Quantum Information Processing / Edition 2

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Overview

Quantum processing and communication is emerging as a challenging technique at the beginning of the new millennium. This is an up-to-date insight into the current research of quantum superposition, entanglement, and the quantum measurement process - the key ingredients of quantum information processing. The authors further address quantum protocols and algorithms. Complementary to similar programmes in other countries and at the European level, the German Research Foundation (DFG) realized a focused research program on quantum information. The contributions - written by leading experts - bring together the latest results in quantum information as well as addressing all the relevant questions.

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Editorial Reviews

From the Publisher
"This revised edition provides up-to-date insights into the current research of quantum superposition, entanglement, and the quantum measurement process…" (IEEE Computer Magazine, September 2005)
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Product Details

  • ISBN-13: 9783527405411
  • Publisher: Wiley
  • Publication date: 4/22/2005
  • Edition description: 2nd, Revised and Enlarged Edition
  • Edition number: 2
  • Pages: 471
  • Product dimensions: 6.87 (w) x 9.78 (h) x 1.12 (d)

Meet the Author

Thomas Beth studied mathematics, physics and medicine. Hereceived his Ph.D. in 1978 and his Postdoctoral LecturerQualification (Dr.-Ing. habil.) in informatics in 1984. From aposition as Professor of computer science at the University ofLondon he was apppointed to a chair of informatics at theUniversity of Karlsruhe. He also is the director of the EuropeanInstitute for System Security (E.I.S.S.). In the past decade he hasbuilt up a research center for quantum information at the Institutefor Algorithms and Cognitive Systems (IAKS).

Gerd Leuchs studied physics and mathematics at theUniversity of Cologne and received his Ph.D. in 1978. After tworesearch visits at the University of Colorado, Boulder, he headedthe German Gravitational Wave Detection Group from 1985 to 1989. Hethen went on to be the technical director of Nanomach AG inSwitzerland for four years. Since 1994 he holds the chair foroptics at the Friedrich-Alexander-University of Erlangen-Nuremberg,Germany. His fields of research span the range from modern aspectsof classical optics to quantum optics and quantum information.

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Table of Contents

Preface.

List of Contributors.

1 Algorithms for Quantum Systems— QuantumAlgorithms (Th. Beth, M. Grassl, D. Janzing, M.Rötteler, P. Wocjan, and R. Zeier).

1.1 Introduction.

1.2 Fast Quantum Signal Transforms.

1.3 Quantum Error-correcting Codes.

1.4 Efficient Decomposition of Quantum Operations into GivenOne-parameter Groups.

1.5 Simulation of Hamiltonians.

References.

2 Quantum Information Processing and Error Correction withJump Codes (G. Alber, M. Mussinger, and A. Delgado).

2.1 Introduction.

2.2 Invertible Quantum Operations and Error Correction.

2.3 Quantum Error Correction by Jump Codes.

2.4 Universal Quantum Gates in Code Spaces.

2.5 Summary and Outlook.

References.

3 Computational Model for the One-Way Quantum Computer:Concepts and Summary (R. Raussendorf and H. J.Briegel).

3.1 Introduction.

3.2 The QCc as a UniversalSimulator of Quantum Logic Networks.

3.3 Non-Network Character of theQCc.

3.4 Computational Model.

3.5 Conclusion.

References.

4 Quantum Correlations as Basic Resource for Quantum KeyDistribution (M. Curty, O. Gühne, M. Lewenstein, and N.Lütkenhaus).

4.1 Introduction.

4.2 Background of Classical Information Theoretic Security.

4.3 Link Between Classical and Quantum.

4.4 Searching for Effective Entanglement.

4.5 Verification Sets.

4.6 Examples for Evaluation.

4.7 Realistic Experiments.

4.8 Conclusions.

References.

5 Increasing the Size of NMR Quantum Computers (S. J.Glaser, R. Marx, T. Reiss, T. Schulte-Herbrüggen, N. Khaneja,J. M. Myers, and A. F. Fahmy).

5.1 Introduction.

5.2 Suitable Molecules.

5.3 Scaling Problem for Experiments Based on Pseudo-pureStates.

5.4 Approaching Pure States.

5.5 Scalable NMR Quantum Computing Based on the Thermal DensityOperator.

5.6 Time-optimal Implementation of Quantum Gates.

5.7 Conclusion.

References.

6 On Lossless Quantum Data Compression and QuantumVariable-length Codes (R. Ahlswede and N. Cai).

6.1 Introduction.

6.2 Codes, Lengths, Kraft Inequality and von Neumann EntropyBound.

6.3 Construct Long Codes from Variable-length Codes.

6.4 Lossless Quantum Data Compression, if the Decoder isInformed about the Base Lengths.

6.5 Code Analysis Based on the Base Length.

6.6 Lossless Quantum Data Compression with a ClassicalHelper.

6.7 Lossless Quantum Data Compression for Mixed StateSources.

6.8 A Result on Tradeoff between Quantum and Classical Resourcesin Lossy Quantum Data Compression.

References . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . 81

7 Entanglement Properties of Composite Quantum Systems(K. Eckert, O. Gühne, F. Hulpke, P. Hyllus, J. Korbicz, J.Mompart, D. Bruß, M. Lewenstein, and A. Sanpera).

7.1 Introduction.

7.2 Separability of Composite Quantum Systems.

7.3 The Distillability Problem.

7.4 Witness Operators for the Detection of Entanglement.

7.5 Quantum Correlations in Systems of Fermionic and BosonicStates.

7.6 Summary.

References.

8 Non-Classical Gaussian States in Noisy Environments(S. Scheel and D.-G. Welsch).

8.1 Introduction.

8.2 Gaussian States and Gaussian Operations.

8.3 Entanglement Degradation.

8.4 Quantum Teleportation in Noisy Environments.

References.

9 Quantum Estimation with Finite Resources

(T. C. Bschorr, D. G. Fischer, H. Mack, W. P. Schleich, andM. Freyberger).

9.1 Introduction.

9.2 Quantum Devices and Channels.

9.3 Estimating Quantum Channels.

9.4 Entanglement and Estimation.

9.5 Generalized Estimation Schemes.

9.6 Outlook.

References.

10 Size Scaling of Decoherence Rates (C. S. Maierleand D. Suter).

10.1 Introduction.

10.2 Decoherence Models.

10.3 Collective and Independent Decoherence.

10.4 Average Decoherence Rate as a Measure of Decoherence.

10.5 Decoherence Rate Scaling due to Partially CorrelatedFields.

10.6 Conclusion.

References.

11 Reduced Collective Description of Spin-Ensembles(M. Michel, H. Schmidt, F. Tonner, and G. Mahler).

11.1 Introduction.

11.2 Operator Representations.

11.3 Hamilton Models.

11.4 State Models.

11.5 Ensembles.

11.6 Summary and Outlook.

References.

12 Quantum Information Processing with Defects

(F. Jelezko and J. Wrachtrup) 150

12.1 Introduction.

12.2 Properties of Nitrogen-vacancy Centers in Diamond.

12.3 Readout of Spin State via Site-selective Excitation.

12.4 Magnetic Resonance on a Single Spin at RoomTemperature.

12.5 Magnetic Resonance on a Single 13CnuclearSpin.

12.6 Two-qubit Gate with Electron Spin and 13C Nuclear Spin ofSingle NV Defect.

12.7 Outlook: Towards Scalable NV Based Quantum Processor.

References.

13 Quantum Dynamics of Vortices and Vortex Qubits (A.Wallraff, A. Kemp, and A. V. Ustinov).

13.1 Introduction.

13.2 Macroscopic Quantum Effects with Single Vortices.

13.3 Vortex–Antivortex Pairs.

13.4 The Josephs on Vortex Qubit.

13.5 Conclusions.

References.

14 Decoherence in Resonantly Driven Bistable Systems(S. Kohler and P. Hänggi).

14.1 Introduction.

14.2 The Model and its Symmetries.

14.3 Coherent Tunneling.

14.4 Dissipative Tunneling.

14.5 Conclusions.

References.

15 Entanglement and Decoherence in Cavity QED with a TrappedIon (W. Vogel and Ch. DiFidio).

15.1 Introduction.

15.2 Decoherence Effects.

15.3 Greenberger–Horne–Zeilinger State.

15.4 Photon-number Control.

15.5 Entanglement of Separated Atoms.

15.6 Summary.

References.

16 Quantum Information Processing with Ions DeterministicallyCoupled to an Optical Cavity (M. Keller, B. Lange, K.Hayasaka, W. Lange, and H. Walther).

16.1 Introduction.

16.2 Deterministic Coupling of Ions and Cavity Field.

16.3 Single-ion Mapping of Cavity-Modes.

16.4 Atom–Photon Interface.

16.5 Single-Photon Source.

16.6 Cavity-mediated Two-Ion Coupling.

References.

17 Strongly Coupled Atom–Cavity Systems (A.Kuhn, M. Hennrich, and G. Rempe).

17.1 Introduction.

17.2 Atoms, Cavities and Light.

17.3 Single-Photon Sources.

17.4 Summary and Outlook.

References.

18 A Relaxation-free Verification of the Quantum Zeno Paradoxon an Individual Atom (Ch. Balzer, Th. Hannemann, D.Reiß, Ch. Wunderlich, W. Neuhauser, and P. E.Toschek).

18.1 Introduction.

18.2 The Hardware and Basic Procedure.

18.3 First Scheme: Statistics of the Sequences of EqualResults.

18.4 Second Scheme: Driving the Ion by Fractionatedπ-Pulses.

18.5 Conclusions.

18.6 Survey of Related Work.

References.

19 Spin Resonance with Trapped Ions: Experiments and NewConcepts (K. Abich, Ch. Balzer, T. Hannemann, F. Mintert, W.Neuhauser, D. Reiß, P. E. Toschek, and Ch.Wunderlich).

19.1 Introduction.

19.2 Self-learning Estimation of Quantum States.

19.3 Experimental Realization of Quantum Channels.

19.4 New Concepts for QIP with Trapped Ions.

19.5 Raman Cooling of two Trapped Ions.

References.

20 Controlled Single Neutral Atoms as Qubits (V.Gomer, W. Alt, S. Kuhr, D. Schrader, and D. Meschede).

20.1 Introduction.

20.2 Cavity QED for QIP.

20.3 Single Atom Controlled Manipulation.

20.4 HowtoPrepareExactly2Atoms in a Dipole Trap?

20.5 Optical Dipole Trap.

20.6 Relaxation and Decoherence.

20.7 Qubit Conveyor Belt.

20.8 Outlook.

References.

21 Towards Quantum Logic with Cold Atoms in a CO2Laser Optical Lattice (G. Cennini, G. Ritt, C. Geckeler,R. Scheunemann, and M. Weitz).

21.1 Introduction.

21.2 Entanglement and Beyond.

21.3 Quantum Logic and Far-detuned Optical Lattices.

21.4 Resolving and Addressing Cold Atoms in Single LatticeSites.

21.5 Recent Work.

References.

22 Quantum Information Processing with Atoms in OpticalMicro-Structures (R. Dumke, M. Volk, T. Müther, F. B.J. Buchkremer, W. Ertmer, and G. Birkl).

22.1 Introduction.

22.2 Microoptical Elements for Quantum InformationProcessing.

22.3 Experimental Setup.

22.4 Scalable Qubit Registers Based on Arrays of DipoleTraps.

22.5 Initialization, Manipulation and Readout.

22.6 Variation of Trap Separation.

22.7 Implementation of Qubit Gates.

References.

23 Quantum Information Processing with Neutral Atoms on AtomChips (P. Krüger, A. Haase, M. Andersson, and J.Schmiedmayer).

23.1 Introduction.

23.2 The Atom Chip.

23.3 The Qubit.

23.4 Entangling Qubits.

23.5 Input/Output.

23.6 Noise and Decoherence.

23.7 Summary and Conclusion.

References.

24 Quantum Gates and Algorithms Operating on MolecularVibrations (U. Troppmann, C. M. Tesch, and R. deVivie-Riedle).

24.1 Introduction.

24.2 Qubit States Encoded in Molecular Vibrations.

24.3 Optimal Control Theory for Molecular Dynamics.

24.4 Multi-target OCT for Global Quantum Gates.

24.5 Basis Set Independence and Quantum Algorithms.

24.6 Towards More Complex Molecular Systems.

24.7 Outlook.

References.

25 Fabrication and Measurement of Aluminum and Niobium BasedSingle-Electron Transistors and Charge Qubits (W. Krech, D.Born, M. Mihalik, and M. Grajcar).

25.1 Introduction.

25.2 Motivation for this Work.

25.3 Sample Preparation.

25.4 Experimental Results.

25.5 Conclusions.

References.

26 Quantum Dot Circuits for Quantum Computation (R. H.Blick, A. K. Hüttel, A. W. Holleitner, L. Pescini, and H.Lorenz).

26.1 Introduction.

26.2 Realizing Quantum Bits in Double Quantum Dots.

26.3 Controlling the Electron Spin in Single Dots.

26.4 Summary.

References.

27 Manipulation and Control of Individual Photons and DistantAtoms via Linear Optical Elements (X.-B. Zou and W.Mathis).

27.1 Introduction.

27.2 Manipulation and Control of Individual Photons via LinearOptical Elements.

27.3 Quantum Entanglement Between Distant Atoms Trapped inDifferent Optical Cavities.

27.4 Conclusion.

References.

28 Conditional Linear Optical Networks (S.Scheel).

28.1 Introduction.

28.2 Measurement-induced Nonlinearities.

28.3 Probability of Success and Permanents.

28.4 Upper Bounds on Success Probabilities.

28.5 Extension Using Weak Nonlinearities.

References.

29 Multiphoton Entanglement (M. Bourennane, M. Eibl,S. Gaertner, N. Kiesel, Ch. Kurtsiefer, M. ˙ Zukowski, and H.Weinfurter).

29.1 Introduction.

29.2 Entangled Multiphoton State Preparation.

29.3 Experiment.

29.4 Quantum Correlations.

29.5 Bell Inequality.

29.6 Genuine Four-photon Entanglement.

29.7 Entanglement Persistence.

29.8 Conclusions.

References.

30 Quantum Polarization for Continuous Variable InformationProcessing (N. Korolkova).

30.1 Introduction.

30.2 Nonseparability and Squeezing.

30.3 Applications.

30.4 Stokes Operators Questioned: Degree of Polarization inQuantum Optics.

References.

31 A Quantum Optical XOR Gate (H. Becker, K. Schmid,W. Dultz, W. Martienssen, and H. Roskos).

31.1 Introduction.

31.2 Double Bump Photons.

31.3 The XOR Gate.

31.4 Quad Bump Photons.

31.5 Outlook.

References.

32 Quantum Fiber Solitons—Generation, Entanglement, andDetection (G. Leuchs, N. Korolkova, O. Glöckl, St.Lorenz, J. Heersink, Ch. Silberhorn, Ch. Marquardt, and U. L.Andersen).

32.1 Introduction.

32.2 Quantum Correlations and Entanglement.

32.3 Multimode Quantum Correlations.

32.4 Generation of Bright Entangled Beams.

32.5 Detection of Entanglement of Bright Beams.

32.6 Entanglement Swapping.

32.7 Polarization Variables.

References.

Index.

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