this can often be demonstrated by solving a set of linear equations. The method also allows one to design a LOCC protocol to implement the channel whenever such a protocol exists in any finite number of rounds. Perhaps surprisingly, the computational expense for analyzing LOCC channels is not much greater than that for LOCC measurements. We apply the method to several examples, two of which provide numerical evidence that the set of quantum channels that are not LOCC is not closed and that there exist channels that can be implemented by LOCC either in one round or in three rounds that are on the boundary of the set of all LOCC channels. Although every LOCC protocol must implement a separable quantum channel, it is a very difficult task to determine whether or not a given channel is separable. Fortunately, prior knowledge that the channel is separable is not required for application of our method.
Directory of Open Access Journals (Sweden)
Stefan Hollands
2009-09-01
Full Text Available In this paper, we propose a new framework for quantum field theory in terms of consistency conditions. The consistency conditions that we consider are ''associativity'' or ''factorization'' conditions on the operator product expansion (OPE of the theory, and are proposed to be the defining property of any quantum field theory. Our framework is presented in the Euclidean setting, and is applicable in principle to any quantum field theory, including non-conformal ones. In our framework, we obtain a characterization of perturbations of a given quantum field theory in terms of a certain cohomology ring of Hochschild-type. We illustrate our framework by the free field, but our constructions are general and apply also to interacting quantum field theories. For such theories, we propose a new scheme to construct the OPE which is based on the use of non-linear quantized field equations.
The generic quantum superintegrable system on the sphere and Racah operators
Iliev, Plamen
2017-06-01
We consider the generic quantum superintegrable system on the d-sphere with potential V(y)=\\sum _{k=1}^{d+1}b_k/y_k^2 , where b_k are parameters. Appropriately normalized, the symmetry operators for the Hamiltonian define a representation of the Kohno-Drinfeld Lie algebra on the space of polynomials orthogonal with respect to the Dirichlet distribution. The Gaudin subalgebras generated by Jucys-Murphy elements are diagonalized by families of Jacobi polynomials in d variables on the simplex. We define a set of generators for the symmetry algebra, and we prove that their action on the Jacobi polynomials is represented by the multivariable Racah operators introduced in Geronimo and Iliev (Constr Approx 31(3):417-457, 2010). The constructions also yield a new Lie-theoretic interpretation of the bispectral property for Tratnik's multivariable Racah polynomials.
All-high-Tc superconductor rapid-single-flux-quantum circuit operating at ˜30 K
Shokhor, S.; Nadgorny, B.; Gurvitch, M.; Semenov, V.; Polyakov, Yu.; Likharev, K.; Hou, S. Y.; Phillips, Julia M.
1995-11-01
We have implemented a simple circuit of the rapid single-flux-quantum (RSFQ) logic family using a single-layer YBa2Cu3O7-x thin-film structure with 14 in-plane Josephson junctions formed by direct electron beam writing. The circuit includes two dc/SFQ converters, two Josephson transmission lines, a complete RS SFQ flip-flop, and an SFQ/dc converter (readout SQUID). Low-frequency testing has shown that the dc-current-biased circuit operates correctly and reliably at T˜30 K, a few degrees below the effective critical temperature of the junctions. Prospects for a further increase of the operation temperature and implementation of more complex RSFQ circuits are discussed in brief.
A finite-dimensional representation of the quantum angular momentum operator
Campos, R G; Campos, Rafael G.
2000-01-01
A useful finite-dimensional matrix representation of the derivative of periodic functions is obtained by using some elementary facts of trigonometric interpolation. This NxN matrix becomes a projection of the angular derivative into polynomial subspaces of finite dimension and it can be interpreted as a generator of discrete rotations associated to the z-component of the projection of the angular momentum operator in such subspaces, inheriting thus some properties of the continuum operator. The group associated to these discrete rotations is the cyclic group of order N. Since the square of the quantum angular momentum L^2 is associated to a partial differential boundary value problem in the angular variables $\\theta$ and $\\phi$ whose solution is given in terms of the spherical harmonics, we can project such a differential equation to obtain an eigenvalue matrix problem of finite dimension by extending to several variables a projection technique for solving numerically two point boundary value problems and usi...
Energy Technology Data Exchange (ETDEWEB)
Niccoli, G.
2009-12-15
In an earlier paper (G. Niccoli and J. Teschner, 2009), the spectrum (eigenvalues and eigenstates) of a lattice regularizations of the Sine-Gordon model has been completely characterized in terms of polynomial solutions with certain properties of the Baxter equation. This characterization for cyclic representations has been derived by the use of the Separation of Variables (SOV) method of Sklyanin and by the direct construction of the Baxter Q-operator family. Here, we reconstruct the Baxter Q-operator and the same characterization of the spectrum by only using the SOV method. This analysis allows us to deduce the main features required for the extension to cyclic representations of other integrable quantum models of this kind of spectrum characterization. (orig.)
A non-equilibrium equation-of-motion approach to quantum transport utilizing projection operators.
Ochoa, Maicol A; Galperin, Michael; Ratner, Mark A
2014-11-12
We consider a projection operator approach to the non-equilibrium Green function equation-of-motion (PO-NEGF EOM) method. The technique resolves problems of arbitrariness in truncation of an infinite chain of EOMs and prevents violation of symmetry relations resulting from the truncation (equivalence of left- and right-sided EOMs is shown and symmetry with respect to interchange of Fermi or Bose operators before truncation is preserved). The approach, originally developed by Tserkovnikov (1999 Theor. Math. Phys. 118 85) for equilibrium systems, is reformulated to be applicable to time-dependent non-equilibrium situations. We derive a canonical form of EOMs, thus explicitly demonstrating a proper result for the non-equilibrium atomic limit in junction problems. A simple practical scheme applicable to quantum transport simulations is formulated. We perform numerical simulations within simple models and compare results of the approach to other techniques and (where available) also to exact results.
40-GHz operation of a single-flux-quantum (SFQ) 4 × 4 switch scheduler
Kameda, Y.; Yorozu, S.; Hashimoto, Y.; Terai, H.; Fujimaki, A.; Yoshikawa, N.
2006-10-01
We designed a single-flux-quantum (SFQ) scheduler for a 4 × 4 network switch. It receives requests serially and arbitrates them. Fair scheduling is achieved by using a round-robin priority pointer at each output port. The pointer is updated so that the input port that was granted permission has the lowest priority in the next scheduling cycle. We divided the scheduler into sub-blocks, which were separately designed. The sub-blocks, which have asynchronous interfaces, were then connected with passive transmission lines. Ladder-type on-chip clock generators were included in the circuit for high-speed operation. Using logic simulation, we verified the scheduler test circuit. The scheduler test circuit was composed of about 3000 Josephson junctions. We tested the scheduler circuit at high speed and confirmed correct operations at over 40 GHz.
Distinct Lasing Operation From Chirped InAs/InP Quantum-Dash Laser
Khan, Mohammed Zahed Mustafa
2013-08-01
We study the enhanced inhomogeneity across the InAs quantum-dash (Qdash) layers by incorporating a chirped AlGaInAs barrier thickness in the InAs/InP laser structure. The lasing operation is investigated via Fabry-Pérot ridge-waveguide laser characterization, which shows a peculiar behavior under quasi-continuous-wave (QCW) operation. Continuous energy transfer between different dash ensembles initiated quenching of lasing action among certain dash groups, causing a reduced intensity gap in the lasing spectra. We discuss these characteristics in terms of the quasi-zero-dimensional density of states (DOS) of dashes and the active region inhomogeneity. © 2009-2012 IEEE.
Zaari, Ryan R; Brown, Alex
2010-01-07
Frequency domain shaped binary laser pulses were optimized to perform 2 qubit quantum gate operations in (12)C(16)O. The qubit rovibrational state representation was chosen so that all gate operations consisted of one-photon transitions. The amplitude and phase varied binary pulses were determined using a genetic algorithm optimization routine. Binary pulses have two possible amplitudes, 0 or 1, and two phases, 0 or pi, for each frequency component of the pulse. Binary pulses are the simplest to shape experimentally and provide a minimum fidelity limit for amplitude and phase shaped pulses. With the current choice of qubit representation and using optimized binary pulses, fidelities of 0.80 and as high as 0.97 were achieved for the controlled-NOT and alternative controlled-NOT quantum gates. This indicates that with a judicious choice of qubits, most of the required control can be obtained with a binary pulse. Limited control was observed for 2 qubit NOT and Hadamard gates due to the need to control multiple excitations. The current choice of qubit representation produces pulses with decreased energies and superior fidelities when compared with rovibrational qubit representations consisting of two-photon transitions. The choice of input pulse energy is important and applying pulses of increased energy does not necessarily lead to a better fidelity.
Al-Khalili, Jim
2003-01-01
In this lively look at quantum science, a physicist takes you on an entertaining and enlightening journey through the basics of subatomic physics. Along the way, he examines the paradox of quantum mechanics--beautifully mathematical in theory but confoundingly unpredictable in the real world. Marvel at the Dual Slit experiment as a tiny atom passes through two separate openings at the same time. Ponder the peculiar communication of quantum particles, which can remain in touch no matter how far apart. Join the genius jewel thief as he carries out a quantum measurement on a diamond without ever touching the object in question. Baffle yourself with the bizzareness of quantum tunneling, the equivalent of traveling partway up a hill, only to disappear then reappear traveling down the opposite side. With its clean, colorful layout and conversational tone, this text will hook you into the conundrum that is quantum mechanics.
Towards optimizing two-qubit operations in three-electron double quantum dots
Frees, Adam; Gamble, John King; Mehl, Sebastian; Friesen, Mark; Coppersmith, S. N.
The successful implementation of single-qubit gates in the quantum dot hybrid qubit motivates our interest in developing a high fidelity two-qubit gate protocol. Recently, extensive work has been done to characterize the theoretical limitations and advantages in performing two-qubit operations at an operation point located in the charge transition region. Additionally, there is evidence to support that single-qubit gate fidelities improve while operating in the so-called ``far-detuned'' region, away from the charge transition. Here we explore the possibility of performing two-qubit gates in this region, considering the challenges and the benefits that may present themselves while implementing such an operational paradigm. This work was supported in part by ARO (W911NF-12-0607) (W911NF-12-R-0012), NSF (PHY-1104660), ONR (N00014-15-1-0029). The authors gratefully acknowledge support from the Sandia National Laboratories Truman Fellowship Program, which is funded by the Laboratory Directed Research and Development (LDRD) Program. Sandia is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the US Department of Energy's National Nuclear Security Administration under Contract No. DE-AC04-94AL85000.
Q-operators, Yangian invariance and the quantum inverse scattering method
Frassek, Rouven
2014-01-01
Inspired by the integrable structures appearing in weakly coupled planar N=4 super Yang-Mills theory, we study Q-operators and Yangian invariants of rational integrable spin chains. We review the quantum inverse scattering method along with the Yang-Baxter equation which is the key relation in this systematic approach to study integrable models. Our main interest concerns rational integrable spin chains and lattice models. We recall the relation among them and how they can be solved using Bethe ansatz methods incorporating so-called Q-functions. In order to remind the reader how the Yangian emerges in this context, an overview of its so-called RTT-realization is provided. The main part is based on the author's original publications. Firstly, we construct Q-operators whose eigenvalues yield the Q-functions for rational homogeneous spin chains. The Q-operators are introduced as traces over certain monodromies of R-operators. Our construction allows us to derive the hierarchy of commuting Q-operators and the fun...
2004-06-01
laser fundamentals , semiconductors, quantum wells and finally ending with a discussion of generic QC lasers. With the a priori knowledge that...quantum cascade laser structure and operation. It begins, in Chapter 2, with a discussion of the atom, continus with laser fundamentals , semiconductors...Aerospace Engineering, Arizona State University. 102 15. Chow, W. W. and Koch, S. W. Semiconductor- Laser Fundamentals . New York: Springer-Verlag
Energy Technology Data Exchange (ETDEWEB)
Aastrup, Johannes; Moeller Grimstrup, Jesper
2016-10-15
We present quantum holonomy theory, which is a non-perturbative theory of quantum gravity coupled to fermionic degrees of freedom. The theory is based on a C*-algebra that involves holonomy-diffeo-morphisms on a 3-dimensional manifold and which encodes the canonical commutation relations of canonical quantum gravity formulated in terms of Ashtekar variables. Employing a Dirac type operator on the configuration space of Ashtekar connections we obtain a semi-classical state and a kinematical Hilbert space via its GNS construction. We use the Dirac type operator, which provides a metric structure over the space of Ashtekar connections, to define a scalar curvature operator, from which we obtain a candidate for a Hamilton operator. We show that the classical Hamilton constraint of general relativity emerges from this in a semi-classical limit and we then compute the operator constraint algebra. Also, we find states in the kinematical Hilbert space on which the expectation value of the Dirac type operator gives the Dirac Hamiltonian in a semi-classical limit and thus provides a connection to fermionic quantum field theory. Finally, an almost-commutative algebra emerges from the holonomy-diffeomorphism algebra in the same limit. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Directory of Open Access Journals (Sweden)
Kutbi Marwan Amin
2016-01-01
Full Text Available The aim of this paper is to introduce the concept of a new nonlinear multi-valued mapping so called weakly (α, ψ, ξ-contractive mapping and prove fixed point results for such mappings in metric spaces. Our results unify, generalize and complement various results from the literature. We give some examples which support our main results while previous results in literature are not applicable. Also, we analyze the existence of fixed points for mappings satisfying a general contractive inequality of integral type. Many fixed point results for multi-valued mappings in metric spaces endowed with an arbitrary binary relation and metric spaces endowed with graph are given here to illustrate the results in this paper.
Microwave-driven coherent operation of a semiconductor quantum dot charge qubit.
Kim, Dohun; Ward, D R; Simmons, C B; Gamble, John King; Blume-Kohout, Robin; Nielsen, Erik; Savage, D E; Lagally, M G; Friesen, Mark; Coppersmith, S N; Eriksson, M A
2015-03-01
An intuitive realization of a qubit is an electron charge at two well-defined positions of a double quantum dot. This qubit is simple and has the potential for high-speed operation because of its strong coupling to electric fields. However, charge noise also couples strongly to this qubit, resulting in rapid dephasing at all but one special operating point called the 'sweet spot'. In previous studies d.c. voltage pulses have been used to manipulate semiconductor charge qubits but did not achieve high-fidelity control, because d.c. gating requires excursions away from the sweet spot. Here, by using resonant a.c. microwave driving we achieve fast (greater than gigahertz) and universal single qubit rotations of a semiconductor charge qubit. The Z-axis rotations of the qubit are well protected at the sweet spot, and we demonstrate the same protection for rotations about arbitrary axes in the X-Y plane of the qubit Bloch sphere. We characterize the qubit operation using two tomographic approaches: standard process tomography and gate set tomography. Both methods consistently yield process fidelities greater than 86% with respect to a universal set of unitary single-qubit operations.
Huang, Ai-Jun; Shi, Jia-Dong; Wang, Dong; Ye, Liu
2017-02-01
In this work, we investigate the dynamic features of the entropic uncertainty for two incompatible measurements under local unital and nonunital channels. Herein, we choose Pauli operators σ _x and σ _z as a pair of observables of interest measuring on particle A, and the uncertainty can be predicted when particle A is entangled with quantum memory B. We explore the dynamics of the uncertainty for the measurement under local unitary (phase-damping) and nonunitary (amplitude-damping) channels, respectively. Remarkably, we derive the entropic uncertainty relation under three different kinds of measurements of Pauli-observable pair under various realistic noisy environments; it has been found that the entropic uncertainty has the same tendency of its evolution during the AD and PD channel when we choose σ _x and σ _y measurement. Besides, we find out that the entropic uncertainty will have an optimal value if one chooses σ _x and σ _z as the measurement incompatibility, comparing with others. Furthermore, in order to reduce the entropic uncertainty in noisy environment, we propose an effective strategy to steer the amount by means of implementing a filtering operation on the particle under the two types of channels, respectively. It turns out that this operation can greatly reduce the entropic uncertainty by modulation of the operation strength. Thus, our investigations might offer an insight into the dynamics and steering of the entropic uncertainty in an open system.
Bovino, Fabio Antonio; Messina, Angelo
2016-10-01
In a very simplistic way, the Command and Control functions can be summarized as the need to provide the decision makers with an exhaustive, real-time, situation picture and the capability to convey their decisions down to the operational forces. This two-ways data and information flow is vital to the execution of current operations and goes far beyond the border of military operations stretching to Police and disaster recovery as well. The availability of off-the shelf technology has enabled hostile elements to endanger the security of the communication networks by violating the traditional security protocols and devices and hacking sensitive databases. In this paper an innovative approach based to implementing Device Independent Quantum Key Distribution system is presented. The use of this technology would prevent security breaches due to a stolen crypto device placed in an end-to-end communication chain. The system, operating with attenuated laser, is practical and provides the increasing of the distance between the legitimate users.
Above room temperature continuous wave operation of a broad-area quantum-cascade laser
Semtsiv, M. P.; Masselink, W. T.
2016-11-01
We describe the design and implementation of a broad-area (w ≈ 30 μm) quantum-cascade laser operating in a continuous wave mode up to heat-sink temperatures beyond +100 °C. The room-temperature emission wavelength is 4.6 μm. The temperature gradient in the active region of such a wide laser stripe is essentially perpendicular to the epitaxial layers and the resulting steady-state active region temperature offset scales approximately with the square of the number of cascades. With only 10 cascades in the active region, the threshold electrical power density in the current quantum-cascade laser in the continuous-wave mode is as low as Vth × Ith = 3.8 V × 0.9 kA/cm2 = 3.4 kW/cm2 at room temperature for 2 mm-long two-side high-reflectivity coated laser stripe. A 4 mm-long one-side high-reflectivity coated laser stripe delivers in continuous-wave mode above 0.6 W at +20 °C and above 1.3 W at -27 °C (cooled with a single-stage Peltier element). A 2 mm-long two-side high-reflectivity coated laser stripe demonstrates continuous-wave lasing up to at least +102 °C (375 K). The thermal conductance, Gth, ranges between 235 W/K cm2 and 140 W/K cm2 for temperatures between -33 °C and +102 °C. This demonstration opens the route for continuous-wave power scaling of quantum-cascade lasers via broad-area laser ridges.
Energy Technology Data Exchange (ETDEWEB)
Moroder, Tobias
2009-07-31
In this thesis we address several different topics within the field of quantum information theory. These results can be classified to either enhance the applicability of certain conceptual ideas to be more suited for an actual experimental situation or to ease the analysis for further investigation of central problems. In detail, the present thesis contains the following achievements: We start our discussion with the question under which conditions a given set of expectation values is compatible with the first and second moments of the spin operators of a generic spin j state. We link this characterization of physical moments to the Bosesymmetric extension problem for a particular two qubit state that is completely determined by the given moments. Via this reformulation we can provide operational sub- and superset approximations in order to identify moments which are assured to be physical and others which are clearly incompatible with quantum mechanics. We show that this operational approximate solution becomes more accurate for increasing total spin numbers j and converges to the exact solution in the limiting case. Another part deals with the theoretical concept of entanglement witnesses. In particular, we concentrate how to improve the detection strength of a linear entanglement witness by nonlinear terms. We analyze two distinguished cases: Either we optimize the iteration method for a given target state or we try to improve the entanglement witness with respect to all entangled states equally. In the remaining parts we discuss different options in order to make already existing ideas more applicable for actual experiments, since most of the famous applications in quantum information theory have only been introduced on a very idealized level and hence are not directly valid for the real experiment. We investigate the theoretical concept of a squash model, that represents an elegant ''evaluation trick'' to directly apply for instance the
Energy Technology Data Exchange (ETDEWEB)
Ferrari, Frank, E-mail: frank.ferrari@ulb.ac.be [Service de Physique Theorique et Mathematique, Universite Libre de Bruxelles and International Solvay Institutes, Campus de la Plaine, CP 231, 1050 Bruxelles (Belgium); Klevtsov, Semyon, E-mail: semyon.klevtsov@ulb.ac.be [Service de Physique Theorique et Mathematique, Universite Libre de Bruxelles and International Solvay Institutes, Campus de la Plaine, CP 231, 1050 Bruxelles (Belgium); ITEP, B. Cheremushkinskaya 25, Moscow 117218 (Russian Federation); Zelditch, Steve, E-mail: zelditch@math.northwestern.edu [Department of Mathematics, Northwestern University, Evanston, IL 60208 (United States)
2013-04-01
The purpose of this article is to propose a new method to define and calculate path integrals over metrics on a Kaehler manifold. The main idea is to use finite dimensional spaces of Bergman metrics, as an approximation to the full space of Kaehler metrics. We use the theory of large deviations to decide when a sequence of probability measures on the spaces of Bergman metrics tends to a limit measure on the space of all Kaehler metrics. Several examples are considered.
Directory of Open Access Journals (Sweden)
Karen de la Vega-Hernández
2016-01-01
Full Text Available It is usually accepted that most 2D-NMR experiments cannot be approached using classical models. Instructors argue that Product Operators (PO or density matrix formalisms are the only alternative to get insights into complex spin evolution for experiments involving Multiple-Quantum Coherence, such as the Heteronuclear Multiple-Quantum Correlation (HMQC technique. Nevertheless, in recent years, several contributions have been published to provide vectorial descriptions for the HMQC taking PO formalism as the starting point. In this work we provide a graphical representation of the HMQC experiment, taking the basic elements of Bloch’s vector model as building blocks. This description bears an intuitive and comfortable understanding of spin evolution during the pulse sequence, for those who are novice in 2D-NMR. Finally, this classical vectorial depiction is tested against the PO formalism and nonclassical vectors, conveying the didactic advantage of shedding light on a single phenomenon from different perspectives. This comparative approach could be useful to introduce PO and nonclassical vectors for advanced upper-division undergraduate and graduate education.
High Operating Temperature Midwave Quantum Dot Barrier Infrared Detector (QD-BIRD)
Ting, David Z.; Soibel, Alexander; Hill, Cory J.; Keo, Sam A.; Mumolo, Jason M.; Gunapala, Sarath D.
2012-01-01
The nBn or XBn barrier infrared detector has the advantage of reduced dark current resulting from suppressed Shockley-Read-Hall (SRH) recombination and surface leakage. High performance detectors and focal plane arrays (FPAs) based on InAsSb absorber lattice matched to GaSb substrate, with a matching AlAsSb unipolar electron barrier, have been demonstrated. The band gap of lattice-matched InAsSb yields a detector cutoff wavelength of approximately 4.2 ??m when operating at 150K. We report results on extending the cutoff wavelength of midwave barrier infrared detectors by incorporating self-assembled InSb quantum dots into the active area of the detector. Using this approach, we were able to extend the detector cutoff wavelength to 6 ?m, allowing the coverage of the full midwave infrared (MWIR) transmission window. The quantum dot barrier infrared detector (QD-BIRD) shows infrared response at temperatures up to 225 K.
High Operating Temperature Midwave Quantum Dot Barrier Infrared Detector (QD-BIRD)
Ting, David Z.; Soibel, Alexander; Hill, Cory J.; Keo, Sam A.; Mumolo, Jason M.; Gunapala, Sarath D.
2012-01-01
The nBn or XBn barrier infrared detector has the advantage of reduced dark current resulting from suppressed Shockley-Read-Hall (SRH) recombination and surface leakage. High performance detectors and focal plane arrays (FPAs) based on InAsSb absorber lattice matched to GaSb substrate, with a matching AlAsSb unipolar electron barrier, have been demonstrated. The band gap of lattice-matched InAsSb yields a detector cutoff wavelength of approximately 4.2 ??m when operating at 150K. We report results on extending the cutoff wavelength of midwave barrier infrared detectors by incorporating self-assembled InSb quantum dots into the active area of the detector. Using this approach, we were able to extend the detector cutoff wavelength to 6 ?m, allowing the coverage of the full midwave infrared (MWIR) transmission window. The quantum dot barrier infrared detector (QD-BIRD) shows infrared response at temperatures up to 225 K.
Greene, Samuel M; Batista, Victor S
2017-09-12
We introduce the "tensor-train split-operator Fourier transform" (TT-SOFT) method for simulations of multidimensional nonadiabatic quantum dynamics. TT-SOFT is essentially the grid-based SOFT method implemented in dynamically adaptive tensor-train representations. In the same spirit of all matrix product states, the tensor-train format enables the representation, propagation, and computation of observables of multidimensional wave functions in terms of the grid-based wavepacket tensor components, bypassing the need of actually computing the wave function in its full-rank tensor product grid space. We demonstrate the accuracy and efficiency of the TT-SOFT method as applied to propagation of 24-dimensional wave packets, describing the S1/S2 interconversion dynamics of pyrazine after UV photoexcitation to the S2 state. Our results show that the TT-SOFT method is a powerful computational approach for simulations of quantum dynamics of polyatomic systems since it avoids the exponential scaling problem of full-rank grid-based representations.
Operation of a quantum dot in the finite-state machine mode: Single-electron dynamic memory
Energy Technology Data Exchange (ETDEWEB)
Klymenko, M. V. [Department of Chemistry, University of Liège, B4000 Liège (Belgium); Klein, M. [The Fritz Haber Center for Molecular Dynamics and the Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904 (Israel); Levine, R. D. [The Fritz Haber Center for Molecular Dynamics and the Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904 (Israel); Crump Institute for Molecular Imaging and Department of Molecular and Medical Pharmacology, David Geffen School of Medicine and Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095 (United States); Remacle, F., E-mail: fremacle@ulg.ac.be [Department of Chemistry, University of Liège, B4000 Liège (Belgium); The Fritz Haber Center for Molecular Dynamics and the Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904 (Israel)
2016-07-14
A single electron dynamic memory is designed based on the non-equilibrium dynamics of charge states in electrostatically defined metallic quantum dots. Using the orthodox theory for computing the transfer rates and a master equation, we model the dynamical response of devices consisting of a charge sensor coupled to either a single and or a double quantum dot subjected to a pulsed gate voltage. We show that transition rates between charge states in metallic quantum dots are characterized by an asymmetry that can be controlled by the gate voltage. This effect is more pronounced when the switching between charge states corresponds to a Markovian process involving electron transport through a chain of several quantum dots. By simulating the dynamics of electron transport we demonstrate that the quantum box operates as a finite-state machine that can be addressed by choosing suitable shapes and switching rates of the gate pulses. We further show that writing times in the ns range and retention memory times six orders of magnitude longer, in the ms range, can be achieved on the double quantum dot system using experimentally feasible parameters, thereby demonstrating that the device can operate as a dynamic single electron memory.
Operation of a quantum dot in the finite-state machine mode: Single-electron dynamic memory
Klymenko, M. V.; Klein, M.; Levine, R. D.; Remacle, F.
2016-07-01
A single electron dynamic memory is designed based on the non-equilibrium dynamics of charge states in electrostatically defined metallic quantum dots. Using the orthodox theory for computing the transfer rates and a master equation, we model the dynamical response of devices consisting of a charge sensor coupled to either a single and or a double quantum dot subjected to a pulsed gate voltage. We show that transition rates between charge states in metallic quantum dots are characterized by an asymmetry that can be controlled by the gate voltage. This effect is more pronounced when the switching between charge states corresponds to a Markovian process involving electron transport through a chain of several quantum dots. By simulating the dynamics of electron transport we demonstrate that the quantum box operates as a finite-state machine that can be addressed by choosing suitable shapes and switching rates of the gate pulses. We further show that writing times in the ns range and retention memory times six orders of magnitude longer, in the ms range, can be achieved on the double quantum dot system using experimentally feasible parameters, thereby demonstrating that the device can operate as a dynamic single electron memory.
Benítez Rodríguez, E.; Arévalo Aguilar, L. M.; Piceno Martínez, E.
2017-03-01
To the quantum mechanics specialists community it is a well-known fact that the famous original Stern–Gerlach experiment (SGE) produces entanglement between the external degrees of freedom (position) and the internal degree of freedom (spin) of silver atoms. Despite this fact, almost all textbooks on quantum mechanics explain this experiment using a semiclassical approach, where the external degrees of freedom are considered classical variables, the internal degree is treated as a quantum variable, and Newton's second law is used to describe the dynamics. In the literature there are some works that analyze this experiment in its full quantum mechanical form. However, astonishingly, to the best of our knowledge the original experiment, where the initial states of the spin degree of freedom are randomly oriented coming from the oven, has not been analyzed yet in the available textbooks using the Schrödinger equation (to the best of our knowledge there is only one paper that treats this case: Hsu et al (2011 Phys. Rev. A 83 012109)). Therefore, in this contribution we use the time-evolution operator to give a full quantum mechanics analysis of the SGE when the initial state of the internal degree of freedom is completely random, i.e. when it is a statistical mixture. Additionally, as the SGE and the development of quantum mechanics are heavily intermingled, we analyze some features and drawbacks in the current teaching of quantum mechanics. We focus on textbooks that use the SGE as a starting point, based on the fact that most physicist do not use results from physics education research, and comment on traditional pedagogical attitudes in the physics community.
Quantum limited noise figure operation of high gain erbium doped fiber amplifiers
DEFF Research Database (Denmark)
Lumholt, Ole; Povlsen, Jørn Hedegaard; Schüsler, Kim;
1993-01-01
powers below -5 dBm, and an improvement of 2.0 dB with a simultaneous gain increase of 4.1 dB is measured relative to a gain-optimized fiber. The optimum isolator location is evaluated for different pump and signal wavelengths in both an Al/Er-doped and a Ge/Er-doped fiber, for pump and signal power......Performance improvements obtained by using an isolator as an amplified-spontaneous-emission-suppressing component within erbium-doped fibers are evaluated. Simultaneous high-gain and near-quantum-limited noise figures can be obtained by such a scheme. The noise figure improves for input signal...... variations and different pump configurations. In all cases the optimum isolator position lies within 10-37% of the total fiber length for small signal operation...
Das, Ashok; Kalauni, Pushpa
2016-06-01
We develop an operator description, much like thermofield dynamics, for quantum field theories on a real time path with an arbitrary parameter σ (0 ≤σ ≤β ) . We point out new features which arise when σ ≠β/2 in that the Hilbert space develops a natural, modified inner product different from the standard Dirac inner product. We construct the Bogoliubov transformation which connects the doubled vacuum state at zero temperature to the thermal vacuum in this case. We obtain the thermal Green's function (propagator) for the real massive Klein-Gordon theory as an expectation value in this thermal vacuum (with a modified inner product). The factorization of the thermal Green's function follows from this analysis. We also discuss, in the main text as well as in two appendices, various other interesting features which arise in such a description.
How to Derive the Hilbert-Space Formulation of Quantum Mechanics From Purely Operational Axioms
D'Ariano, G M
2006-01-01
In the present paper I show how it is possible to derive the Hilbert space formulation of Quantum Mechanics from a comprehensive definition of "physical experiment" and assuming "experimental accessibility and simplicity" as specified by five simple Postulates. This accomplishes the program presented in form of conjectures in the previous paper quant-ph/0506034. Pivotal roles are played by the "local observability principle", which reconciles the holism of nonlocality with the reductionism of local observation, and by the postulated existence of "informationally complete observables" and of a "symmetric faithful state". This last notion allows one to introduce an operational definition for the real version of the "adjoint"--i. e. the transposition--from which one can derive a real Hilbert-space structure via either the Mackey-Kakutani or the Gelfand-Naimark-Segal constructions. Here I analyze in detail only the Gelfand-Naimark-Segal construction, which leads to a real Hilbert space structure analogous to that...
Velocity operator and velocity field for spinning particles in (non-relativistic) quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Recami, E. [Bergamo Univ. (Italy). Facolta` di Ingegneria]|[INFN, Milan (Italy)]|[Campinas State Univ., SP (Brazil). Dept. of Applied Math.; Salesi, G. [Catania Univ. (Italy). Dip. di Fisica
1995-06-01
Starting from the formal expressions of the hydrodynamical (or local) quantities employed in the applications of Clifford Algebras to quantum mechanics, the paper introduces - in terms of the ordinary tensorial framework - a new definition for the field of a generic quantity. By translating from Clifford into tensor algebra, a new (non-relativistic) velocity operator for a spin 1/2 particle is also proposed. This operator is the sum of the ordinary part p/m describing the mean motion (the motion of the center-of-mass), and of a second part associated with the so-called Zitterbewegung, which is the spin internal motion observed in the center-of- mass frame. This spin component of the velocity operator is non-zero not only in the Pauli theoretical framework, i.e. in presence of external magnetic fields and spin precession, but also in the Schroedinger case, when the wave-function is a spin eigenstate. In the latter case, one gets a decomposition of the velocity field for the Madelueng fluid into two distinct parts: which the constitutes the non-relativistic analogue of the Gordon decomposition for the Dirac current.
Quantum theory with an energy operator defined as a quartic form of the momentum
Bezák, Viktor
2016-09-01
Quantum theory of the non-harmonic oscillator defined by the energy operator proposed by Yurke and Buks (2006) is presented. Although these authors considered a specific problem related to a model of transmission lines in a Kerr medium, our ambition is not to discuss the physical substantiation of their model. Instead, we consider the problem from an abstract, logically deductive, viewpoint. Using the Yurke-Buks energy operator, we focus attention on the imaginary-time propagator. We derive it as a functional of the Mehler kernel and, alternatively, as an exact series involving Hermite polynomials. For a statistical ensemble of identical oscillators defined by the Yurke-Buks energy operator, we calculate the partition function, average energy, free energy and entropy. Using the diagonal element of the canonical density matrix of this ensemble in the coordinate representation, we define a probability density, which appears to be a deformed Gaussian distribution. A peculiarity of this probability density is that it may reveal, when plotted as a function of the position variable, a shape with two peaks located symmetrically with respect to the central point.
Horizon Quantum Mechanics: a hitchhiker's guide to quantum black holes
Casadio, R; Micu, O
2015-01-01
It is congruous with the quantum nature of the world to view the space-time geometry as an emergent structure that shows classical features only at some observational level. One can thus conceive the space-time manifold as a purely theoretical arena, where quantum states are defined, with the additional freedom of changing coordinates like any other symmetry. Observables, including positions and distances, should then be described by suitable operators acting on such quantum states. In principle, the top-down (canonical) quantisation of Einstein-Hilbert gravity falls right into this picture, but is notoriously very involved. The complication stems from allowing all the classical canonical variables that appear in the (presumably) fundamental action to become quantum observables acting on the "superspace" of all metrics, regardless of whether they play any role in the description of a specific physical system. On can instead revisit the more humble "minisuperspace" approach and choose the gravitational observa...
Amaku, Marcos; Coutinho, Francisco A. B.; Masafumi Toyama, F.
2017-09-01
The usual definition of the time evolution operator e-i H t /ℏ=∑n=0∞1/n ! (-i/ℏHt ) n , where H is the Hamiltonian of the system, as given in almost every book on quantum mechanics, causes problems in some situations. The operators that appear in quantum mechanics are either bounded or unbounded. Unbounded operators are not defined for all the vectors (wave functions) of the Hilbert space of the system; when applied to some states, they give a non-normalizable state. Therefore, if H is an unbounded operator, the definition in terms of the power series expansion does not make sense because it may diverge or result in a non-normalizable wave function. In this article, we explain why this is so and suggest, as an alternative, another definition used by mathematicians.
Projectively related metrics, Weyl nullity, and metric projectively invariant equations
Gover, A Rod
2015-01-01
A metric projective structure is a manifold equipped with the unparametrised geodesics of some pseudo-Riemannian metric. We make acomprehensive treatment of such structures in the case that there is a projective Weyl curvature nullity condition. The analysis is simplified by a fundamental and canonical 2-tensor invariant that we discover. It leads to a new canonical tractor connection for these geometries which is defined on a rank $(n+1)$-bundle. We show this connection is linked to the metrisability equations that govern the existence of metrics compatible with the structure. The fundamental 2-tensor also leads to a new class of invariant linear differential operators that are canonically associated to these geometries; included is a third equation studied by Gallot et al. We apply the results to study the metrisability equation, in the nullity setting described. We obtain strong local and global results on the nature of solutions and also on the nature of the geometries admitting such solutions, obtaining ...
Goudarzi, H.; Dousti, M. J.; Shafaei, A.; Pedram, M.
2014-05-01
This paper presents a physical mapping tool for quantum circuits, which generates the optimal universal logic block (ULB) that can, on average, perform any logical fault-tolerant (FT) quantum operations with the minimum latency. The operation scheduling, placement, and qubit routing problems tackled by the quantum physical mapper are highly dependent on one another. More precisely, the scheduling solution affects the quality of the achievable placement solution due to resource pressures that may be created as a result of operation scheduling, whereas the operation placement and qubit routing solutions influence the scheduling solution due to resulting distances between predecessor and current operations, which in turn determines routing latencies. The proposed flow for the quantum physical mapper captures these dependencies by applying (1) a loose scheduling step, which transforms an initial quantum data flow graph into one that explicitly captures the no-cloning theorem of the quantum computing and then performs instruction scheduling based on a modified force-directed scheduling approach to minimize the resource contention and quantum circuit latency, (2) a placement step, which uses timing-driven instruction placement to minimize the approximate routing latencies while making iterative calls to the aforesaid force-directed scheduler to correct scheduling levels of quantum operations as needed, and (3) a routing step that finds dynamic values of routing latencies for the qubits. In addition to the quantum physical mapper, an approach is presented to determine the single best ULB size for a target quantum circuit by examining the latency of different FT quantum operations mapped onto different ULB sizes and using information about the occurrence frequency of operations on critical paths of the target quantum algorithm to weigh these latencies. Experimental results show an average latency reduction of about 40 % compared to previous work.
Thermodynamic Metrics and Optimal Paths
Energy Technology Data Exchange (ETDEWEB)
Sivak, David; Crooks, Gavin
2012-05-08
A fundamental problem in modern thermodynamics is how a molecular-scale machine performs useful work, while operating away from thermal equilibrium without excessive dissipation. To this end, we derive a friction tensor that induces a Riemannian manifold on the space of thermodynamic states. Within the linear-response regime, this metric structure controls the dissipation of finite-time transformations, and bestows optimal protocols with many useful properties. We discuss the connection to the existing thermodynamic length formalism, and demonstrate the utility of this metric by solving for optimal control parameter protocols in a simple nonequilibrium model.
Cibella, S.; Beck, M.; Carelli, P.; Castellano, M. G.; Chiarello, F.; Faist, J.; Leoni, R.; Ortolani, M.; Sabbatini, L.; Scalari, G.; Torrioli, G.; Turcinkova, D.
2012-06-01
We make use of a niobium film to produce a micrometric vacuum-bridge superconducting bolometer responding to THz frequency. The bolometer works anywhere in the temperature range 2-7 K, which can be easily reached in helium bath cryostats or closed-cycle cryocoolers. In this work the bolometer is mounted on a pulse tube refrigerator and operated to measure the equivalent noise power (NEP) and the response to fast (μs) terahertz pulses. The NEP above 100 Hz equals that measured in a liquid helium cryostat showing that potential drawbacks related to the use of a pulse tube refrigerator (like mechanical and thermal oscillations, electromagnetic interference, noise) are irrelevant. At low frequency, instead, the pulse tube expansion-compression cycles originate lines at 1 Hz and harmonics in the noise spectrum. The bolometer was illuminated with THz single pulses coming either from a Quantum Cascade Laser operating at liquid nitrogen temperature or from a frequency-multiplied electronic oscillator. The response of the bolometer to the single pulses show that the device can track signals with a rise time as fast as about 450 ns.
,
2011-01-01
Around the globe several observatories are seeking the first direct detection of gravitational waves (GWs). These waves are predicted by Einstein's General Theory of Relativity [Einstein, A., Annalen der Physik 49, 769-822 (1916)] and are generated e.g. by black-hole binary systems [Sathyaprakash, B. S. and Schutz, B. F., Living Rev. Relativity 12, 2 (2009)]. Current GW detectors are Michelson-type kilometer-scale laser interferometers measuring the distance changes between in vacuum suspended mirrors. The sensitivity of these detectors at frequencies above several hundred hertz is limited by the vacuum (zero-point) fluctuations of the electromagnetic field. A quantum technology - the injection of squeezed light [Caves, C. M., Phys. Rev. D 23, 1693-1708 (1981)] - offers a solution to this problem. Here we demonstrate the squeezed-light enhancement of GEO600, which will be the GW observatory operated by the LIGO Scientific Collaboration in its search for GWs for the next 3-4 years. GEO600 now operates with its...
Quantum-mechanical tunneling differential operators, zeta-functions and determinants
Casahorrán, J
2002-01-01
We consider in detail the quantum-mechanical problem associated with the motion of a one-dimensional particle under the action of the double-well potential. Our main tool will be the euclidean (imaginary time) version of the path-integral method. Once we perform the Wick rotation, the euclidean equation of motion is the same as the usual one for the point particle in real time, except that the potential at issue is turned upside down. In doing so, our double-well potential becomes a two-humped potential. As required by the semiclassical approximation we may study the quadratic fluctuations over the instanton which represents in this context the localised finite-action solutions of the euclidean equation of motion. The determinants of the quadratic differential operators are evaluated by means of the zeta-function method. We write in closed form the eigenfunctions as well as the energy eigenvalues corresponding to such operators by using the shape-invariance symmetry. The effect of the multi-instantons configu...
THE QUALITY METRICS OF INFORMATION SYSTEMS
Directory of Open Access Journals (Sweden)
Zora Arsovski
2008-06-01
Full Text Available Information system is a special kind of products which is depend upon great number variables related to nature, conditions during implementation and organizational clime and culture. Because that quality metrics of information system (QMIS has to reflect all previous aspects of information systems. In this paper are presented basic elements of QMIS, characteristics of implementation and operation metrics for IS, team - management quality metrics for IS and organizational aspects of quality metrics. In second part of this paper are presented results of study of QMIS in area of MIS (Management IS.
Distance between Quantum States and Gauge-Gravity Duality
Miyaji, Masamichi; Numasawa, Tokiro; Shiba, Noburo; Takayanagi, Tadashi; Watanabe, Kento
2015-12-01
We study a quantum information metric (or fidelity susceptibility) in conformal field theories with respect to a small perturbation by a primary operator. We argue that its gravity dual is approximately given by a volume of maximal time slice in an anti-de Sitter spacetime when the perturbation is exactly marginal. We confirm our claim in several examples.
Quantum cascade lasers operating from 1.4 to 4 THz
Institute of Scientific and Technical Information of China (English)
Sushil Kumar
2011-01-01
The development of teranertz (THz) quantum cascade lasers (QCLs) has progressed considerably since their advent almost a decade ago. THz QCLs operating in a frequency range from 1.4 to 4 THz with electron-phonon scattering mediated depopulation schemes are described. Several different types of GaAs/AlGaAs superlattice designs are reviewed. Some of the best temperature performances are obtained by the so-called resonant-phonon designs that are described. Operation above a temperature of 160 K has been obtained across the spectrum for THz QCLs operating at v > 1.8 THz. The maximum operating temperature of previously reported THz QCLs has empirically been limited to a value of ~ hω/kB- A new design scheme for THz QCLs with scattering-assisted injection is shown to surpass this empirical temperature barrier, and is promising to improve the maximum operating temperatures of THz QCLs even further.%1.IntroductionHigh-power sources of terahertz (THz) radiation are required for a multitude of applications in sensing,imaging,and spectroscopy in fields as diverse as astronomy,medicine,security,pharmaceuticals and so-forth.THz science and technology has advanced significantly in the recent years[1,2] especially toward the realization of novel THz radiation sources.In comparison to narrow-band sources such as lasers,broadband sources of terahertz radiation are more widely available;however,such sources are inherently low power (average power is of the order of few micro-Watts).They are useful nevertheless because of room temperature operation and for their ability to be detected coherently.Techniques such as generation of THz bandwidth time-domain pulses in high resistivity semiconductors[3],non-linear generation by electrooptical-rectification in crystals such as ZnTe[4],or nonlinear generation by optical parametric conversion in materials such as LiNbO3[5] or by difference-frequency generation in semiconductors[6],have been used for various raster-scanned imaging and
Daza, Maicol A Ochoa
2011-01-01
We introduce and develop the theory of metric sheaves. A metric sheaf $\\A$ is defined on a topological space $X$ such that each fiber is a metric model. We describe the construction of the generic model as the quotient space of the sheaf through an appropriate filter. Semantics in this model is completely controlled and understood by the forcing rules in the sheaf.
High-power, surface-emitting quantum cascade laser operating in a symmetric grating mode
Energy Technology Data Exchange (ETDEWEB)
Boyle, C.; Sigler, C.; Kirch, J. D.; Botez, D.; Mawst, L. J., E-mail: mawst@engr.wisc.edu [Department of Electrical and Computer Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706 (United States); Lindberg, D. F.; Earles, T. [Intraband, LLC, Madison, Wisconsin 53726 (United States)
2016-03-21
Grating-coupled surface-emitting (GCSE) lasers generally operate with a double-lobed far-field beam pattern along the cavity-length direction, which is a result of lasing being favored in the antisymmetric grating mode. We experimentally demonstrate a GCSE quantum-cascade laser design allowing high-power, nearly single-lobed surface emission parallel to the longitudinal cavity. A 2nd-order Au-semiconductor distributed-feedback (DFB)/distributed-Bragg-reflector (DBR) grating is used for feedback and out-coupling. The DFB and DBR grating regions are 2.55 mm- and 1.28 mm-long, respectively, for a total grating length of 5.1 mm. The lasers are designed to operate in a symmetric (longitudinal) grating mode by causing resonant coupling of the guided optical mode to the antisymmetric surface-plasmon modes of the 2nd-order metal/semiconductor grating. Then, the antisymmetric modes are strongly absorbed by the metal in the grating, causing the symmetric mode to be favored to lase, which, in turn, produces a single-lobed beam over a range of grating duty-cycle values of 36%–41%. Simulations indicate that the symmetric mode is always favored to lase, independent of the random phase of reflections from the device's cleaved ends. Peak pulsed output powers of ∼0.4 W were measured with nearly single-lobe beam-pattern (in the longitudinal direction), single-spatial-mode operation near 4.75 μm wavelength. Far-field measurements confirm a diffraction-limited beam pattern, in agreement with simulations, for a source-to-detector separation of 2 m.
Aastrup, Johannes
2015-01-01
We present quantum holonomy theory, which is a non-perturbative theory of quantum gravity coupled to fermionic degrees of freedom. The theory is based on a C*-algebra that involves holonomy-diffeomorphisms on a 3-dimensional manifold and which encodes the canonical commutation relations of canonical quantum gravity formulated in terms of Ashtekar variables. Employing a Dirac type operator on the configuration space of Ashtekar connections we obtain a semi-classical state and a kinematical Hilbert space via its GNS construction. We use the Dirac type operator, which provides a metric structure over the space of Ashtekar connections, to define a scalar curvature operator, from which we obtain a candidate for a Hamilton operator. We show that the classical Hamilton constraint of general relativity emerges from this in a semi-classical limit and we then compute the operator constraint algebra. Also, we find states in the kinematical Hilbert space on which the expectation value of the Dirac type operator gives the...
Quantum Space-Time and Reference Frames in Gravity and Flat Space-Time
Mayburov, S
2000-01-01
The quantum space-time model which accounts material Reference Frames (RF) quantum effects considered for flat space-time and ADM canonical gravity. As was shown by Aharonov for RF - free material object its c.m. nonrelativistic motion in vacuum described by Schrodinger wave packet evolution which modify space coordinate operator of test particle in this RF and changes its Heisenberg uncertainty relations. In the relativistic case we show that Lorentz transformations between two RFs include the quantum corrections for RFs momentum uncertainty and in general can be formulated as the quantum space-time transformations. As the result for moving RF its Lorentz time boost acquires quantum fluctuations which calculated solving relativistic Heisenberg equations for the quantum clocks models. It permits to calculate RF proper time for the arbitrary RF quantum motion including quantum gravity metrics fluctuations. Space-time structure of canonical Quantum Gravity and its observables evolution for RF proper time discus...
Warm inflation and scalar perturbations of the metric
Bellini, M
2001-01-01
A second-order expansion for the quantum fluctuations of the matter field was considered in the framework of the warm inflation scenario. The friction and Hubble parameters were expended by means of a semiclassical approach. The fluctuations of the Hubble parameter generates fluctuations of the metric. These metric fluctuations produce an effective term of curvature. The power spectrum for the metric fluctuations can be calculated on the infrared sector.
Ermilov, A. S.; Zobov, V. E.
2007-12-01
To experimentally realize quantum computations on d-level basic elements (qudits) at d > 2, it is necessary to develop schemes for the technical realization of elementary logical operators. We have found sequences of selective rotation operators that represent the operators of the quantum Fourier transform (Walsh-Hadamard matrices) for d = 3-10. For the prime numbers 3, 5, and 7, the well-known method of linear algebra is applied, whereas, for the factorable numbers 6, 9, and 10, the representation of virtual spins is used (which we previously applied for d = 4, 8). Selective rotations can be realized, for example, by means of pulses of an RF magnetic field for systems of quadrupole nuclei or laser pulses for atoms and ions in traps.
2003-01-01
Japanese Journal of Applied Physics , 40, part 1, (no. 3B), 1857-1895 2001 P. P. Paskov, P. O. Holtz, B. Monemar, J. M...Garcia, W. V. Schoenfeld, P. M. Petroff “Excited state magnetoluminescence of InAs/GaAs self-assembled quantum dots” Japanese Journal of Applied Physics , 40...heterostructures grown by plasma-assisted molecular beam epitaxy” Japanese Journal of Applied Physics , 40, part 1, (no. 11),
Francis, C
2006-01-01
A Relational Quantum Theory Incorporating Gravity developed the concept of quantum covariance and argued that this is the correct expression of the fundamental physical principle that the behaviour of matter is everywhere the same in the quantum domain, as well as being the required condition for the unification of general relativity with quantum mechanics for non-interacting particles. This paper considers the interactions of elementary particles. Quantum covariance describes families of finite dimensional Hilbert spaces with an inbuilt cut-off in energy-momentum and using flat space metric (quantum coordinates) between initial and final states. It is shown by direct construction that it is possible to construct a quantum field theory of operators on members of these families, obeying locality, suitable for a description of particle interactions, and leading to a general formulation of particle theoretic field theory incorporating qed. The construction is consistent and effectively identical in the continuum...
Ingoing Eddington-Finkelstein Metric of an Evaporating Black Hole
Abdolrahimi, Shohreh; Tzounis, Christos
2016-01-01
We present an approximate time-dependent metric in ingoing Eddington-Finkelstein coordinates for an evaporating black hole as a first-order perturbation of the Schwarzschild metric, using the linearized back reaction from a realistic approximation to the stress-energy tensor for the Hawking radiation in the Unruh quantum state.
On the Relationship between the Moyal Algebra and the Quantum Operator Algebra of von Neumann
Hiley, B. J.
2012-01-01
The primary motivation for Moyal's approach to quantum mechanics was to develop a phase space formalism for quantum phenomena by generalising the techniques of classical probability theory. To this end, Moyal introduced a quantum version of the characteristic function which immediately provides a probability distribution. The approach is sometimes perceived negatively merely as an attempt to return to classical notions, but the mathematics Moyal develops is simply a re-expression of what is a...
Chang, Mou-Hsiung
2015-01-01
The classical probability theory initiated by Kolmogorov and its quantum counterpart, pioneered by von Neumann, were created at about the same time in the 1930s, but development of the quantum theory has trailed far behind. Although highly appealing, the quantum theory has a steep learning curve, requiring tools from both probability and analysis and a facility for combining the two viewpoints. This book is a systematic, self-contained account of the core of quantum probability and quantum stochastic processes for graduate students and researchers. The only assumed background is knowledge of the basic theory of Hilbert spaces, bounded linear operators, and classical Markov processes. From there, the book introduces additional tools from analysis, and then builds the quantum probability framework needed to support applications to quantum control and quantum information and communication. These include quantum noise, quantum stochastic calculus, stochastic quantum differential equations, quantum Markov semigrou...
Non-trivial topologies in quantum gravity
Hawking, S. W.
1984-09-01
This paper examines recent objections to the proposal that topologically non-trivial metrics could cause pure quantum states to decay into mixed states. It is shown that the Kaluza-Klein examples proposed by Gross in which this did not happen are special cases and that there are other Kaluza-Klein metrics in which it does. The objections of Banks, Peskin and Susskind about energy and momentum conservation arise because they assume that the evolution of density operator can be localized to a few Planck lengths. However, it is shown that energy and momentum are conserved only because of the asymptotic field equations and that this requires a large asymptotic region.
Institute of Scientific and Technical Information of China (English)
ZHOU Nan-run; GONG Li-hua; LIU Ye
2006-01-01
In this letter a cascade quantum teleportation scheme is proposed. The proposed scheme needs less local quantum operations than those of quantum multi-teleportation. A quantum teleportation scheme based on entanglement swapping is presented and compared with the cascade quantum teleportation scheme. Those two schemes can effectively teleport quantum information and extend the distance of quantum communication.
Ma, Shao-Qiang; Zhu, Han-Jie; Zhang, Guo-Feng
2017-04-01
The effects of different quantum feedback types on the estimation precision of the detection efficiency are studied. It is found that the precision can be more effective enhanced by a certain feedback type through comparing these feedbacks and the precision has a positive relation with detection efficiency for the optimal feedback when the system reach the state of dynamic balance. In addition, the bigger the proportion of |1> is the higher the precision is and we will not obtain any information about the parameter to be estimated if |0> is chosen as initial state for the feedback type λσz.
The Heteronuclear Single-Quantum Correlation (HSQC) Experiment: Vectors versus Product Operators
de la Vega-Herna´ndez, Karen; Antuch, Manuel
2015-01-01
A vectorial representation of the full sequence of events occurring during the 2D-NMR heteronuclear single-quantum correlation (HSQC) experiment is presented. The proposed vectorial representation conveys an understanding of the magnetization evolution during the HSQC pulse sequence for those who have little or no quantum mechanical background.…
2017-03-06
in nitrogen-vacancy diamond, high-dimensional quantum key distribution, and photonic integrated circuits for quantum communication and computation ...Raytheon BBN Technologies; Dr. Saikat Guha Contractor Address: 10 Moulton Street, Cambridge, MA 02138 Title of the Project: COmmunications and...Contract Data Requirements List In accordance with the reference requirement of the subject contract, Raytheon BBN Technologies (BBN) hereby submits
Dynamic Quantum Allocation and Swap-Time Variability in Time-Sharing Operating Systems.
Bhat, U. Narayan; Nance, Richard E.
The effects of dynamic quantum allocation and swap-time variability on central processing unit (CPU) behavior are investigated using a model that allows both quantum length and swap-time to be state-dependent random variables. Effective CPU utilization is defined to be the proportion of a CPU busy period that is devoted to program processing, i.e.…
The Quantum-Like Brain Operating on Subcognitive and Cognitive Time Scales
Khrennikov, Andrei
2007-01-01
We propose a {\\it quantum-like} (QL) model of the functioning of the brain. It should be sharply distinguished from the reductionist {\\it quantum} model. By the latter cognition is created by {\\it physical quantum processes} in the brain. The crucial point of our modelling is that discovery of the mathematical formalism of quantum mechanics (QM) was in fact discovery of a very general formalism describing {\\it consistent processing of incomplete information} about contexts (physical, mental, economic, social). The brain is an advanced device which developed the ability to create a QL representation of contexts. Therefore its functioning can also be described by the mathematical formalism of QM. The possibility of such a description has nothing to do with composing of the brain of quantum systems (photons, electrons, protons,...). Moreover, we shall propose a model in that the QL representation is based on conventional neurophysiological model of the functioning of the brain. The brain uses the QL rule (given ...
Metric diffusion along foliations
Walczak, Szymon M
2017-01-01
Up-to-date research in metric diffusion along compact foliations is presented in this book. Beginning with fundamentals from the optimal transportation theory and the theory of foliations; this book moves on to cover Wasserstein distance, Kantorovich Duality Theorem, and the metrization of the weak topology by the Wasserstein distance. Metric diffusion is defined, the topology of the metric space is studied and the limits of diffused metrics along compact foliations are discussed. Essentials on foliations, holonomy, heat diffusion, and compact foliations are detailed and vital technical lemmas are proved to aide understanding. Graduate students and researchers in geometry, topology and dynamics of foliations and laminations will find this supplement useful as it presents facts about the metric diffusion along non-compact foliation and provides a full description of the limit for metrics diffused along foliation with at least one compact leaf on the two dimensions.
Enterprise Sustainment Metrics
The Air Force sustainment enterprise does not have metrics that . . . adequately measure key sustainment parameters, according to the 2011 National...standardized and do not contribute to the overall assessment of the sustainment enterprise . This paper explores the development of a single metric...is not feasible. To answer the question does the sustainment enterprise provide cost-effective readiness for a weapon system, a suite of metrics is
-Metric Space: A Generalization
Directory of Open Access Journals (Sweden)
Farshid Khojasteh
2013-01-01
Full Text Available We introduce the notion of -metric as a generalization of a metric by replacing the triangle inequality with a more generalized inequality. We investigate the topology of the spaces induced by a -metric and present some essential properties of it. Further, we give characterization of well-known fixed point theorems, such as the Banach and Caristi types in the context of such spaces.
Prognostic Performance Metrics
National Aeronautics and Space Administration — This chapter presents several performance metrics for offline evaluation of prognostics algorithms. A brief overview of different methods employed for performance...
Topics in Metric Approximation
Leeb, William Edward
This thesis develops effective approximations of certain metrics that occur frequently in pure and applied mathematics. We show that distances that often arise in applications, such as the Earth Mover's Distance between two probability measures, can be approximated by easily computed formulas for a wide variety of ground distances. We develop simple and easily computed characterizations both of norms measuring a function's regularity -- such as the Lipschitz norm -- and of their duals. We are particularly concerned with the tensor product of metric spaces, where the natural notion of regularity is not the Lipschitz condition but the mixed Lipschitz condition. A theme that runs throughout this thesis is that snowflake metrics (metrics raised to a power less than 1) are often better-behaved than ordinary metrics. For example, we show that snowflake metrics on finite spaces can be approximated by the average of tree metrics with a distortion bounded by intrinsic geometric characteristics of the space and not the number of points. Many of the metrics for which we characterize the Lipschitz space and its dual are snowflake metrics. We also present applications of the characterization of certain regularity norms to the problem of recovering a matrix that has been corrupted by noise. We are able to achieve an optimal rate of recovery for certain families of matrices by exploiting the relationship between mixed-variable regularity conditions and the decay of a function's coefficients in a certain orthonormal basis.
Directory of Open Access Journals (Sweden)
Nakasho Kazuhisa
2016-09-01
Full Text Available In this article, we mainly formalize in Mizar [2] the equivalence among a few compactness definitions of metric spaces, norm spaces, and the real line. In the first section, we formalized general topological properties of metric spaces. We discussed openness and closedness of subsets in metric spaces in terms of convergence of element sequences. In the second section, we firstly formalize the definition of sequentially compact, and then discuss the equivalence of compactness, countable compactness, sequential compactness, and totally boundedness with completeness in metric spaces.
Operation of a superconducting nanowire quantum interference device with mesoscopic leads
Pekker, David; Bezryadin, Alexey; Hopkins, David S.; Goldbart, Paul M.
2005-09-01
A theory describing the operation of a superconducting nanowire quantum interference device (NQUID) is presented. The device consists of a pair of thin-film superconducting leads connected by a pair of topologically parallel ultranarrow superconducting wires. It exhibits intrinsic electrical resistance, due to thermally activated dissipative fluctuations of the superconducting order parameter. Attention is given to the dependence of this resistance on the strength of an externally applied magnetic field aligned perpendicular to the leads, for lead dimensions such that there is essentially complete and uniform penetration of the leads by the magnetic field. This regime, in which at least one of the lead dimensions—length or width—lies between the superconducting coherence and penetration lengths, is referred to as the mesoscopic regime. The magnetic field causes a pronounced oscillation of the device resistance, with a period not dominated by the Aharonov-Bohm effect through the area enclosed by the wires and the film edges but, rather, in terms of the geometry of the leads, in contrast to the well-known Little-Parks resistance of thin-walled superconducting cylinders. A detailed theory, encompassing this phenomenology quantitatively, is developed through extensions, to the setting of parallel superconducting wires, of the Ivanchenko-Zil’berman-Ambegaokar-Halperin theory of intrinsic resistive fluctuations in a current-biased Josephson junction and the Langer-Ambegaokar-McCumber-Halperin theory of intrinsic resistive fluctuations in a superconducting wire. In particular, it is demonstrated that via the resistance of the NQUID, the wires act as a probe of spatial variations in the superconducting order parameter along the perimeter of each lead: in essence, a superconducting phase gradiometer.
On almost surely bounded semigroups of random linear operators
Energy Technology Data Exchange (ETDEWEB)
Zhang, Xia; Liu, Ming [Department of Mathematics, School of Science, Tianjin Polytechnic University, Tianjin 300387 (China)
2013-05-15
Menger proposed transferring the probabilistic notions of quantum mechanics to the underlying geometry. Following Menger's idea, the notion of random metric spaces is a random generalization of that of metric spaces and also plays an important role in the study of random operator equations. The main difficulty of this article is to work out a skill to give a property peculiar to a special semigroup of random operators, which is not involved in the classical case. Subsequently, some random operators equations are studied, in particular, we discuss the Schroedinger-type random equation, which considerably generalizes the corresponding result in the sense of Skorohod.
Sudha,; Rajagopal, A K
2011-01-01
The limitation on the shareability of quantum entanglement over several parties, the so-called monogamy of entanglement, is an issue that has caught considerable attention of quantum informa- tion community over the last decade. A natural question of interest in this connection is whether monogamy of correlations is true for correlations other than entanglement. This issue is examined here by choosing quantum deficit, proposed by Rajagopal and Rendell, an operational measure of correlations. In addition to establishing the polygamous nature of the class of three qubit sym- metric pure states characterized by two distinct Majorana spinors (to which the W states belong), those with three distinct Majorana spinors (to which GHZ states belong) are shown to either obey or violate monogamy relations. While the generalized W states can be mono/polygamous, the generalized GHZ states exhibit monogamy with respect to quantum deficit. The issue of us- ing monogamy conditions based on quantum deficit to witness the state...
Cheon, T
2004-01-01
We show that the U(2) family of point interactions on a line can be utilized to provide the U(2) family of qubit operations for quantum information processing. Qubits are realized as localized states in either side of the point interaction which represents a controllable gate. The manipulation of qubits proceeds in a manner analogous to the operation of an abacus. Keywords: quantum computation, quantum contact interaction, quantum wire
Measurement-induced operation of two-ion quantum heat machines
Chand, Suman; Biswas, Asoka
2017-03-01
We show how one can implement a quantum heat machine by using two interacting trapped ions, in presence of a thermal bath. The electronic states of the ions act like a working substance, while the vibrational mode is modelled as the cold bath. The heat exchange with the cold bath is mimicked by the projective measurement of the electronic states. We show how such measurement in a suitable basis can lead to either a quantum heat engine or a refrigerator, which undergoes a quantum Otto cycle. The local magnetic field is adiabatically changed during the heat cycle. The performance of the heat machine depends upon the interaction strength between the ions, the magnetic fields, and the measurement cost. In our model, the coupling to the hot and the cold baths is never switched off in an alternative fashion during the heat cycle, unlike other existing proposals of quantum heat engines. This makes our proposal experimentally realizable using current tapped-ion technology.
Lanzagorta, Marco
2011-01-01
This book offers a concise review of quantum radar theory. Our approach is pedagogical, making emphasis on the physics behind the operation of a hypothetical quantum radar. We concentrate our discussion on the two major models proposed to date: interferometric quantum radar and quantum illumination. In addition, this book offers some new results, including an analytical study of quantum interferometry in the X-band radar region with a variety of atmospheric conditions, a derivation of a quantum radar equation, and a discussion of quantum radar jamming.This book assumes the reader is familiar w
Dhuria, Mansi
2012-01-01
We show that it is possible to realize a "mu-split SUSY" scenario [1] in the context of large volume limit of type IIB compactifications on Swiss-Cheese Calabi-Yau's in the presence of a mobile space-time filling D3-brane and a (stack of) D7-brane(s) wrapping the "big" divisor Sigma_B. For this, we investigate the possibility of getting one Higgs to be light while other to be heavy in addition to a heavy Higgsino mass parameter. Further, we examine the existence of long lived gluino that manifests one of the major consequences of mu-split SUSY scenario, by computing its decay width as well as lifetime corresponding to the 3-body decays of the gluino into a quark, a squark and a neutralino or Goldstino, as well as 2-body decays of the gluino into either a neutralino or a Goldstino and a gluon. Guided by the geometric Kaehler potential for Sigma_B obtained in [2] based on GLSM techniques, and the Donaldson's algorithm [3] for obtaining numerically a Ricci-flat metric, we give details of our calculation in [4] p...
Energy Technology Data Exchange (ETDEWEB)
Arcos-Olalla, Rafael, E-mail: olalla@fisica.ugto.mx [Departamento de Física, DCI Campus León, Universidad de Guanajuato, Apdo. Postal E143, 37150 León, Gto. (Mexico); Reyes, Marco A., E-mail: marco@fisica.ugto.mx [Departamento de Física, DCI Campus León, Universidad de Guanajuato, Apdo. Postal E143, 37150 León, Gto. (Mexico); Rosu, Haret C., E-mail: hcr@ipicyt.edu.mx [IPICYT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo. Postal 3-74 Tangamanga, 78231 San Luis Potosí, S.L.P. (Mexico)
2012-10-01
We introduce an alternative factorization of the Hamiltonian of the quantum harmonic oscillator which leads to a two-parameter self-adjoint operator from which the standard harmonic oscillator, the one-parameter oscillators introduced by Mielnik, and the Hermite operator are obtained in certain limits of the parameters. In addition, a single Bernoulli-type parameter factorization, which is different from the one introduced by M.A. Reyes, H.C. Rosu, and M.R. Gutiérrez [Phys. Lett. A 375 (2011) 2145], is briefly discussed in the final part of this work. -- Highlights: ► Factorizations with operators which are not mutually adjoint are presented. ► New two-parameter and one-parameter self-adjoint oscillator operators are introduced. ► Their eigenfunctions are two- and one-parameter deformed Hermite functions.
Energy Technology Data Exchange (ETDEWEB)
Kalay, Berfin; Demiralp, Metin [İstanbul Technical University, Informatics Institute, Maslak, 34469, İstanbul (Turkey)
2015-12-31
This proceedings paper aims to show the efficiency of an expectation value identity for a given algebraic function operator which is assumed to be depending pn only position operator. We show that this expectation value formula becomes enabled to determine the eigenstates of the quantum system Hamiltonian as long as it is autonomous and an appropriate basis set in position operator is used. This approach produces a denumerable infinite recursion which may be considered as revisited but at the same time generalized form of the recursions over the natural number powers of the position operator. The content of this short paper is devoted not only to the formulation of the new method but also to show that this novel approach is capable of catching the eigenvalues and eigenfunctions for Hydrogen-like systems, beyond that, it can give a hand to us to reveal the wavefunction structure. So it has also somehow a confirmative nature.
Surveillance Metrics Sensitivity Study
Energy Technology Data Exchange (ETDEWEB)
Bierbaum, R; Hamada, M; Robertson, A
2011-11-01
In September of 2009, a Tri-Lab team was formed to develop a set of metrics relating to the NNSA nuclear weapon surveillance program. The purpose of the metrics was to develop a more quantitative and/or qualitative metric(s) describing the results of realized or non-realized surveillance activities on our confidence in reporting reliability and assessing the stockpile. As a part of this effort, a statistical sub-team investigated various techniques and developed a complementary set of statistical metrics that could serve as a foundation for characterizing aspects of meeting the surveillance program objectives. The metrics are a combination of tolerance limit calculations and power calculations, intending to answer level-of-confidence type questions with respect to the ability to detect certain undesirable behaviors (catastrophic defects, margin insufficiency defects, and deviations from a model). Note that the metrics are not intended to gauge product performance but instead the adequacy of surveillance. This report gives a short description of four metrics types that were explored and the results of a sensitivity study conducted to investigate their behavior for various inputs. The results of the sensitivity study can be used to set the risk parameters that specify the level of stockpile problem that the surveillance program should be addressing.
Cooper, Gloria S., Ed.; Magisos, Joel H., Ed.
Designed to meet the job-related metric measurement needs of students interested in transportation, this instructional package is one of five for the marketing and distribution cluster, part of a set of 55 packages for metric instruction in different occupations. The package is intended for students who already know the occupational terminology,…
Metrics for Food Distribution.
Cooper, Gloria S., Ed.; Magisos, Joel H., Ed.
Designed to meet the job-related metric measurement needs of students interested in food distribution, this instructional package is one of five for the marketing and distribution cluster, part of a set of 55 packages for metric instruction in different occupations. The package is intended for students who already know the occupational…
Metric Education Evaluation Package.
Kansky, Bob; And Others
This document was developed out of a need for a complete, carefully designed set of evaluation instruments and procedures that might be applied in metric inservice programs across the nation. Components of this package were prepared in such a way as to permit local adaptation to the evaluation of a broad spectrum of metric education activities.…
Computational visual distinctness metric
Martínez-Baena, J.; Toet, A.; Fdez-Vidal, X.R.; Garrido, A.; Rodríguez-Sánchez, R.
1998-01-01
A new computational visual distinctness metric based on principles of the early human visual system is presented. The metric is applied to quantify (1) the visual distinctness of targets in complex natural scenes and (2) the perceptual differences between compressed and uncompressed images. The new
Institute of Scientific and Technical Information of China (English)
ZHAOZhen-gang
2005-01-01
We have constructed the positive definite metric matrixes for the bounded domains of Rn and proved an inequality which is about the Jacobi matrix of a harmonic mapping on a bounded domain of Rn and the metric matrix of the same bounded domain.
Privacy Metrics and Boundaries
L-F. Pau (Louis-François)
2005-01-01
textabstractThis paper aims at defining a set of privacy metrics (quantitative and qualitative) in the case of the relation between a privacy protector ,and an information gatherer .The aims with such metrics are: -to allow to assess and compare different user scenarios and their differences; for ex
Metric Diophantine approximation on homogeneous varieties
Ghosh, Anish; Nevo, Amos
2012-01-01
We develop the metric theory of Diophantine approximation on homogeneous varieties of semisimple algebraic groups and prove results analogous to the classical Khinchin and Jarnik theorems. In full generality our results establish simultaneous Diophantine approximation with respect to several completions, and Diophantine approximation over general number fields using S-algebraic integers. In several important examples, the metric results we obtain are optimal. The proof uses quantitative equidistribution properties of suitable averaging operators, which are derived from spectral bounds in automorphic representations.
GRC GSFC TDRSS Waveform Metrics Report
Mortensen, Dale J.
2013-01-01
The report presents software metrics and porting metrics for the GGT Waveform. The porting was from a ground-based COTS SDR, the SDR-3000, to the CoNNeCT JPL SDR. The report does not address any of the Operating Environment (OE) software development, nor the original TDRSS waveform development at GSFC for the COTS SDR. With regard to STRS, the report presents compliance data and lessons learned.
Carrasco-Casado, Alberto; Fernandez, Veronica
2014-01-01
Free-space quantum key distribution links in urban environment have demanding operating needs, such as functioning in daylight and under atmospheric turbulence, which can dramatically impact their performance. Both effects are usually mitigated with a careful design of the field of view of the receiver. However, a trade-off is often required, since a narrow field of view improves background noise rejection but it is linked to an increase in turbulence-related losses. In this paper, we present a high-speed automatic tracking system to overcome these limitations. Both a reduction in the field-of-view to decrease the background noise and the mitigation of the losses caused by atmospheric turbulence are addressed. Two different designs are presented and discussed, along with technical considerations for the experimental implementation. Finally, preliminary experimental results of beam wander correction are used to estimate the potential improvement of both the quantum bit error rate and secret key rate of a free ...
Energy Technology Data Exchange (ETDEWEB)
Baykara, N. A. [Marmara University, Faculty of Sciences and Letters, Mathematics Department, Göztepe Campus, 34730, Istanbul (Turkey)
2015-12-31
Recent studies on quantum evolutionary problems in Demiralp’s group have arrived at a stage where the construction of an expectation value formula for a given algebraic function operator depending on only position operator becomes possible. It has also been shown that this formula turns into an algebraic recursion amongst some finite number of consecutive elements in a set of expectation values of an appropriately chosen basis set over the natural number powers of the position operator as long as the function under consideration and the system Hamiltonian are both autonomous. This recursion corresponds to a denumerable infinite number of algebraic equations whose solutions can or can not be obtained analytically. This idea is not completely original. There are many recursive relations amongst the expectation values of the natural number powers of position operator. However, those recursions may not be always efficient to get the system energy values and especially the eigenstate wavefunctions. The present approach is somehow improved and generalized form of those expansions. We focus on this issue for a specific system where the Hamiltonian is defined on the coordinate of a curved space instead of the Cartesian one.
Linear connections on the quantum plane
Dubois-Violette, M; Masson, T; Mourad, J; Dubois-Violette, Michel; Madore, John; Masson, Thierry; Mourad, Jihad
1994-01-01
A general definition has been proposed recently of a linear connection and a metric in noncommutative geometry. It is shown that to within normalization there is a unique linear connection on the quantum plane and there is no metric.
Hofer's metrics and boundary depth
Usher, Michael
2011-01-01
We show that if (M,\\omega) is a closed symplectic manifold which admits a nontrivial Hamiltonian vector field all of whose contractible closed orbits are constant, then Hofer's metric on the group of Hamiltonian diffeomorphisms of (M,\\omega) has infinite diameter, and indeed admits infinite-dimensional quasi-isometrically embedded normed vector spaces. A similar conclusion applies to Hofer's metric on various spaces of Lagrangian submanifolds, including those Hamiltonian-isotopic to the diagonal in M x M when M satisfies the above dynamical condition. To prove this, we use the properties of a Floer-theoretic quantity called the boundary depth, which measures the nontriviality of the boundary operator on the Floer complex in a way that encodes robust symplectic-topological information.
A Naturally Renormalized Quantum Field Theory
2006-01-01
It was shown that quantum metric fluctuations smear out the singularities of Green's functions on the light cone [1], but it does not remove other ultraviolet divergences of quantum field theory. We have proved that the quantum field theory in Krein space, {\\it i.e.} indefinite metric quantization, removes all divergences of quantum field theory with exception of the light cone singularity [2,3]. In this paper, it is discussed that the combination of quantum field theory in Krein space togeth...
2008-01-01
As Global Positioning Satellite (GPS) applications become more prevalent for land- and air-based vehicles, GPS applications for space vehicles will also increase. The Applied Technology Directorate of Kennedy Space Center (KSC) has developed a lightweight, low-cost GPS Metric Tracking Unit (GMTU), the first of two steps in developing a lightweight, low-cost Space-Based Tracking and Command Subsystem (STACS) designed to meet Range Safety's link margin and latency requirements for vehicle command and telemetry data. The goals of STACS are to improve Range Safety operations and expand tracking capabilities for space vehicles. STACS will track the vehicle, receive commands, and send telemetry data through the space-based asset, which will dramatically reduce dependence on ground-based assets. The other step was the Low-Cost Tracking and Data Relay Satellite System (TDRSS) Transceiver (LCT2), developed by the Wallops Flight Facility (WFF), which allows the vehicle to communicate with a geosynchronous relay satellite. Although the GMTU and LCT2 were independently implemented and tested, the design collaboration of KSC and WFF engineers allowed GMTU and LCT2 to be integrated into one enclosure, leading to the final STACS. In operation, GMTU needs only a radio frequency (RF) input from a GPS antenna and outputs position and velocity data to the vehicle through a serial or pulse code modulation (PCM) interface. GMTU includes one commercial GPS receiver board and a custom board, the Command and Telemetry Processor (CTP) developed by KSC. The CTP design is based on a field-programmable gate array (FPGA) with embedded processors to support GPS functions.
Holographic Spherically Symmetric Metrics
Petri, Michael
The holographic principle (HP) conjectures, that the maximum number of degrees of freedom of any realistic physical system is proportional to the system's boundary area. The HP has its roots in the study of black holes. It has recently been applied to cosmological solutions. In this article we apply the HP to spherically symmetric static space-times. We find that any regular spherically symmetric object saturating the HP is subject to tight constraints on the (interior) metric, energy-density, temperature and entropy-density. Whenever gravity can be described by a metric theory, gravity is macroscopically scale invariant and the laws of thermodynamics hold locally and globally, the (interior) metric of a regular holographic object is uniquely determined up to a constant factor and the interior matter-state must follow well defined scaling relations. When the metric theory of gravity is general relativity, the interior matter has an overall string equation of state (EOS) and a unique total energy-density. Thus the holographic metric derived in this article can serve as simple interior 4D realization of Mathur's string fuzzball proposal. Some properties of the holographic metric and its possible experimental verification are discussed. The geodesics of the holographic metric describe an isotropically expanding (or contracting) universe with a nearly homogeneous matter-distribution within the local Hubble volume. Due to the overall string EOS the active gravitational mass-density is zero, resulting in a coasting expansion with Ht = 1, which is compatible with the recent GRB-data.
Metrics and causality on Moyal planes
Franco, Nicolas
2015-01-01
Metrics structures stemming from the Connes distance promote Moyal planes to the status of quantum metric spaces. We discuss this aspect in the light of recent developments, emphasizing the role of Moyal planes as representative examples of a recently introduced notion of quantum (noncommutative) locally compact space. We move then to the framework of Lorentzian noncommutative geometry and we examine the possibility of defining a notion of causality on Moyal plane, which is somewhat controversial in the area of mathematical physics. We show the actual existence of causal relations between the elements of a particular class of pure (coherent) states on Moyal plane with related causal structure similar to the one of the usual Minkowski space, up to the notion of locality.
On the operation of machines powered by quantum non-thermal baths
Niedenzu, Wolfgang; Gelbwaser-Klimovsky, David; Kofman, Abraham G.; Kurizki, Gershon
2016-08-01
Diverse models of engines energised by quantum-coherent, hence non-thermal, baths allow the engine efficiency to transgress the standard thermodynamic Carnot bound. These transgressions call for an elucidation of the underlying mechanisms. Here we show that non-thermal baths may impart not only heat, but also mechanical work to a machine. The Carnot bound is inapplicable to such a hybrid machine. Intriguingly, it may exhibit dual action, concurrently as engine and refrigerator, with up to 100% efficiency. We conclude that even though a machine powered by a quantum bath may exhibit an unconventional performance, it still abides by the traditional principles of thermodynamics.
Fujita, Kazuue; Ito, Akio; Hitaka, Masahiro; Dougakiuchi, Tatsuo; Edamura, Tadataka
2017-08-01
The performance of a room-temperature continuous-wave (CW) terahertz source based on intracavity difference-frequency generation in a mid-infrared (λ ∼ 6.8 µm) quantum cascade laser with a dual-upper-state active region is reported. The fabricated buried heterostructure device, with a two-section buried distributed feedback grating, operates at two mid-infrared wavelengths and demonstrates a terahertz output of 2.92 THz with a very low threshold current density of 0.89 kA/cm2 in pulsed operation. Consequently, despite an epitaxial-side-up mounting configuration, the device achieves CW operation at room temperature in which a low CW threshold current density of 1.3 kA/cm2 is obtained.
Characterization of Multiplicative Metric Completeness
Directory of Open Access Journals (Sweden)
Badshshah e Romer
2016-03-01
Full Text Available We established fixed point theorems in multiplicative metric spaces. The obtained results generalize Banach contraction principle in multiplicative metric spaces and also characterize completeness of the underlying multiplicative metric space.
Kiefer, Claus
2012-01-01
The search for a quantum theory of the gravitational field is one of the great open problems in theoretical physics. This book presents a self-contained discussion of the concepts, methods and applications that can be expected in such a theory. The two main approaches to its construction - the direct quantisation of Einstein's general theory of relativity and string theory - are covered. Whereas the first attempts to construct a viable theory for the gravitational field alone, string theory assumes that a quantum theory of gravity will be achieved only through a unification of all the interactions. However, both employ the general method of quantization of constrained systems, which is described together with illustrative examples relevant for quantum gravity. There is a detailed presentation of the main approaches employed in quantum general relativity: path-integral quantization, the background-field method and canonical quantum gravity in the metric, connection and loop formulations. The discussion of stri...
Zaari, Ryan R; Brown, Alex
2011-07-28
The importance of the ro-vibrational state energies on the ability to produce high fidelity binary shaped laser pulses for quantum logic gates is investigated. The single frequency 2-qubit ACNOT(1) and double frequency 2-qubit NOT(2) quantum gates are used as test cases to examine this behaviour. A range of diatomics is sampled. The laser pulses are optimized using a genetic algorithm for binary (two amplitude and two phase parameter) variation on a discretized frequency spectrum. The resulting trends in the fidelities were attributed to the intrinsic molecular properties and not the choice of method: a discretized frequency spectrum with genetic algorithm optimization. This is verified by using other common laser pulse optimization methods (including iterative optimal control theory), which result in the same qualitative trends in fidelity. The results differ from other studies that used vibrational state energies only. Moreover, appropriate choice of diatomic (relative ro-vibrational state arrangement) is critical for producing high fidelity optimized quantum logic gates. It is also suggested that global phase alignment imposes a significant restriction on obtaining high fidelity regions within the parameter search space. Overall, this indicates a complexity in the ability to provide appropriate binary laser pulse control of diatomics for molecular quantum computing.
Webb, Ted
1976-01-01
Describes the program to convert to the metric system all of General Motors Corporation products. Steps include establishing policy regarding employee-owned tools, setting up training plans, and making arrangements with suppliers. (MF)
Schweizer, B
2005-01-01
Topics include special classes of probabilistic metric spaces, topologies, and several related structures, such as probabilistic normed and inner-product spaces. 1983 edition, updated with 3 new appendixes. Includes 17 illustrations.
Carver, Gary P.
1994-05-01
The federal agencies are working with industry to ease adoption of the metric system. The goal is to help U.S. industry compete more successfully in the global marketplace, increase exports, and create new jobs. The strategy is to use federal procurement, financial assistance, and other business-related activities to encourage voluntary conversion. Based upon the positive experiences of firms and industries that have converted, federal agencies have concluded that metric use will yield long-term benefits that are beyond any one-time costs or inconveniences. It may be time for additional steps to move the Nation out of its dual-system comfort zone and continue to progress toward metrication. This report includes 'Metric Highlights in U.S. History'.
Quantum Computation and Quantum Spin Dynamics
Raedt, Hans De; Michielsen, Kristel; Hams, Anthony; Miyashita, Seiji; Saito, Keiji
2001-01-01
We analyze the stability of quantum computations on physically realizable quantum computers by simulating quantum spin models representing quantum computer hardware. Examples of logically identical implementations of the controlled-NOT operation are used to demonstrate that the results of a quantum
Quantum Computation and Quantum Spin Dynamics
Raedt, Hans De; Michielsen, Kristel; Hams, Anthony; Miyashita, Seiji; Saito, Keiji
2001-01-01
We analyze the stability of quantum computations on physically realizable quantum computers by simulating quantum spin models representing quantum computer hardware. Examples of logically identical implementations of the controlled-NOT operation are used to demonstrate that the results of a quantum
Mass Customization Measurements Metrics
DEFF Research Database (Denmark)
Nielsen, Kjeld; Brunø, Thomas Ditlev; Jørgensen, Kaj Asbjørn
2014-01-01
A recent survey has indicated that 17 % of companies have ceased mass customizing less than 1 year after initiating the effort. This paper presents measurement for a company’s mass customization performance, utilizing metrics within the three fundamental capabilities: robust process design, choice...... navigation, and solution space development. A mass customizer when assessing performance with these metrics can identify within which areas improvement would increase competitiveness the most and enable more efficient transition to mass customization....
Balvín, Radek
2013-01-01
With growing amount of data produced by users on social media the need of extraction of relevant data for marketing, research and other uses grows as well. The bachelor thesis named "Social media metrics" presents the issues of monitoring, measurement and metrics of social media. In the research part it also maps and captures the present Czech practice in measurement and monitoring of social media. I also rate the use of social media monitoring tools and usual methods of social media measurem...
Cheng, Liwei
Quantum cascade lasers (QCLs) that emit in the mid-infrared (IR) range between 3 and 10 µm of the electromagnetic spectrum play an important role in optical gas sensing and molecular spectroscopic applications because several important environmental molecules such as CO, CO2, CH 4, and NH3 are known to exhibit strong absorption lines in this mid-IR range. To differentiate such fine absorption features as narrow as a few angstroms, a single-mode QCL with an extremely narrow spectral linewidth, broadly tunable over the molecular absorption fingerprints and operating at sufficient optical power at room temperature, is highly desirable. We present, in this dissertation, two major studies on mid-IR QCLs, one being an improvement in device performance through a buried-heterostructure (BH) regrowth study, and the other being a realization of single-mode, tunable QCLs integrated with a distributed-Bragg-reflector (DBR) grating and thermal tuning mechanism. Efficient heat dissipation in the QCL active region, which is crucial for high optical-power operation, can be effectively achieved using BH waveguides laterally embedded with InP grown by metal-organic chemical vapor disposition (MOCVD). We have experimentally examined the effects of the structural features of mesas, such as the mesa orientation, geometry, sidewall-etched profile, and the length of oxide overhang, on the BH regrowth. We find that the mesa oriented in the [011¯] direction with smoothly etched sidewalls produces a satisfactory planar growth profile and uniform lateral growth coverage and that a mesa-height-to-overhang-length ratio between 2.5 and 3.0 is effective in reducing anomalous growth in the vicinity of oxide edges. As a result, high-power QCLs capable of producing multi-hundred milliwatts at room temperature at ˜4.6 µm and ˜7.9 µm through reproducible BH regrowth results have been demonstrated. We have also demonstrated single-mode tunable QCLs operating at ˜7.9 µm with an internal DBR
Injection locking of quantum dot microlasers operating in the few photon regime
Schlottmann, Elisabeth; Lingnau, Benjamin; Lüdge, Kathy; Schneider, Christian; Kamp, Martin; Höfling, Sven; Wolters, Janik; Reitzenstein, Stephan
2016-01-01
We experimentally and theoretically investigate injection locking of quantum dot (QD) microlasers in the regime of cavity quantum electrodynamics (cQED). We observe frequency locking and phase-locking where cavity enhanced spontaneous emission enables simultaneous stable oscillation at the master frequency and at the solitary frequency of the slave microlaser. Measurements of the second-order autocorrelation function prove this simultaneous presence of both master and slave-like emission, where the former has coherent character with $g^{(2)}(0)=1$ while the latter one has thermal character with $g^{(2)}(0)=2$. Semi-classical rate-equations explain this peculiar behavior by cavity enhanced spontaneous emission and a low number of photons in the laser mode.
Quantum geometry and gravitational entropy
Energy Technology Data Exchange (ETDEWEB)
Simon, Joan; Balasubramanian, Vijay; Czech, Bart Iomiej; Larjo, Klaus; Marolf, Donald; Simon, Joan
2007-05-29
Most quantum states have wavefunctions that are widely spread over the accessible Hilbert space and hence do not have a good description in terms of a single classical geometry. In order to understand when geometric descriptions are possible, we exploit the AdS/CFT correspondence in the half-BPS sector of asymptotically AdS_5 x S5 universes. In this sector we devise a"coarse-grained metric operator" whose eigenstates are well described by a single spacetime topology and geometry. We show that such half-BPS universes have a non-vanishing entropy if and only if the metric is singular, and that the entropy arises from coarse-graining the geometry. Finally, we use our entropy formula to find the most entropic spacetimes with fixed asymptotic moments beyond the global charges.
Quantum-Wave Equation and Heisenberg Inequalities of Covariant Quantum Gravity
Directory of Open Access Journals (Sweden)
Claudio Cremaschini
2017-07-01
Full Text Available Key aspects of the manifestly-covariant theory of quantum gravity (Cremaschini and Tessarotto 2015–2017 are investigated. These refer, first, to the establishment of the four-scalar, manifestly-covariant evolution quantum wave equation, denoted as covariant quantum gravity (CQG wave equation, which advances the quantum state ψ associated with a prescribed background space-time. In this paper, the CQG-wave equation is proved to follow at once by means of a Hamilton–Jacobi quantization of the classical variational tensor field g ≡ g μ ν and its conjugate momentum, referred to as (canonical g-quantization. The same equation is also shown to be variational and to follow from a synchronous variational principle identified here with the quantum Hamilton variational principle. The corresponding quantum hydrodynamic equations are then obtained upon introducing the Madelung representation for ψ , which provides an equivalent statistical interpretation of the CQG-wave equation. Finally, the quantum state ψ is proven to fulfill generalized Heisenberg inequalities, relating the statistical measurement errors of quantum observables. These are shown to be represented in terms of the standard deviations of the metric tensor g ≡ g μ ν and its quantum conjugate momentum operator.
On the class of possible nonlocal anyon-like operators and quantum groups
Chaichian, Masud; Montonen, Claus
1993-01-01
We find a class of nonlocal operators constructed by attaching a disorder operator to fermionic degrees of freedom, which can be used to generate q-deformed algebras following the Schwinger approach. This class includes the recently proposed anyonic operators defined on a lattice.
Topological Combinatorics of a Quantized String Gravitational Metric
Lundberg, Wayne R.
1997-01-01
A string-theoretic structure of the standard model is defined having a 4-D quantum gravity metric consistent with topological and algebraic first principles. Unique topological diagrams of string states, strong and weak interactions and quark families are evolved from this metric (but published separately). The theoretical structure includes known static and dynamic symmetries. A philosophical perspective on modern physics originates numerous opportunities for formal mathematical discussion.
Logarithm Versus Square Root:Comparing Quantum Fisher Information
Institute of Scientific and Technical Information of China (English)
LUO Shun-Long
2007-01-01
In classical statistics,the Fisher information is unique in the sense that it is essentially the only monotone Riemannian metric on the space of probability densities.In quantum theory,this uniqueness breaks down,and there are many natural quantum analogues of the Fisher information,among which two particular versions distinguish themselves by their intuitive and informational significance:The first has its origin in the skew information introduced by Wigner and Yanase in 1963 in the context of quantum measurement,and is defined via the square root of the density operator.The second arises from Helstrom's study of quantum detection in 1967,and is defined via the symmetric logarithmic derivative.The aim of this paper is to compare these two versions of quantum Fisher information,and to establish two informational inequalities relating them.
Einstein Metrics on Complex Surfaces
Lebrun, C
1995-01-01
We consider compact complex surfaces with Hermitian metrics which are Einstein but not Kaehler. It is shown that the manifold must be CP2 blown up at 1,2, or 3 points, and the isometry group of the metric must contain a 2-torus. Thus the Page metric on CP2#(-CP2) is almost the only metric of this type.
Quantum healing of classical singularities in power-law spacetimes
Energy Technology Data Exchange (ETDEWEB)
Helliwell, T M [Department of Physics, Harvey Mudd College, Claremont, CA 91711 (United States); Konkowski, D A [Department of Mathematics, US Naval Academy, Annapolis, MD 21402 (United States)
2007-07-07
We study a broad class of spacetimes whose metric coefficients reduce to powers of a radius r in the limit of small r. Among these four-parameter 'power-law' metrics, we identify those parameters for which the spacetimes have classical singularities as r {yields} 0. We show that a large set of such classically-singular spacetimes is nevertheless non-singular quantum mechanically, in that the Hamiltonian operator is essentially self-adjoint, so that the evolution of quantum wave packets lacks the ambiguity associated with scattering off singularities. Using these metrics, the broadest class yet studied to compare classical with quantum singularities, we explore the physical reasons why some that are singular classically are 'healed' quantum mechanically, while others are not. We show that most (but not all) of the remaining quantum-mechanically singular spacetimes can be excluded if either the weak energy condition or the dominant energy condition is invoked, and we briefly discuss the effect of this work on the strong cosmic censorship conjecture.
Quantum Diaries Blog: Is the moon full? Just ask the LHC operators
Pauline Gagnon
2012-01-01
Corrections to proton orbits in the LHC appear as regular dips in the instantaneous luminosity measured by CMS (beige) and ATLAS (green). The LHC is so large that the gravitational force exerted by the moon is not the same at all points, which creates small distortions of the tunnel. And the machine is sensitive enough to detect minute deformations created by the small differences in gravitational force across its diameter. Therefore, the orbits of protons in the accelerator have to be adjusted regularly to account for the gravitational effect of the moon. Read more on the Quantum Diaries Blog post.
RT CW operation of InGaN multi-quantum-well structure laser diodes
Shuji Nakamura
1998-01-01
Gallium nitride and other III–Vnitride-based semiconductors have a direct band gap that is suitable for blue light-emitting devices. The band gap energy of aluminium gallium indium nitride (AIInGaN) varies between 6.2 and 2.0 eV, depending on its composition at room temperature. Thus, using these semiconductors, red to UV emitting devices are fabricated. High efficient UV, blue and green InGaN single-quantum-well (SQW) structure light-emitting diodes (LEDs) have been fabricated with the exter...
A Quantum Computational Semantics for Epistemic Logical Operators. Part II: Semantics
Beltrametti, Enrico; Dalla Chiara, Maria Luisa; Giuntini, Roberto; Leporini, Roberto; Sergioli, Giuseppe
2014-10-01
By using the abstract structures investigated in the first Part of this article, we develop a semantics for an epistemic language, which expresses sentences like "Alice knows that Bob does not understand that π is irrational". One is dealing with a holistic form of quantum computational semantics, where entanglement plays a fundamental role; thus, the meaning of a global expression determines the contextual meanings of its parts, but generally not the other way around. The epistemic situations represented in this semantics seem to reflect some characteristic limitations of the real processes of acquiring information. Since knowledge is not generally closed under logical consequence, the unpleasant phenomenon of logical omniscience is here avoided.
Adiabatic phase-conserving processes for executing quantum operations with ultracold atoms
Beterov, I. I.; Tret'yakov, D. B.; Entin, V. M.; Yakshina, E. A.; Khamzina, G. N.; Ryabtsev, I. I.
2017-06-01
We have studied the regimes of deterministic single-atom Rydberg excitation in the conditions of Rydberg blockade and the methods of compensation for the dynamic phase of the wave function during the adiabatic passage. Using these methods, we have proposed schemes of single-qubit and two-qubit quantum states with mesoscopic atomic ensembles containing a random number of atoms, considred as quibits. The double adiabatic passage of the Förster resonance for two interacting atoms with a deterministic phase shift can be used for the implementation of two-qubit gates with reduced sensitivity of the gate fidelity to the fluctuations of the interatomic distance.
Isospectral Metrics on Projective Spaces
Rueckriemen, Ralf
2011-01-01
We construct isospectral non isometric metrics on real and complex projective space. We recall the construction using isometric torus actions by Carolyn Gordon in chapter 2. In chapter 3 we will recall some facts about complex projective space. In chapter 4 we build the isospectral metrics. Chapter 5 is devoted to the non isometry proof of the metrics built in chapter 4. In chapter 6 isospectral metrics on real projective space are derived from metrics on the sphere.
Quantum singular operator limits of thin Dirichlet tubes via $\\Gamma$-convergence
de Oliveira, Cesar R.
2010-01-01
The $\\Gamma$-convergence of lower bounded quadratic forms is used to study the singular operator limit of thin tubes (i.e., the vanishing of the cross section diameter) of the Laplace operator with Dirichlet boundary conditions; a procedure to obtain the effective Schr\\"odinger operator (in different subspaces) is proposed, generalizing recent results in case of compact tubes. Finally, after scaling curvature and torsion the limit of a broken line is briefly investigated.
Vortices as degenerate metrics
Baptista, J M
2012-01-01
We note that the Bogomolny equation for abelian vortices is precisely the condition for invariance of the Hermitian-Einstein equation under a degenerate conformal transformation. This leads to a natural interpretation of vortices as degenerate hermitian metrics that satisfy a certain curvature equation. Using this viewpoint, we rephrase standard results about vortices and make some new observations. We note the existence of a conceptually simple, non-linear rule for superposing vortex solutions, and we describe the natural behaviour of the L^2-metric on the moduli space upon certain restrictions.
Uniformly Convex Metric Spaces
Kell Martin
2014-01-01
In this paper the theory of uniformly convex metric spaces is developed. These spaces exhibit a generalized convexity of the metric from a fixed point. Using a (nearly) uniform convexity property a simple proof of reflexivity is presented and a weak topology of such spaces is analyzed. This topology called co-convex topology agrees with the usualy weak topology in Banach spaces. An example of a $CAT(0)$-spaces with weak topology which is not Hausdorff is given. This answers questions raised b...
Convexity and the "Pythagorean" metric of space(-time)
Kalogeropoulos, Nikos
2016-01-01
We address the question about the reasons why the "Wick-rotated", positive-definite, space-time metric obeys the Pythagorean theorem. An answer is proposed based on the convexity and smoothness properties of the functional spaces providing the kinematic framework for the statistical or quantum treatments of gravity. We rely on particular moduli of convexity and smoothness which are extremized by Hilbert spaces. In the spirit of the variational principles employed in classical and quantum Physics, such Hilbert spaces dominate in a functional integral approach. The "Pythagorean" metric of space(-time) is then induced by such Hilbert spaces.
Weaver, Nik
2010-01-01
We define a "quantum relation" on a von Neumann algebra M \\subset B(H) to be a weak* closed operator bimodule over its commutant M'. Although this definition is framed in terms of a particular representation of M, it is effectively representation independent. Quantum relations on l^\\infty(X) exactly correspond to subsets of X^2, i.e., relations on X. There is also a good definition of a "measurable relation" on a measure space, to which quantum relations partially reduce in the general abelian case. By analogy with the classical setting, we can identify structures such as quantum equivalence relations, quantum partial orders, and quantum graphs, and we can generalize Arveson's fundamental work on weak* closed operator algebras containing a masa to these cases. We are also able to intrinsically characterize the quantum relations on M in terms of families of projections in M \\otimes B(l^2).
Dynamical Systems on Spectral Metric Spaces
Bellissard, Jean V; Reihani, Kamran
2010-01-01
Let (A,H,D) be a spectral triple, namely: A is a C*-algebra, H is a Hilbert space on which A acts and D is a selfadjoint operator with compact resolvent such that the set of elements of A having a bounded commutator with D is dense. A spectral metric space, the noncommutative analog of a complete metric space, is a spectral triple (A,H,D) with additional properties which guaranty that the Connes metric induces the weak*-topology on the state space of A. A *-automorphism respecting the metric defined a dynamical system. This article gives various answers to the question: is there a canonical spectral triple based upon the crossed product algebra AxZ, characterizing the metric properties of the dynamical system ? If $\\alpha$ is the noncommutative analog of an isometry the answer is yes. Otherwise, the metric bundle construction of Connes and Moscovici is used to replace (A,$\\alpha$) by an equivalent dynamical system acting isometrically. The difficulties relating to the non compactness of this new system are di...
Razavipour, S. G.; Dupont, E.; Fathololoumi, S.; Chan, C. W. I.; Lindskog, M.; Wasilewski, Z. R.; Aers, G.; Laframboise, S. R.; Wacker, A.; Hu, Q.; Ban, D.; Liu, H. C.
2013-05-01
We designed and demonstrated a terahertz quantum cascade laser based on indirect pump injection to the upper lasing state and phonon scattering extraction from the lower lasing state. By employing a rate equation formalism and a genetic algorithm, an optimized active region design with four-well GaAs/Al0.25Ga0.75As cascade module was obtained and epitaxially grown. A figure of merit which is defined as the ratio of modal gain versus injection current was maximized at 150 K. A fabricated device with a Au metal-metal waveguide and a top n+ GaAs contact layer lased at 2.4 THz up to 128.5 K, while another one without the top n+ GaAs lased up to 152.5 K (1.3ℏω /kB). The experimental results have been analyzed with rate equation and nonequilibrium Green's function models. A high population inversion is achieved at high temperature using a small oscillator strength of 0.28, while its combination with the low injection coupling strength of 0.85 meV results in a low current. The carefully engineered wavefunctions enhance the quantum efficiency of the device and therefore improve the output optical power even with an unusually low injection coupling strength.
Continuous operation of four-state continuous-variable quantum key distribution system
Matsubara, Takuto; Ono, Motoharu; Oguri, Yusuke; Ichikawa, Tsubasa; Hirano, Takuya; Kasai, Kenta; Matsumoto, Ryutaroh; Tsurumaru, Toyohiro
2016-10-01
We report on the development of continuous-variable quantum key distribution (CV-QKD) system that are based on discrete quadrature amplitude modulation (QAM) and homodyne detection of coherent states of light. We use a pulsed light source whose wavelength is 1550 nm and repetition rate is 10 MHz. The CV-QKD system can continuously generate secret key which is secure against entangling cloner attack. Key generation rate is 50 kbps when the quantum channel is a 10 km optical fiber. The CV-QKD system we have developed utilizes the four-state and post-selection protocol [T. Hirano, et al., Phys. Rev. A 68, 042331 (2003).]; Alice randomly sends one of four states {|+/-α⟩,|+/-𝑖α⟩}, and Bob randomly performs x- or p- measurement by homodyne detection. A commercially available balanced receiver is used to realize shot-noise-limited pulsed homodyne detection. GPU cards are used to accelerate the software-based post-processing. We use a non-binary LDPC code for error correction (reverse reconciliation) and the Toeplitz matrix multiplication for privacy amplification.
RT CW operation of InGaN multi-quantum-well structure laser diodes
Directory of Open Access Journals (Sweden)
Shuji Nakamura
1998-01-01
Full Text Available Gallium nitride and other III–Vnitride-based semiconductors have a direct band gap that is suitable for blue light-emitting devices. The band gap energy of aluminium gallium indium nitride (AIInGaN varies between 6.2 and 2.0 eV, depending on its composition at room temperature. Thus, using these semiconductors, red to UV emitting devices are fabricated. High efficient UV, blue and green InGaN single-quantum-well (SQW structure light-emitting diodes (LEDs have been fabricated with the external quantum efficiencies of 7.5% at 371 nm (UV, 11.2% at 468 nm (blue and 11.6% at 520 nm (green, respectively, which were the highest values ever reported for the LEDs with those shorter emission wavelengths. The luminous efficiencies of blue and green LEDs were 5 lm/W and 30 lm/W, respectively, which values are almost identical to that of the white conventional incandescent bulb lamp (20 lm/W. By combining the blue, green and red LEDs, we could fabricate white LEDs with a luminous efficiency of 20–30 im/W which is almost comparable to that of the incandescent bulb lamp. Thus, we can replace the conventional incandescent bulb lamps with these LEDs in order to save an energy consumption and natural resources now.
Quantum catastrophes: a case study
Znojil, Miloslav
2012-11-01
The bound-state spectrum of a Hamiltonian H is assumed real in a non-empty domain D of physical values of parameters. This means that for these parameters, H may be called crypto-Hermitian, i.e. made Hermitian via an ad hoc choice of the inner product in the physical Hilbert space of quantum bound states (i.e. via an ad hoc construction of the operator Θ called the metric). The name quantum catastrophe is then assigned to the N-tuple-exceptional-point crossing, i.e. to the scenario in which we leave the domain D along such a path that at the boundary of D, an N-plet of bound-state energies degenerates and, subsequently, complexifies. At any fixed N ⩾ 2, this process is simulated via an N × N benchmark effective matrix Hamiltonian H. It is being assigned such a closed-form metric which is made unique via an N-extrapolation-friendliness requirement. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’.
Metrics for building performance assurance
Energy Technology Data Exchange (ETDEWEB)
Koles, G.; Hitchcock, R.; Sherman, M.
1996-07-01
This report documents part of the work performed in phase I of a Laboratory Directors Research and Development (LDRD) funded project entitled Building Performance Assurances (BPA). The focus of the BPA effort is to transform the way buildings are built and operated in order to improve building performance by facilitating or providing tools, infrastructure, and information. The efforts described herein focus on the development of metrics with which to evaluate building performance and for which information and optimization tools need to be developed. The classes of building performance metrics reviewed are (1) Building Services (2) First Costs, (3) Operating Costs, (4) Maintenance Costs, and (5) Energy and Environmental Factors. The first category defines the direct benefits associated with buildings; the next three are different kinds of costs associated with providing those benefits; the last category includes concerns that are broader than direct costs and benefits to the building owner and building occupants. The level of detail of the various issues reflect the current state of knowledge in those scientific areas and the ability of the to determine that state of knowledge, rather than directly reflecting the importance of these issues; it intentionally does not specifically focus on energy issues. The report describes work in progress and is intended as a resource and can be used to indicate the areas needing more investigation. Other reports on BPA activities are also available.
Enhanced Accident Tolerant LWR Fuels: Metrics Development
Energy Technology Data Exchange (ETDEWEB)
Shannon Bragg-Sitton; Lori Braase; Rose Montgomery; Chris Stanek; Robert Montgomery; Lance Snead; Larry Ott; Mike Billone
2013-09-01
The Department of Energy (DOE) Fuel Cycle Research and Development (FCRD) Advanced Fuels Campaign (AFC) is conducting research and development on enhanced Accident Tolerant Fuels (ATF) for light water reactors (LWRs). This mission emphasizes the development of novel fuel and cladding concepts to replace the current zirconium alloy-uranium dioxide (UO2) fuel system. The overall mission of the ATF research is to develop advanced fuels/cladding with improved performance, reliability and safety characteristics during normal operations and accident conditions, while minimizing waste generation. The initial effort will focus on implementation in operating reactors or reactors with design certifications. To initiate the development of quantitative metrics for ATR, a LWR Enhanced Accident Tolerant Fuels Metrics Development Workshop was held in October 2012 in Germantown, MD. This paper summarizes the outcome of that workshop and the current status of metrics development for LWR ATF.
Development of testing metrics for military robotics
Resendes, Raymond J.
1993-05-01
The use of robotics or unmanned systems offers significant benefits to the military user by enhancing mobility, logistics, material handling, command and control, reconnaissance, and protection. The evaluation and selection process for the procurement of an unmanned robotic system involves comparison of performance and physical characteristics such as operating environment, application, payloads and performance criteria. Testing an unmanned system for operation in an unstructured environment using emerging technologies, which have not yet been fully tested, presents unique challenges for the testing community. Standard metrics, test procedures, terminologies, and methodologies simplify comparison of different systems. A procedure was developed to standardize the test and evaluation process for UGVs. This procedure breaks the UGV into three components: the platform, the payload, and the command and control link. Standardized metrics were developed for these components which permit unbiased comparison of different systems. The development of these metrics and their application will be presented.
Tice, Bradley S.
Metrical phonology, a linguistic process of phonological stress assessment and diagrammatic simplification of sentence and word stress, is discussed as it is found in the English language with the intention that it may be used in second language instruction. Stress is defined by its physical and acoustical correlates, and the principles of…
1991-07-01
March 1979, pp. 121-128. Gorla, Narasimhaiah, Alan C. Benander, and Barbara A. Benander, "Debugging Effort Estimation Using Software Metrics", IEEE...Society, IEEE Guide for the Use of IEEE Standard Dictionary of Measures to Produce Reliable Software, IEEE Std 982.2-1988, June 1989. Jones, Capers
Adaptive metric kernel regression
DEFF Research Database (Denmark)
Goutte, Cyril; Larsen, Jan
2000-01-01
regression by minimising a cross-validation estimate of the generalisation error. This allows to automatically adjust the importance of different dimensions. The improvement in terms of modelling performance is illustrated on a variable selection task where the adaptive metric kernel clearly outperforms...
Adaptive Metric Kernel Regression
DEFF Research Database (Denmark)
Goutte, Cyril; Larsen, Jan
1998-01-01
by minimising a cross-validation estimate of the generalisation error. This allows one to automatically adjust the importance of different dimensions. The improvement in terms of modelling performance is illustrated on a variable selection task where the adaptive metric kernel clearly outperforms the standard...
Engineering performance metrics
Delozier, R.; Snyder, N.
1993-03-01
Implementation of a Total Quality Management (TQM) approach to engineering work required the development of a system of metrics which would serve as a meaningful management tool for evaluating effectiveness in accomplishing project objectives and in achieving improved customer satisfaction. A team effort was chartered with the goal of developing a system of engineering performance metrics which would measure customer satisfaction, quality, cost effectiveness, and timeliness. The approach to developing this system involved normal systems design phases including, conceptual design, detailed design, implementation, and integration. The lessons teamed from this effort will be explored in this paper. These lessons learned may provide a starting point for other large engineering organizations seeking to institute a performance measurement system accomplishing project objectives and in achieving improved customer satisfaction. To facilitate this effort, a team was chartered to assist in the development of the metrics system. This team, consisting of customers and Engineering staff members, was utilized to ensure that the needs and views of the customers were considered in the development of performance measurements. The development of a system of metrics is no different than the development of any type of system. It includes the steps of defining performance measurement requirements, measurement process conceptual design, performance measurement and reporting system detailed design, and system implementation and integration.
Parniak, Michał; Wasilewski, Wojciech
2015-01-01
We analyze the properties of a Raman quantum light-atom interface in long atomic ensemble and its applications as a quantum memory or two-mode squeezed state generator. We include both Stokes and anti-Stokes scattering and the effects of Doppler broadening in buffer gas assuming frequent velocity-averaging collisions. We find the Green functions describing multimode transformation from input to output fields of photons and atomic excitations. Proper mode basis is found via singular value decomposition. It reveals that triples of modes are coupled by a transformation equivalent to a combination of two beamsplitters and a two-mode squeezing operation. We analyze the possible transformations on an example of warm rubidium-87 vapor. We find that the fidelity of the mapping of a single excitation between the memory and light is strictly limited by the fractional contribution of the Stokes scattering in predominantly anti-Stokes process. The model we present bridges the gap between the Stokes only and anti-Stokes o...
Efficiency at maximum power output of quantum heat engines under finite-time operation
Wang, Jianhui; He, Jizhou; Wu, Zhaoqi
2012-03-01
We study the efficiency at maximum power, ηm, of irreversible quantum Carnot engines (QCEs) that perform finite-time cycles between a hot and a cold reservoir at temperatures Th and Tc, respectively. For QCEs in the reversible limit (long cycle period, zero dissipation), ηm becomes identical to the Carnot efficiency ηC=1-Tc/Th. For QCE cycles in which nonadiabatic dissipation and the time spent on two adiabats are included, the efficiency ηm at maximum power output is bounded from above by ηC/(2-ηC) and from below by ηC/2. In the case of symmetric dissipation, the Curzon-Ahlborn efficiency ηCA=1-Tc/Th is recovered under the condition that the time allocation between the adiabats and the contact time with the reservoir satisfy a certain relation.
Experimental evidence of hot carriers solar cell operation in multi-quantum wells heterostructures
Energy Technology Data Exchange (ETDEWEB)
Rodière, Jean; Lombez, Laurent, E-mail: laurent.lombez@chimie-paristech.fr [IRDEP, Institute of R and D on Photovoltaic Energy, UMR 7174, CNRS-EDF-Chimie ParisTech, 6 Quai Watier-BP 49, 78401 Chatou Cedex (France); Le Corre, Alain; Durand, Olivier [INSA, FOTON-OHM, UMR 6082, F-35708 Rennes (France); Guillemoles, Jean-François [IRDEP, Institute of R and D on Photovoltaic Energy, UMR 7174, CNRS-EDF-Chimie ParisTech, 6 Quai Watier-BP 49, 78401 Chatou Cedex (France); NextPV, LIA CNRS-RCAST/U. Tokyo-U. Bordeaux, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8904 (Japan)
2015-05-04
We investigated a semiconductor heterostructure based on InGaAsP multi quantum wells (QWs) using optical characterizations and demonstrate its potential to work as a hot carrier cell absorber. By analyzing photoluminescence spectra, the quasi Fermi level splitting Δμ and the carrier temperature are quantitatively measured as a function of the excitation power. Moreover, both thermodynamics values are measured at the QWs and the barrier emission energy. High values of Δμ are found for both transition, and high carrier temperature values in the QWs. Remarkably, the quasi Fermi level splitting measured at the barrier energy exceeds the absorption threshold of the QWs. This indicates a working condition beyond the classical Shockley-Queisser limit.
Quantum logic operations on two distant atoms trapped in two optical-fibre-connected cavities
Institute of Scientific and Technical Information of China (English)
Zhang Ying-Qiao; Zhang Shou; Yeon Kyu-Hwang; Yu Seong-Cho
2011-01-01
Based on the coupling of two distant three-level atoms in two separate optical cavities connected with two optical fibres,schemes on the generation of several two-qubit logic gates are discussed under the conditions of △ =δ -2v cos πk/2 (》) g/2 and (v～ g).Discussion and analysis of the fidelity,gate time and experimental setups show that our schemes are feasible with current optical cavity,atomic trap and optical fibre techniques.Moreover,the atom-cavityfibre coupling can be used to generate an N-qubit nonlocal entanglement and transfer quantum information among N distant atoms by arranging N atom-cavity assemblages in a line and connecting each two adjacent cavities with two optical fibres.
Efficiency at maximum power output of quantum heat engines under finite-time operation.
Wang, Jianhui; He, Jizhou; Wu, Zhaoqi
2012-03-01
We study the efficiency at maximum power, η(m), of irreversible quantum Carnot engines (QCEs) that perform finite-time cycles between a hot and a cold reservoir at temperatures T(h) and T(c), respectively. For QCEs in the reversible limit (long cycle period, zero dissipation), η(m) becomes identical to the Carnot efficiency η(C)=1-T(c)/T(h). For QCE cycles in which nonadiabatic dissipation and the time spent on two adiabats are included, the efficiency η(m) at maximum power output is bounded from above by η(C)/(2-η(C)) and from below by η(C)/2. In the case of symmetric dissipation, the Curzon-Ahlborn efficiency η(CA)=1-√(T(c)/T(h)) is recovered under the condition that the time allocation between the adiabats and the contact time with the reservoir satisfy a certain relation.
Influence of vertical coupling on the lasing operation of quantum-dash laser
Khan, Mohammed Zahed Mustafa
2012-01-01
The authors numerically investigated the consequence of vertical coupling among multi-stack InAs quantum dash (Qdash) laser structure on the lasing bandwidth. The developed model is based on multi-population carrier-photon rate equation and incorporates inhomogeneous broadening due to dash size or composition fluctuation, homogeneous broadening of optical gain, and the multi-longitudinal photon modes. In addition, the effect of Qdash layers emitting at different wavelength, and the carrier coupling (tunneling) between adjacent stacks, are also accounted for. The results predict a direct relation between the lasing bandwidth and the barrier thickness and hence enhanced lasing bandwidth could be achieved by decoupling the Qdash layers (large barrier thickness). Moreover, the model further affirms the non-equilibrium distribution of carriers among Qdash layers in a multi-stack laser structure.
Sokolova, Z. N.; Pikhtin, N. A.; Tarasov, I. S.; Asryan, L. V.
2016-08-01
A model for calculating the operating characteristics of semiconductor quantum well (QW) lasers is presented. The model exploits the condition of global electroneutrality, which includes the charge carriers both in the two-dimensional (2D) active region (QW) and bulk waveguide region (optical confinement layer - OCL). The charge of each sign in the OCL is shown to be significantly larger than that in the QW. As a result of this, (i) the global electroneutrality condition reduces to the condition of electroneutrality in the OCL and (ii) the local electroneutrality in the QW can be strongly violated, i.e., the 2D electron and hole densities in the QW can significantly differ from each other.
Xie, Feng; Caneau, Catherine; LeBlanc, Herve P.; Coleman, Sean; Hughes, Lawrence C.; Zah, Chung-en
2012-03-01
We demonstrated the room temperature continuous wave (CW) operation of mid-infrared distributed feedback (DFB) quantum cascade lasers (QCLs) made of strain balanced GaInAs/AlInAs material on InP substrates for sensing CO2 isotope and N2O gas for potential applications that need battery powered portable devices in a sensor network. For the former device at 4.35 μm wavelength, we demonstrated a low threshold voltage of less than 8 V for battery operation and a near circular far field pattern with small divergent angles of 33 by 28 degrees full width at half maximum (FWHM) in vertical and horizontal directions, respectively, for easy collimation. For the latter device at 4.5 μm wavelength, we demonstrated a low CW threshold power consumption of 0.7 W at 20 °C. A side mode suppression ratio (SMSR) of 30 dB was achieved within the whole operating current and temperature ranges for both lasers.
Spectral Metric Spaces on Extensions of C*-Algebras
Hawkins, Andrew; Zacharias, Joachim
2017-03-01
We construct spectral triples on C*-algebraic extensions of unital C*-algebras by stable ideals satisfying a certain Toeplitz type property using given spectral triples on the quotient and ideal. Our construction behaves well with respect to summability and produces new spectral quantum metric spaces out of given ones. Using our construction we find new spectral triples on the quantum 2- and 3-spheres giving a new perspective on these algebras in noncommutative geometry.
Finite-Temperature Fidelity-Metric Approach to the Lipkin-Meshkov-Glick Model
Scherer, D D; Kästner, M
2009-01-01
The fidelity metric has recently been proposed as a useful and elegant approach to identify and characterize both quantum and classical phase transitions. We study this metric on the manifold of thermal states for the Lipkin-Meshkov-Glick (LMG) model. For the isotropic LMG model, we find that the metric reduces to a Fisher-Rao metric, reflecting an underlying classical probability distribution. Furthermore, this metric can be expressed in terms of derivatives of the free energy, indicating a relation to Ruppeiner geometry. This allows us to obtain exact expressions for the (suitably rescaled) metric in the thermodynamic limit. The phase transition of the isotropic LMG model is signalled by a degeneracy of this (improper) metric in the paramagnetic phase. Due to the integrability of the isotropic LMG model, ground state level crossings occur, leading to an ill-defined fidelity metric at zero temperature.