Quantum Information Processing

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ISBN: 9783527405411 | 3527405410
Cover: Hardcover
Copyright: 5/6/2005

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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) started a focused research program on quantum information in 1999. The contributions - written by leading experts - bring together the latest results in quantum information as well as addressing all the relevant questions.

Preface

List of Contributors

XIX

1 Algorithms for Quantum Systems - Quantum Algorithms

Th. Beth, M. Grassi, D. Janzing, M. Rötteler, P. Wocjan, and R. Zeier

(13)

1.1 Introduction

(1)

1.2 Fast Quantum Signal Transforms

(2)

1.3 Quantum Error-correcting Codes

(2)

1.4 Efficient Decomposition of Quantum Operations into Given One-parameter Groups

(3)

1.5 Simulation of Hamiltonians

(2)

References

(4)

2 Quantum Information Processing and Error Correction with Jump Codes

G. Alber, M. Mussinger, and A. Delgado

(14)

2.1 Introduction

(1)

2.2 Invertible Quantum Operations and Error Correction

(2)

2.3 Quantum Error Correction by Jump Codes

(4)

2.3.1 Spontaneous Decay and Quantum Trajectories

(2)

2.3.2 Jump Codes

(2)

2.4 Universal Quantum Gates in Code Spaces

(4)

2.4.1 Universal Sets of Quantum Gates for Qudit-Systems

(1)

2.4.2 Universal One-Qutrit Gates

(1)

2.4.3 A Universal Entanglement Gate

(2)

2.5 Summary and Outlook

(1)

References

(2)

3 Computational Model for the One-Way Quantum Computer: Concepts and Summary

R. Raussendorf and H.J. Briegel

(16)

3.1 Introduction

(2)

3.2 The QCc as a Universal Simulator of Quantum Logic Networks

(5)

3.3 Non-Network Character of the QCc

(1)

3.4 Computational Model

(6)

3.5 Conclusion

(1)

References

(2)

4 Quantum Correlations as Basic Resource for Quantum Key Distribution

M. Curly, O. Gühne, M. Lewenstein, and N. Lütkenhaus

(14)

4.1 Introduction

(1)

4.2 Background of Classical Information Theoretic Security

(1)

4.3 Link Between Classical and Quantum

(3)

4.4 Searching for Effective Entanglement

(2)

4.5 Verification Sets

(2)

4.5.1 6-state Protocol

(1)

4.5.2 4-state Protocol

(1)

4.5.3 2-state Protocol

(1)

4.6 Examples for Evaluation

(1)

4.7 Realistic Experiments

(1)

4.8 Conclusions

(1)

References

(3)

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

(12)

5.1 Introduction

(1)

5.2 Suitable Molecules

(3)

5.3 Scaling Problem for Experiments Based on Pseudo-pure States

(1)

5.4 Approaching Pure States

(1)

5.5 Scalable NMR Quantum Computing Based on the Thermal Density Operator

(1)

5.6 Time-optimal Implementation of Quantum Gates

(3)

5.7 Conclusion

(1)

References

(2)

6 On Lossless Quantum Data Compression and Quantum Variable-length Codes

R. Ahlswede and N. Cai

(13)

6.1 Introduction

(1)

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

(2)

6.2.1 The Codes

(1)

6.2.2 Length Observable and Average Length of Codewords

(1)

6.2.3 Kraft Inequality and von Neumann Entropy Bound

(1)

6.2.4 Base Length

(1)

6.3 Construct Long Codes from Variable-length Codes

(1)

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

(1)

6.5 Code Analysis Based on the Base Length

(1)

6.6 Lossless Quantum Data Compression with a Classical Helper

(3)

6.7 Lossless Quantum Data Compression for Mixed State Sources

(1)

6.8 A Result on Tradeoff between Quantum and Classical Resources in Lossy Quantum Data Compression

(1)

References

(2)

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

(17)

7.1 Introduction

(1)

7.2 Separability of Composite Quantum Systems

(4)

7.2.1 The Separability Problem

(1)

7.2.2 Results on The Separability Problem

(2)

7.3 The Distillability Problem

(2)

7.3.1 Results on the Distillability Problem

(1)

7.4 Witness Operators for the Detection of Entanglement

(4)

7.4.1 Definition and Geometrical Interpretation of Witness Operators

(2)

7.4.2 Results on Witness Operators

(2)

7.5 Quantum Correlations in Systems of Fermionic and Bosonic States

(3)

7.5.1 What is Different with Indistinguishable Particles?

(1)

7.5.2 Results on Quantum Correlations for Indistinguishable Particles

(2)

7.5.3 Implementation of an Entangling Gate with Bosons

(1)

7.6 Summary

(1)

References

(3)

8 Non-Classical Gaussian States in Noisy Environments

S. Scheel and D.-G. Welsch

100

(13)

8.1 Introduction

100

(1)

8.2 Gaussian States and Gaussian Operations

100

(4)

8.2.1 Classicality

102

(1)

8.2.2 CP Maps and Partial Measurements

102

(1)

8.2.3 Separability and Entanglement

103

(1)

8.3 Entanglement Degradation

104

(2)

8.4 Quantum Teleportation in Noisy Environments

106

(5)

8.4.1 Imperfect Teleportation

107

(1)

8.4.2 Teleportation Fidelity

108

(2)

8.4.3 Choice of the Coherent Displacement

110

(1)

References

111

(2)

9 Quantum Estimation with Finite Resources

T.C. Bschorr, D.G. Fischer, H. Mack, W.P. Schleich, and M. Freyberger

113

(12)

9.1 Introduction

113

(1)

9.2 Quantum Devices and Channels

114

(1)

9.3 Estimating Quantum Channels

115

(1)

9.4 Entanglement and Estimation

115

(5)

9.4.1 Estimation using Single Qubits

116

(2)

9.4.2 Estimation using Entangled States

118

(2)

9.5 Generalized Estimation Schemes

120

(3)

9.5.1 Estimation with Two Channels

120

(1)

9.5.2 What is the Optimal Reference Channel?

121

(1)

9.5.3 Estimation with Werner States

122

(1)

9.6 Outlook

123

(1)

References

124

(1)

10 Size Scaling of Decoherence Rates

C.S. Maierle and D. Suter

125

(10)

10.1 Introduction

125

(1)

10.2 Decoherence Models

126

(1)

10.3 Collective and Independent Decoherence

127

(1)

10.4 Average Decoherence Rate as a Measure of Decoherence

128

(2)

10.5 Decoherence Rate Scaling due to Partially Correlated Fields

130

(4)

10.6 Conclusion

134

(1)

References

134

(1)

11 Reduced Collective Description of Spin-Ensembles

M. Michel, H. Schmidt, F. Tanner, and G. Mahler

135

(15)

11.1 Introduction

135

(1)

11.2 Operator Representations

135

(3)

11.3 Hamilton Models

138

(2)

11.3.1 Symmetry-constrained Networks

138

(1)

11.3.2 Topology-constrained Networks

139

(1)

11.4 State Models

140

(1)

11.4.1 Totally Permutation-symmetric Subspace

140

(1)

11.4.2 Collective 1-particle Excitations

140

(1)

11.4.3 1-parameter Families of Non-pure States

141

(1)

11.4.4 Families of Separable States: "Modules"

141

(1)

11.5 Ensembles

141

(6)

11.5.1 Trajectories and Ergodicity

142

(2)

11.5.2 Leakage and Storage Capacity

144

(2)

11.5.3 Mixing Strategies

146

(1)

11.5.4 State Construction and Separability

147

(1)

11.6 Summary and Outlook

147

(1)

References

148

(2)

12 Quantum Information Processing with Defects

F. Jelezko and J. Wrachtrup

150

(12)

12.1 Introduction

150

(1)

12.2 Properties of Nitrogen-vacancy Centers in Diamond

150

(2)

12.3 Readout of Spin State via Site-selective Excitation

152

(3)

12.4 Magnetic Resonance on a Single Spin at Room Temperature

155

(1)

12.5 Magnetic Resonance on a Single ¹³c Nuclear Spin

156

(2)

12.6 Two-qubit Gate with Electron Spin and ¹³C Nuclear Spin of Single NV Defect

158

(2)

12.7 Outlook: Towards Scalable NV Based Quantum Processor

160

(1)

References

160

(2)

13 Quantum Dynamics of Vortices and Vortex Qubits

A. Wallraff, A. Kemp, and A.V. Ustinov

162

(24)

13.1 Introduction

162

(1)

13.2 Macroscopic Quantum Effects with Single Vortices

163

(4)

13.2.1 Quantum Tunneling

163

(2)

13.2.2 Energy Level Quantization

165

(2)

13.3 Vortex-Antivortex Pairs

167

(6)

13.3.1 Thermal and Quantum Dissociation

167

(4)

13.3.2 Energy Levels of a Bound Vortex-Antivortex Pair

171

(2)

13.4 The Josephson Vortex Qubit

173

(9)

13.4.1 Principle of the Vortex Qubit

174

(1)

13.4.2 Model

175

(2)

13.4.3 Perturbative Calculation of Vortex Potential

177

(2)

13.4.4 Quantum Mechanics of a Vortex in a Double Well

179

(1)

13.4.5 Depinning Current and Qubit Readout

180

(2)

13.5 Conclusions

182

(1)

References

183

(3)

14 Decoherence in Resonantly Driven Bistable Systems

S. Kohler and P. Hänggi

186

(12)

14.1 Introduction

186

(1)

14.2 The Model and its Symmetries

186

(2)

14.3 Coherent Tunneling

188

(4)

14.4 Dissipative Tunneling

192

(4)

14.5 Conclusions

196

(1)

References

197

(1)

15 Entanglement and Decoherence in Cavity QED with a Trapped Ion

W. Vogel and Ch. DiFidio

198

(11)

15.1 Introduction

198

(1)

15.2 Decoherence Effects

199

(2)

15.3 Greenberger-Horne-Zeilinger State

201

(2)

15.4 Photon-number Control

203

(2)

15.5 Entanglement of Separated Atoms

205

(2)

15.6 Summary

207

(1)

References

207

(2)

16 Quantum Information Processing with Ions Deterministically Coupled to an Optical Cavity

M. Keller, B. Lange, K. Hayasaka, W. Lange, and H. Walther

209

(14)

16.1 Introduction

209

(1)

16.2 Deterministic Coupling of Ions and Cavity Field

210

(2)

16.3 Single-ion Mapping of Cavity-Modes

212

(3)

16.4 Atom-Photon Interface

215

(2)

16.5 Single-Photon Source

217

(2)

16.6 Cavity-mediated Two-Ion Coupling

219

(2)

References

221

(2)

17 Strongly Coupled Atom-Cavity Systems

A. Kuhn, M. Hennrich, and G. Rempe

223

(14)

17.1 Introduction

223

(1)

17.2 Atoms, Cavities and Light

223

(5)

17.2.1 Field Quantization in a Fabry-Perot Cavity

223

(1)

17.2.2 Two-Level Atom

224

(1)

17.2.3 Three-Level Atom

225

(2)

17.2.4 Adiabatic Passage

227

(1)

17.3 Single-Photon Sources

228

(5)

17.3.1 Vacuum-Stimulated Raman Scattering

229

(1)

17.3.2 Deterministic Single-Photon Sequences

230

(3)

17.4 Summary and Outlook

233

(1)

References

233

(4)

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

237

(14)

18.1 Introduction

237

(1)

18.2 The Hardware and Basic Procedure

238

(3)

18.3 First Scheme: Statistics of the Sequences of Equal Results

241

(2)

18.4 Second Scheme: Driving the Ion by Fractionated π-Pulses

243

(3)

18.5 Conclusions

246

(1)

18.6 Survey of Related Work

247

(2)

References

249

(2)

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

251

(14)

19.1 Introduction

251

(1)

19.2 Self-learning Estimation of Quantum States

252

(2)

19.3 Experimental Realization of Quantum Channels

254

(2)

19.4 New Concepts for QIP with Trapped Ions

256

(5)

19.4.1 Spin Resonance with Trapped Ions

257

(3)

19.4.2 Simultaneous Cooling of Axial Vibrational Modes

260

(1)

19.5 Raman Cooling of two Trapped Ions

261

(2)

References

263

(2)

20 Controlled Single Neutral Atoms as Qubits

V. Gomer, W. Alt, S. Kuhr, D. Schrader, and D. Meschede

265

(10)

20.1 Introduction

265

(1)

20.2 Cavity QED for QIP

265

(1)

20.3 Single Atom Controlled Manipulation

266

(1)

20.4 How to Prepare Exactly 2 Atoms in a Dipole Trap?

267

(1)

20.5 Optical Dipole Trap

267

(1)

20.6 Relaxation and Decoherence

268

(1)

20.7 Qubit Conveyor Belt

269

(1)

20.8 Outlook

270

(1)

References

270

(5)

21 Towards Quantum Logic with Cold Atoms in a CO2 Laser Optical Lattice

G. Cennini, G. Ritt, C. Geckeler, R. Scheunemann, and M. Weitz

275

(12)

21.1 Introduction

275

(1)

21.2 Entanglement and Beyond

276

(1)

21.3 Quantum Logic and Far-detuned Optical Lattices

277

(2)

21.4 Resolving and Addressing Cold Atoms in Single Lattice Sites

279

(3)

21.5 Recent Work

282

(2)

References

284

(3)

22 Quantum Information Processing with Atoms in Optical Micro-Structures

R. Dumke, M. Volk, T. Müther, F.B.J. Buchkremer, W. Earner, and G. Birkl

287

(11)

22.1 Introduction

287

(1)

22.2 Microoptical Elements for Quantum Information Processing

288

(1)

22.3 Experimental Setup

289

(1)

22.4 Scalable Qubit Registers Based on Arrays of Dipole Traps

290

(1)

22.5 Initialization, Manipulation and Readout

291

(1)

22.6 Variation of Trap Separation

292

(1)

22.7 Implementation of Qubit Gates

293

(3)

References

296

(2)

23 Quantum Information Processing with Neutral Atoms on Atom Chips

P. Krüger, A. Haase, MAndersson, and J. Schmiedmayer

298

(14)

23.1 Introduction

298

(1)

23.2 The Atom Chip

298

(4)

23.2.1 Combined Magneto-Electric Traps

299

(1)

23.2.2 RF-induced Adiabatic Potentials for Manipulating Atoms

300

(1)

23.2.3 Imperfections in the Atom Chip: Disorder Potentials

301

(1)

23.3 The Qubit

302

(1)

23.4 Entangling Qubits

303

(2)

23.4.1 Quantum Gate via Cold Controlled Collisions

303

(2)

23.4.2 Motional Qubit Gates with Controlled Collisions

305

(1)

23.5 Input/Output

305

(2)

23.5.1 Qubit Detection

305

(2)

23.5.2 Quantum Input/Output

307

(1)

23.6 Noise and Decoherence

307

(1)

23.7 Summary and Conclusion

308

(1)

References

309

(3)

24 Quantum Gates and Algorithms Operating on Molecular Vibrations

U. Troppmann, C.M. Tesch, and R. de Vivie-Riedle

312

(15)

24.1 Introduction

312

(1)

24.2 Qubit States Encoded in Molecular Vibrations

313

(1)

24.3 Optimal Control Theory for Molecular Dynamics

313

(4)

24.3.1 Local Quantum Gates

315

(2)

24.4 Multi-target OCT for Global Quantum Gates

317

(1)

24.4.1 Global Quantum Gates for Molecular Vibrational Qubits

317

(1)

24.5 Basis Set Independence and Quantum Algorithms

318

(3)

24.6 Towards More Complex Molecular Systems

321

(3)

24.7 Outlook

324

(1)

References

325

(2)

25 Fabrication and Measurement of Aluminum and Niobium Based Single-Electron Transistors and Charge Qubits

W. Krech, D. Born, M. Mihalik, and M. Grajcar

327

(11)

25.1 Introduction

327

(1)

25.2 Motivation for this Work

328

(1)

25.3 Sample Preparation

329

(2)

25.3.1 Scheme of the Junction Preparation Technique

329

(1)

25.3.2 Fabrication of Tunnel Devices: SET and Charge Qubit Structures

330

(1)

25.4 Experimental Results

331

(2)

25.5 Conclusions

333

(2)

References

335

(3)

26 Quantum Dot Circuits for Quantum Computation

R.H. Blick, A.K. Hüttel, A.W. Holleitner, L. Pescini, and H. Lorenz

338

(15)

26.1 Introduction

338

(1)

26.2 Realizing Quantum Bits in Double Quantum Dots

339

(7)

26.3 Controlling the Electron Spin in Single Dots

346

(5)

26.4 Summary

351

(1)

References

351

(2)

27 Manipulation and Control of Individual Photons and Distant Atoms via Linear Optical Elements

X.-B. Zou and W. Mathis

353

(29)

27.1 Introduction

353

(1)

27.2 Manipulation and Control of Individual Photons via Linear Optical Elements

354

(16)

27.2.1 Teleportation Implementation of Non-deterministic NLS Gate and Single-mode Photon Filter

354

(5)

27.2.2 Implementation of Non-deterministic NLS Gate via Parametric Amplifiers

359

(1)

27.2.3 Phase Measurement of Light and Generation of Superposition of Fock States

360

(5)

27.2.4 Joint Measurement of Photon Number Sum and Phase Difference Operators on a Two-mode Field

365

(5)

27.2.5 Remark

370

(1)

27.3 Quantum Entanglement Between Distant Atoms Trapped in Different Optical Cavities

370

(9)

27.3.1 Generation of W States, GHZ States and Cluster States Based on Single-photon Detectors

370

(6)

27.3.2 Generation of W States and GHZ States Based on Four-photon Coincidence Detection

376

(3)

27.4 Conclusion

379

(1)

References

379

(3)

28 Conditional Linear Optical Networks

S. Scheel

382

(11)

28.1 Introduction

382

(1)

28.2 Measurement-induced Nonlinearities

383

(3)

28.2.1 Beam Splitters and Networks

384

(1)

28.2.2 Post-processing of Single-Photon Sources and Number-Resolving Detectors

385

(1)

28.3 Probability of Success and Permanents

386

(2)

28.4 Upper Bounds on Success Probabilities

388

(2)

28.5 Extension Using Weak Nonlinearities

390

(1)

References

391

(2)

29 Multiphoton Entanglement

M. Bourennane, M. Eibl, S. Gaertner, N. Kiesel, Ch. Kurtsiefer, M. Zukowski, and H. Weinfurter

393

(12)

29.1 Introduction

393

(1)

29.2 Entangled Multiphoton State Preparation

394

(1)

29.3 Experiment

395

(1)

29.4 Quantum Correlations

396

(2)

29.5 Bell Inequality

398

(2)

29.6 Genuine Four-photon Entanglement

400

(1)

29.7 Entanglement Persistence

400

(1)

29.8 Conclusions

401

(2)

References

403

(2)

30 Quantum Polarization for Continuous Variable Information Processing

N. Korolkova

405

(13)

30.1 Introduction

405

(1)

30.2 Nonseparability and Squeezing

406

(4)

30.2.1 Polarization Squeezing

406

(1)

30.2.2 Continuous Variable Polarization Entanglement

407

(3)

30.3 Applications

410

(3)

30.4 Stokes Operators Questioned: Degree of Polarization in Quantum Optics

413

(3)

References

416

(2)

31 A Quantum Optical XOR Gate

H. Becker, K. Schmid, W. Dultz, W. Martienssen, and H. Roskos

418

(7)

31.1 Introduction

418

(1)

31.2 Double Bump Photons

418

(2)

31.3 The XOR Gate

420

(3)

31.4 Quad Bump Photons

423

(1)

31.5 Outlook

424

(1)

References

424

(1)

32 Quantum Fiber Solitons - Generation, Entanglement, and Detection

G. Leuchs, N. Korolkova, O. Glöckl, St. Lorenz, T. Heersink, Ch. Silberhorn, Ch. Marquardt, and U.L. Andersen

425

(18)

32.1 Introduction

425

(1)

32.2 Quantum Correlations and Entanglement

426

(2)

32.3 Multimode Quantum Correlations

428

(3)

32.4 Generation of Bright Entangled Beams

431

(1)

32.5 Detection of Entanglement of Bright Beams

432

(3)

32.5.1 Sub-shot-noise Phase Quadrature Measurements on Intense Beams

432

(2)

32.5.2 Direct Experimental Test of Non-Separability

434

(1)

32.6 Entanglement Swapping

435

(2)

32.7 Polarization Variables

437

(2)

References

439

(4)

Index

443

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Quantum Information Processing

Summary

Author Biography

Table of Contents

Supplemental Materials