Quantum cryptography could well be the first application of quantum mechanics at the individual quanta level. The very fast progress in both theory and experiments over the recent years are reviewed, with emphasis on open questions and technological issues.

Quantum Cryptography

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.

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Quantum Information with Continuous Variables

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.

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Gaussian quantum information

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.

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This review covers state-of-the-art quantum teleportation technologies, from photonic qubits and optical modes to atomic ensembles, trapped atoms and solid-state systems. Open issues and potential future implementations are also discussed. Quantum teleportation is one of the most important protocols in quantum information. By exploiting the physical resource of entanglement, quantum teleportation serves as a key primitive across a variety of quantum information tasks and represents an important building block for quantum technologies, with a pivotal role in the continuing progress of quantum communication, quantum computing and quantum networks. Here we summarize the basic theoretical ideas behind quantum teleportation and its variant protocols. We focus on the main experiments, together with the technical advantages and disadvantages associated with the use of the various technologies, from photonic qubits and optical modes to atomic ensembles, trapped atoms and solid-state systems. After analysing the current state-of-the-art, we finish by discussing open issues, challenges and potential future implementations.

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Advances in quantum teleportation

We analyze the possibility of copying (that is, cloning) arbitrary states of a quantum-mechanical spin-1/2 system. We show that there exists a ``universal quantum-copying machine'' (i.e., transformation) which approximately copies quantum-mechanical states such that the quality of its output does not depend on the input. We also examine a machine which combines a unitary transformation and a selective measurement to produce good copies of states in the neighborhood of a particular state. We discuss the problem of measurement of the output states. \textcopyright{} 1996 The American Physical Society.

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Vladimir Buzek

Papers

Quantum copying: Beyond the no-cloning theorem