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 preparation, or generation of coherent states, squeezed states, and photon number states is discussed. The quantum noise is evaluated for various simultaneous measurements of two quadrature components: heterodyning, the beam splitter followed by two single quadrature measurements, the parametric amplifier, the (degenerate and/or nondegenerate) four-wave mixer, the Brillouin and Raman amplifiers, and the laser amplifier. A quantum nondemolition measurement followed by a measurement of the conjugate variable is also categorized as a simultaneous measurement. It is shown that, for all of these schemes, the minimum uncertainty product of the measured variables is exactly equal to that required for a simultaneous measurement of two noncommuting variables. On the other hand, measurements of a single quadrature component are noise-free. Such measurements are degenerate heterodyning, degenerate parametric amplification, and cavity degenerate four-wave mixing and photon counting by a photomultiplier or avalanche photodiode. The Heisenberg uncertainty principle and the quantum-mechanical channel capacity of Shannon are discussed to address the question "How much information can be transmitted by a single photon?" The quantum-mechanical channel capacity provides an upper bound on the achievable information capacity and is ideally realized by photon number states and photon counting detection. Its value is $\frac{\ensuremath{\hbar}\ensuremath{\omega}}{(\mathrm{ln}2)kT}$ bit per photon. The use of coherent or squeezed states and a simultaneous measurement of two quadrature field components or the measurement of one single quadrature field component does not achieve the ultimate limit.

Preparation, measurement and information capacity of optical quantum states

This paper is concerned with the problem of finding the structure and performance of the receiver that yields the best performance in the reception of signals that are described quantum-mechanically. The principles of statistical detection and estimation theory are discussed, with the laws of quantum mechanics taken into account. Several specific communication systems of practical interest are studied as examples of applying these principles. Basic concepts in quantum mechanics that are needed in these discussions are briefly reviewed.

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Quantum-mechanical communication theory

William H. Louisell McGraw-Hill Publishing Co. Ltd. 1964. Pp. xii + 303. Price 116s. This is a textbook which aims to introduce to the graduate physicist or electrical engineer those aspects of quantum field theory and quantum statistics which are necessary for a basic understanding of such processes as the absorption and spontaneous emission of radiation, quantum fluctuations and quantum noise. With the advent of devices such as the maser, this text fills a definite need.

Radiation and Noise in Quantum Electronics

We are concerned with the detection of a set of M messages that are transmitted over a channel disturbed by chaotic thermal noise when quantum effects in the communication systems are taken into account. Our attention is restricted to the special case in which the density operators specifying the state of the received field are commutative. In particular, the performance of two special communication systems is evaluated. For a system in which orthogonal signals with known amplitudes and random phases are transmitted over an additive white Gaussian channel, the structure of an optimum receiver is found. Expressions for the system reliability function and channel capacity are derived. For a system in which orthogonal signals are transmitted over a Rayleigh fading channel, the optimum performance is obtained. The optimum degree of diversity for an equal-strength diversity system is found numerically as a function of the average thermal-noise energy and information rate.

Reliability of quantum-mechanical communication systems

A simple one-dimensional model is taken to illustrate the quantum effects of a narrowband communication system. The system is quantized, and its dynamics are discussed in terms of the Heisenberg equations for field operators. The detection process of a "coherent joint detector," whose compatibility with quantum physics was justified elsewhere, is discussed. The detector, which is capable of measuring the quadrature-modulating components at Nyquist rate with minimum possible uncertainty allowed by quantum theory and which is most suitable for a continuous channel, is used to determine the channel capacity. It is shown that the noise of the channel, due to both thermal and quantum fluctuations, is additive and Gaussian. The classical concepts and expressions for the average mutual information and channel capacity are still valid, provided that the quantum noise of one quantum is included properly. The results obtained approach straightforwardly Shannon's in the classical limit.

Chiao She

Papers

Quantum electrodynamics of a communication channel