Characterization of Gaussian operations and distillation of Gaussian states
TL;DR: It is shown that Gaussian states cannot be distilled by local Gaussian operations and classical communication, and positive (but not completely positive) Gaussian maps are defined.
Abstract: We characterize the class of all physical operations that transform Gaussian states to Gaussian states. We show that this class coincides with that of all operations that can be performed on Gaussian states using linear optical elements and homodyne measurements. For bipartite systems we characterize the processes that can be implemented by local operations and classical communication, as well as those that can be implemented using positive partial transpose preserving maps. As an application, we show that Gaussian states cannot be distilled by local Gaussian operations and classical communication. We also define and characterize positive (but not completely positive) Gaussian maps.
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TL;DR: In this article, the basic aspects of entanglement including its characterization, detection, distillation, and quantification are discussed, and a basic role of entonglement in quantum communication within distant labs paradigm is discussed.
Abstract: All our former experience with application of quantum theory seems to say:
{\it what is predicted by quantum formalism must occur in laboratory} But the
essence of quantum formalism - entanglement, recognized by Einstein, Podolsky,
Rosen and Schr\"odinger - waited over 70 years to enter to laboratories as a
new resource as real as energy This holistic property of compound quantum systems, which involves
nonclassical correlations between subsystems, is a potential for many quantum
processes, including ``canonical'' ones: quantum cryptography, quantum
teleportation and dense coding However, it appeared that this new resource is
very complex and difficult to detect Being usually fragile to environment, it
is robust against conceptual and mathematical tools, the task of which is to
decipher its rich structure This article reviews basic aspects of entanglement including its
characterization, detection, distillation and quantifying In particular, the
authors discuss various manifestations of entanglement via Bell inequalities,
entropic inequalities, entanglement witnesses, quantum cryptography and point
out some interrelations They also discuss a basic role of entanglement in
quantum communication within distant labs paradigm and stress some
peculiarities such as irreversibility of entanglement manipulations including
its extremal form - bound entanglement phenomenon A basic role of entanglement
witnesses in detection of entanglement is emphasized
6,980 citations
TL;DR: In this article, the authors present the Deutsch-Jozsa algorithm for continuous variables, and a deterministic version of it is used for quantum information processing with continuous variables.
Abstract: Preface. About the Editors. Part I: Quantum Computing. 1. Quantum computing with qubits S.L. Braunstein, A.K. Pati. 2. Quantum computation over continuous variables S. Lloyd, S.L. Braunstein. 3. Error correction for continuous quantum variables S.L. Braunstein. 4. Deutsch-Jozsa algorithm for continuous variables A.K. Pati, S.L. Braunstein. 5. Hybrid quantum computing S. Lloyd. 6. Efficient classical simulation of continuous variable quantum information processes S.D. Bartlett, B.C. Sanders, S.L. Braunstein, K. Nemoto. Part II: Quantum Entanglement. 7. Introduction to entanglement-based protocols S.L. Braunstein, A.K. Pati. 8. Teleportation of continuous uantum variables S.L. Braunstein, H.J. Kimble. 9. Experimental realization of continuous variable teleportation A. Furusawa, H.J. Kimble. 10. Dense coding for continuous variables S.L. Braunstein, H.J. Kimble. 11. Multipartite Greenberger-Horne-Zeilinger paradoxes for continuous variables S. Massar, S. Pironio. 12. Multipartite entanglement for continuous variables P. van Loock, S.L. Braunstein. 13. Inseparability criterion for continuous variable systems Lu-Ming Duan, G. Giedke, J.I. Cirac, P. Zoller. 14. Separability criterion for Gaussian states R. Simon. 15. Distillability and entanglement purification for Gaussian states G. Giedke, Lu-Ming Duan, J.I. Cirac, P. Zoller. 16. Entanglement purification via entanglement swapping S. Parke, S. Bose, M.B. Plenio. 17. Bound entanglement for continuous variables is a rare phenomenon P. Horodecki, J.I. Cirac, M. Lewenstein. Part III: Continuous Variable Optical-Atomic Interfacing. 18. Atomic continuous variable processing and light-atoms quantum interface A. Kuzmich, E.S. Polzik. Part IV: Limits on Quantum Information and Cryptography. 19. Limitations on discrete quantum information and cryptography S.L. Braunstein, A.K. Pati. 20. Quantum cloning with continuous variables N.J. Cerf. 21. Quantum key distribution with continuous variables in optics T.C. Ralph. 22. Secure quantum key distribution using squeezed states D. Gottesman, J. Preskill. 23. Experimental demonstration of dense coding and quantum cryptography with continuous variables Kunchi Peng, Qing Pan, Jing Zhang, Changde Xie. 24. Quantum solitons in optical fibres: basic requisites for experimental quantum communication G. Leuchs, Ch. Silberhorn, E. Konig, P.K. Lam, A. Sizmann, N. Korolkova. Index.
2,940 citations
TL;DR: This review focuses on continuous-variable quantum information processes that rely on any combination of Gaussian states, Gaussian operations, and Gaussian measurements, including quantum communication, quantum cryptography, quantum computation, quantum teleportation, and quantum state and channel discrimination.
Abstract: The science of quantum information has arisen over the last two decades centered on the manipulation of individual quanta of information, known as quantum bits or qubits. Quantum computers, quantum cryptography, and quantum teleportation are among the most celebrated ideas that have emerged from this new field. It was realized later on that using continuous-variable quantum information carriers, instead of qubits, constitutes an extremely powerful alternative approach to quantum information processing. This review focuses on continuous-variable quantum information processes that rely on any combination of Gaussian states, Gaussian operations, and Gaussian measurements. Interestingly, such a restriction to the Gaussian realm comes with various benefits, since on the theoretical side, simple analytical tools are available and, on the experimental side, optical components effecting Gaussian processes are readily available in the laboratory. Yet, Gaussian quantum information processing opens the way to a wide variety of tasks and applications, including quantum communication, quantum cryptography, quantum computation, quantum teleportation, and quantum state and channel discrimination. This review reports on the state of the art in this field, ranging from the basic theoretical tools and landmark experimental realizations to the most recent successful developments.
2,781 citations
TL;DR: Different methods for quantifying the quantum and classical parts of correlations are among the more actively studied topics of quantum-information theory over the past decade as mentioned in this paper and different notions of classical and quantum correlations quantified by quantum discord and other related measures are reviewed.
Abstract: One of the best signatures of nonclassicality in a quantum system is the existence of correlations that have no classical counterpart. Different methods for quantifying the quantum and classical parts of correlations are among the more actively studied topics of quantum-information theory over the past decade. Entanglement is the most prominent of these correlations, but in many cases unentangled states exhibit nonclassical behavior too. Thus distinguishing quantum correlations other than entanglement provides a better division between the quantum and classical worlds, especially when considering mixed states. Here different notions of classical and quantum correlations quantified by quantum discord and other related measures are reviewed. In the first half, the mathematical properties of the measures of quantum correlations are reviewed, related to each other, and the classical-quantum division that is common among them is discussed. In the second half, it is shown that the measures identify and quantify the deviation from classicality in various quantum-information-processing tasks, quantum thermodynamics, open-system dynamics, and many-body physics. It is shown that in many cases quantum correlations indicate an advantage of quantum methods over classical ones.
1,504 citations
Cites methods from "Characterization of Gaussian operat..."
...These measurements are all executable using linear optics and homodyne detection (Giedke and Cirac, 2002)....
[...]
01 May 2012
TL;DR: In this article, a review of the state of the art in continuous-variable quantum information processing can be found, ranging from the basic theoretical tools and landmark experimental realizations to the most recent successful developments.
Abstract: The science of quantum information has arisen over the last two decades centered on the manipulation of individual quanta of information, known as quantum bits or qubits. Quantum computers, quantum cryptography and quantum teleportation are among the most celebrated ideas that have emerged from this new field. It was realized later on that using continuous-variable quantum information carriers, instead of qubits, constitutes an extremely powerful alternative approach to quantum information processing. This review focuses on continuous-variable quantum information processes that rely on any combination of Gaussian states, Gaussian operations, and Gaussian measurements. Interestingly, such a restriction to the Gaussian realm comes with various benefits, since on the theoretical side, simple analytical tools are available and, on the experimental side, optical components effecting Gaussian processes are readily available in the laboratory. Yet, Gaussian quantum information processing opens the way to a wide variety of tasks and applications, including quantum communication, quantum cryptography, quantum computation, quantum teleportation, and quantum state and channel discrimination. This review reports on the state of the art in this field, ranging from the basic theoretical tools and landmark experimental realizations to the most recent successful developments.
1,374 citations
References
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TL;DR: In this article, the authors present results of both classic and recent matrix analyses using canonical forms as a unifying theme, and demonstrate their importance in a variety of applications, such as linear algebra and matrix theory.
Abstract: Linear algebra and matrix theory are fundamental tools in mathematical and physical science, as well as fertile fields for research. This new edition of the acclaimed text presents results of both classic and recent matrix analyses using canonical forms as a unifying theme, and demonstrates their importance in a variety of applications. The authors have thoroughly revised, updated, and expanded on the first edition. The book opens with an extended summary of useful concepts and facts and includes numerous new topics and features, such as: - New sections on the singular value and CS decompositions - New applications of the Jordan canonical form - A new section on the Weyr canonical form - Expanded treatments of inverse problems and of block matrices - A central role for the Von Neumann trace theorem - A new appendix with a modern list of canonical forms for a pair of Hermitian matrices and for a symmetric-skew symmetric pair - Expanded index with more than 3,500 entries for easy reference - More than 1,100 problems and exercises, many with hints, to reinforce understanding and develop auxiliary themes such as finite-dimensional quantum systems, the compound and adjugate matrices, and the Loewner ellipsoid - A new appendix provides a collection of problem-solving hints.
23,986 citations
01 Oct 1997
TL;DR: In this paper, the authors present a method for simultaneous measurement of position and momentum in a simple optical instrument with respect to the quantum theory of light and quasiprobability distribution.
Abstract: 1. Introduction 2. Quantum theory of light 3. Quasiprobability distribution 4. Simple optical instruments 5. Quantum tomography 6. Simultaneous measurement of position and momentum 7. Summary Appendices Bibliography Index.
890 citations
Book•
01 Jul 1997
TL;DR: In this paper, the authors present a method for simultaneous measurement of position and momentum in a simple optical instrument with respect to the quantum theory of light and quasiprobability distribution.
Abstract: 1. Introduction 2. Quantum theory of light 3. Quasiprobability distribution 4. Simple optical instruments 5. Quantum tomography 6. Simultaneous measurement of position and momentum 7. Summary Appendices Bibliography Index.
840 citations
TL;DR: In this paper, the generalized coherent states were studied using an operator technique similar to one we have used in a previous paper, and an alternative derivation of the most general coherent state was provided.
Abstract: Using an operator technique similar to one we have used in a previous paper, we study the generalized coherent states which were introduced by Titulaer and Glauber and discussed recently by Bialynicka-Birula. Using this technique, we provide an alternative derivation of the most general coherent state and then derive a number of interesting properties, some of which do not seem to be in the literature. For example, we show that the generalized coherent states are not minimum-uncertainty packets.
166 citations