Quantum Information Processing

This revised edition provides 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 contributions have been carefully revised and enlarged with respect to recent developments in quantum computation, quantum transportation and cryptography. Here, leading experts bring together the latest results in quantum information and address all the relevant questions.

From the contents:

Algorithms for quantum systems Quantum error correction with jump codes Increasing the size of NMR quantum computers Entanglement properties of composite quantum systems Entanglement and decoherence Strongly coupled atom–cavity systems Spin resonance with trapped ions: experiments and new concepts Neutral atoms on atom chips Multiphoton entanglement Quantum gates and algorithms on molecular vibrations Quantum dynamics of vortices and vortex qubits Conditional linear optical networks Quantum dot circuits for quantum computation Quantum optical XOR gate

Preface.

List of Contributors.

1 Algorithms for Quantum Systems Quantum Algorithms (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 Given One–parameter Groups.

1.5 Simulation of Hamiltonians.

References.

2 Quantum Information Processing and Error Correction with Jump 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 QC_c as a Universal Simulator of Quantum Logic Networks.

3.3 Non–Network Character of the QC_c.

3.4 Computational Model.

3.5 Conclusion.

References.

4 Quantum Correlations as Basic Resource for Quantum Key Distribution (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–pure States.

5.4 Approaching Pure States.

5.5 Scalable NMR Quantum Computing Based on the Thermal Density Operator.

5.6 Time–optimal Implementation of Quantum Gates.

5.7 Conclusion.

References.

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

6.1 Introduction.

6.2 Codes, Lengths, Kraft Inequality and von Neumann Entropy Bound.

6.3 Construct Long Codes from Variable–length Codes.

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

6.5 Code Analysis Based on the Base Length.

6.6 Lossless Quantum Data Compression with a Classical Helper.

6.7 Lossless Quantum Data Compression for Mixed State Sources.

6.8 A Result on Tradeoff between Quantum and Classical Resources in 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 Bosonic States.

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, and M. 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. Maierle and 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 Correlated Fields.

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 Room Temperature.

12.5 Magnetic Resonance on a Single 13CnuclearSpin.

12.6 Two–qubit Gate with Electron Spin and 13C Nuclear Spin of Single 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 Trapped Ion (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 Deterministically Coupled 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 Paradox on 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 Equal Results.

18.4 Second Scheme: Driving the Ion by Fractionated –Pulses.

18.5 Conclusions.

18.6 Survey of Related Work.

References.

19 Spin Resonance with Trapped Ions: Experiments and New Concepts (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 CO2 Laser 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 Lattice Sites.

21.5 Recent Work.

References.

22 Quantum Information Processing with Atoms in Optical Micro–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 Information Processing.

22.3 Experimental Setup.

22.4 Scalable Qubit Registers Based on Arrays of Dipole Traps.

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 Atom Chips (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 Molecular Vibrations (U. Troppmann, C. M. Tesch, and R. de Vivie–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 Based Single–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 Distant Atoms via Linear Optical Elements (X.–B. Zou and W. Mathis).

27.1 Introduction.

27.2 Manipulation and Control of Individual Photons via Linear Optical Elements.

27.3 Quantum Entanglement Between Distant Atoms Trapped in Different 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 Information Processing (N. Korolkova).

30.1 Introduction.

30.2 Nonseparability and Squeezing.

30.3 Applications.

30.4 Stokes Operators Questioned: Degree of Polarization in Quantum 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, and Detection (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.

Thomas Beth studied mathematics, physics and medicine. He received his Ph.D. in 1978 and his Postdoctoral Lecturer Qualification (Dr.–Ing. habil.) in informatics in 1984. From a position as Professor of computer science at the University of London he was apppointed to a chair of informatics at the University of Karlsruhe. He also is the director of the European Institute for System Security (E.I.S.S.). In the past decade he has built up a research center for quantum information at the Institute for Algorithms and Cognitive Systems (IAKS).

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

"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)