Part I. Fundamental Concepts: 1. Introduction and overview 2. Introduction to quantum mechanics 3. Introduction to computer science Part II. Quantum Computation: 4. Quantum circuits 5. The quantum Fourier transform and its application 6. Quantum search algorithms 7. Quantum computers: physical realization Part III. Quantum Information: 8. Quantum noise and quantum operations 9. Distance measures for quantum information 10. Quantum error-correction 11. Entropy and information 12. Quantum information theory Appendices References Index.

Quantum Computation and Quantum Information

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

Single trapped ions represent elementary quantum systems that are well isolated from the environment. They can be brought nearly to rest by laser cooling, and both their internal electronic states and external motion can be coupled to and manipulated by light fields. This makes them ideally suited for quantum-optical and quantum-dynamical studies under well-controlled conditions. Theoretical and experimental work on these topics is reviewed in the paper, with a focus on ions trapped in radio-frequency (Paul) traps.

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Quantum dynamics of single trapped ions

Among the numerous types of architecture being explored for quantum computers are systems utilizing ion traps, in which quantum bits (qubits) are formed from the electronic states of trapped ions and coupled through the Coulomb interaction. Although the elementary requirements for quantum computation have been demonstrated in this system, there exist theoretical and technical obstacles to scaling up the approach to large numbers of qubits. Therefore, recent efforts have been concentrated on using quantum communication to link a number of small ion-trap quantum systems. Developing the array-based approach, we show how to achieve massively parallel gate operation in a large-scale quantum computer, based on techniques already demonstrated for manipulating small quantum registers. The use of decoherence-free subspaces significantly reduces decoherence during ion transport, and removes the requirement of clock synchronization between the interaction regions.

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Architecture for a large-scale ion-trap quantum computer

In this review, a general algorithm for constructing coherent states of dynamical groups for a given quantum physical system is presented. The result is that, for a given dynamical group, the coherent states are isomorphic to a coset space of group geometrical space. Thus the topological and algebraic structure of the coherent states as well as the associated dynamical system can be extensively discussed. In addition, a quantum-mechanical phase-space representation is constructed via the coherent-state theory. Several useful methods for employing the coherent states to study the physical phenomena of quantum-dynamic systems, such as the path integral, variational principle, classical limit, and thermodynamic limit of quantum mechanics, are described.

Coherent states: Theory and some Applications

Broad-band squeezed states of light are generated by forward nondegenerate four-wave mixing in a single-mode optical fiber cooled below 4.2 K. The minimum total noise level was (12.5 \ifmmode\pm\else\textpm\fi{} 0.5)% below the standard quantum limit.

https://link.aps.org/pdf/10.1103/PhysRevLett.57.691

Broad-band parametric deamplification of quantum noise in an optical fiber.

Summary form only given. We report a laboratory realization of the gedanken experiment that Dicke used to introduce superradiance. Two Ba/sup +/ ions are laser-cooled and crystallized in a microscopic Paul trap so that they come to rest 1.5 microns from each other. This is about 3 wavelengths of the 493 nm light used to laser cool the transition. Micromotion and residual thermal motion are low so that they are essentially stationary relative to 493 nm light.

Observation of superradiant and subradiant spontaneous emission of two trapped ions

We have created an atomic fountain starting with a sample of laser cooled Na atoms. Excitation of the atoms between the F=1, mF=0 and F=2, mF=0 ground states have an observed linwidth of 2.0 Hz at ν = 1,772,626,129. +1/−10 Hz using the Ramsey resonance technique.

RF Spectroscopy in an Atomic Fountain

Laser-cooled sodium atoms pushed up on a vertical trajectory by radiation pressure are observed to turn around due to gravity. The reatively long time the atoms spent freely falling in this ``atomic fountain'' allowed the ground-state hyperfine splitting to be measured with a linewidth of 2 Hz. After a 1000-s integration time, the center of the line was resolved to \ifmmode\pm\else\textpm\fi{}10 mHz. The absolute splitting was measured to be 1 771 626 129(2) Hz.

rf spectroscopy in an atomic fountain.

This paper provides the first experimental test of the Bloch equations for an optical transition in a low-temperature impurity-ion solid, ${\mathrm{Pr}}^{3+}$: La${\mathrm{F}}_{3}$, where the condition ${T}_{1}\ensuremath{\gg}{T}_{2}$ applies. Intensity-dependent optical free-induction-decay measurements are performed by use of an ultrastable cw dye laser (linewidth, 300 Hz) and reveal an $\mathrm{exp}(\ensuremath{-}\frac{2t}{{T}_{2}})$ decay law at low Rabi frequency ($\ensuremath{\chi}$), as predicted by the Bloch equations, and an $\mathrm{exp}(\ensuremath{-}\ensuremath{\chi}t)$ decay at high $\ensuremath{\chi}$, which violates the Bloch prediction but agrees with Redfield's characterization of NMR saturation in solids.

Ralph G. Devoe

Papers

Broad-band parametric deamplification of quantum noise in an optical fiber.

Observation of superradiant and subradiant spontaneous emission of two trapped ions

RF Spectroscopy in an Atomic Fountain

rf spectroscopy in an atomic fountain.

Experimental test of the optical Bloch equations for solids