Quantum Entanglement and Information Processing (eBook)

Front Cover 1
Quantum Entanglement and Information Processing: Intrication Quantique Et Traitement De L'Information 4
Copyright Page 5
CONTENTS 20
Lecturers 10
Participants 12
Preface 16
Course 1. Principles of quantum computation 32
1. Introduction 36
2. Fundamentals: quantum mechanics and computer science 36
3. Quantum circuits 43
4. Entanglement as a physical resource 53
5. Information theory 63
6. Open quantum systems 71
7. Quantum error correction and fault tolerance 78
References 85
Course 2. Mesoscopic state superpositions and decoherence in quantum optics 86
1. An overview of quantum optics 91
2. Beam splitters and interferences in quantum optics 117
3. Schrödinger cats in cavity QED 143
4. Collapse and revivals of matter-waves: proposals for atomic Schrödinger cats 170
5. Conclusion: a brief comparison with other mesoscopic state superpositions in quantum optics 184
References 186
Course 3. Cavity quantum electrodynamics 192
1. Introduction 196
2. Microwave CQED experiments: The strong coupling regime 198
3. "Quantum logic" operations based on the vacuum Rabi oscillation 202
4. Step by step synthesis of a three particles entangled state 204
5. Direct atom-atom entanglement: cavity-assisted collision 211
6. Conclusion and perspectives 213
References 214
Course 4. Quantum optical implementation of quantum information processing 218
1. Introduction 222
2. Trapped ions 222
3. Atoms in optical lattices 233
4. Quantum information processing with atomic ensembles 239
5. Conclusions 250
References 251
Course 5. Quantum information processing in ion traps I 254
1. Introduction 258
2. Ion trap quantum computer- the concept 259
3. Physics of ion traps 261
4. Coherent manipulation of quantum information 270
5. Deutsch-Jozsa algorithm 276
6. Cirac-Zoller CNOT–gate operation 279
7. Entanglement and Bell state generation 283
8. Summary and perspectives 285
References 286
Course 6. Quantum information processing in ion traps II 292
1. Introduction 296
2. Linear RF (Paul) ion traps 297
3. Ion qubits 308
4. Stimulated Raman transitions 309
5. Multiple modes, multiple excited states 317
References 320
Course 7. Quantum cryptography with and without entanglement 326
1. Introduction 330
2. Intuitions 330
3. Experiments: a lesson in applied physics 332
4. Security 338
5. Conclusion 342
References 343
Course 8. Quantum cryptography: from one to many photons 346
1. Introduction 350
2. Single photons sources for quantum cryptography 350
3. Quantum key distribution using gaussian-modulated coherent states 356
4. Conclusion 362
References 364
Course 9. Entangled photons and quantum communication 368
1. Introduction 372
2. Distributing quantum entanglement 372
3. Quantum teleportation and entanglement swapping 375
4. Purification of entanglement 377
5. Quantum entanglement and information 379
References 384
Course 10. Nuclear magnetic resonance quantum computation 388
1. Nuclear magnetic resonance 392
2. NMR and quantum logic gates 399
3. NMR quantum computers 406
4. Robust logic gates 413
5. An NMR miscellany 421
6. Summary 427
Appendix A. Commutators and product operators 428
References 429
Course 11. Introduction to quantum conductors 432
1. Introduction 436
2. The scattering approach to quantum conduction 441
3. Electronic quantum noise 457
4. Quasi-particle entanglement in ballistics conductors 464
5. Conclusion 471
References 471
Course 12. Superconducting qubits 474
1. Introduction 478
2. Basic features of quantum integrated circuits 479
3. The simplest quantum circuit 483
4. The Josephson non-linear inductance 486
5. The quantum isolated Josephson junction 488
6. Why three basic types of Josephson qubits? 490
7. Qubit relaxation and decoherence 499
8. Readout of superconducting qubits 500
9. Coupling superconducting qubits 507
10. Can coherence be improved with better materials? 507
11. Concluding remarks and perspectives 508
12. Appendix 1: Quantum circuit theory 509
13. Appendix 2: Eigenenergies and eigenfunctions of the Cooper pair box 512
14. Appendix 3: Relaxation and decoherence rates for a qubit 512
References 514
Course 13. Superconducting qubits and the physics of Josephson junctions 518
1. Introduction 522
2. The nonlinear Josephson inductance 523
3. Phase, flux, and charge qubits 525
4. BCS theory and the superconducting state 528
5. The Josephson effect, derived from perturbation theory 533
6. The Josephson effect, derived from quasiparticle bound states 540
7. Generation of quasiparticles from nonadiabatic transitions 544
8. Quasiparticle bound states and qubit coherence 548
9. Summary 549
References 550
Course 14. Josephson quantum bits based on a Cooper pair box 552
1. Introduction 556
2. The Cooper pair box 557
3. The Cooper pair box as a quantum bit 565
4. Decoherence of Josephson charge qubits 574
5. Two-qubit-gates with capacitively coupled Cooper pair boxes 586
6. Conclusions 588
References 589
Course 15. Quantum tunnelling of magnetization in molecular nanomagnets 592
1. Introduction 596
2. Giant spin model for nanomagnets 598
3. Quantum dynamics of a dimer of nanomagnets 605
4. Environmental decoherence effects in nanomagnets 612
5. Conclusion 617
References 618
Course 16. Prospects for strong cavity quantum electrodynamics with superconducting circuits 622
1. Introduction 626
2. Brief review of cavity QED 626
3. Circuit implementation of cavity QED 628
4. Zero detuning 631
5. Large detuning: lifetime enhancement 632
6. Dispersive QND readout of qubit 633
7. Resonator as quantum bus: entanglement of multiple qubits 637
8. Summary and conclusions 638
References 639