Quantum information and computing

Contents......Page 8
Preface......Page 6
1 Introduction......Page 14
2 An atom in a laser field......Page 16
3 The stochastic limit......Page 18
4 The quantum master equation......Page 22
5 Stationary states for a two-level atom......Page 23
6 Stationary states for a three-level atom......Page 25
7 Three-level lambda-atom......Page 27
8 Two-level 3-times degenerate atom......Page 28
9 Conclusions......Page 29
References......Page 30
1 Emergence of white noise equations from classical quantum mechanics......Page 31
2 Quantum white noise unitary evolutions......Page 33
3 Higher powers of white noise......Page 35
4 Appplications to quantum stochastic control......Page 36
References......Page 39
1 Introduction......Page 41
2 A master equation driving to a pre-assigned state......Page 43
3 A microscopic model......Page 44
4 The Master equation......Page 45
5 Assimilation of the state......Page 48
6 Purification......Page 52
7 Example: Entangled state with Spin-Boson model......Page 53
References......Page 58
Logical Operations Realized on the Ising Chain of N Qubits......Page 59
1 Introduction......Page 65
3 Product Extension......Page 66
4 A Pair of Pure and General States for Two Subsystems......Page 68
5 Examples......Page 70
References......Page 71
1 Inroduction......Page 72
2 The Model......Page 73
3 Quantum Filtering......Page 75
4 Control......Page 78
References......Page 81
1 Introduction and the result......Page 85
2 Proof sketch of Theorems 1.1 and 1.2......Page 89
3 An example......Page 92
References......Page 93
1 Introduction......Page 94
2 Generalities and notation......Page 95
3 Control procedures......Page 98
4 The Zeno subspaces......Page 105
5 Summary and concluding remarks......Page 106
References......Page 108
1 Introduction......Page 110
2 CH inequality for the full counting statistics......Page 112
3 Results......Page 114
References......Page 124
1 Introduction......Page 126
2 Basic Notions and Notations......Page 127
3 Teleportation scheme with tests 4......Page 134
4 Teleportation and fidelity......Page 135
References......Page 142
Quantum Logical Gates Realized by Beam Splittings......Page 144
1 Introduction......Page 145
2 The Boson Fock Space......Page 147
3 A General Beam Splitting Model......Page 150
4 The Splitting Procedures......Page 155
5 Splitting Functions fulfilling the Truth Table......Page 156
References......Page 159
1 Introduction......Page 162
2 Axiomatic Properties of Relative Information......Page 163
3 Examples of Relative Information for States......Page 165
4 Relative Information for Channels......Page 169
References......Page 176
0 Introduction......Page 180
1 Extended Chentsov Theorem for noncommutative (finite-dimensional matrix) manifolds......Page 182
2 Derivation and Frechet differentiation......Page 184
3 Classical and quantum a-divergence......Page 185
4 Proof of the uniqueness for matrix manifolds-Main theorem in the nonparametric version......Page 188
5 Parametrization of the matrix manifold......Page 191
6 A Concluding Remark-on Tsallis statistics......Page 192
References......Page 193
1 Introduction......Page 194
2 d-dimensional Brownian motions......Page 195
References......Page 198
2 White noise analysis......Page 199
4 Innovation......Page 201
References......Page 207
2 White noise analysis......Page 208
4 Innovation......Page 210
5 Path integrals......Page 212
References......Page 215
1 Introduction......Page 217
2 Generalized Quantum Turing Machine......Page 218
3 SAT Problem......Page 223
4 SAT Algorithm......Page 226
5 SAT algorithm in GQTM......Page 231
References......Page 237
1 Introduction......Page 239
2 Polynomial Representation of Flows......Page 242
3 The Minimal Number of Observables for Qudits Governed by Gaussian Semigroups......Page 244
References......Page 247
1 Introduction......Page 248
2 A Class of Positive Maps in Mn......Page 250
References......Page 256
1 Introduction......Page 258
2 Quantum Brownian motion: the exact dynamics......Page 260
3 Time evolution of the mean energy: Lindblad-type and non-Lindblad-type dynamics......Page 263
4 Experiment for simulating QBM with trapped ions......Page 266
References......Page 269
1 Introduction......Page 272
2 General Framework of Purification Through Repeated Measurements......Page 273
3 Purification of a Qubit......Page 276
4 Entanglement Distillation I......Page 278
5 Entanglement Distillation II......Page 281
6 Summary......Page 284
References......Page 285
1 Unified scheme for micro and macro......Page 287
2 Broken symmetry in micro-macro composite system; B=order parameter of broken scale inv.......Page 291
3 Summary and outlook: method of "variation of natural constants"......Page 296
References......Page 297
1 Introduction......Page 298
2 Strong subadditivity of entropy......Page 299
3 Quantum Markov states......Page 301
References......Page 303
1 Introduction......Page 305
2 Basic Elememts of White Noise Calculus......Page 306
3 The Levy Laplacian Acting on Levy White Noise Functionals......Page 308
4 The Levy Laplacian Acting on WNF-valued Functions......Page 310
5 An Infinite Dimensional Stochastic Process Associated with the Levy Laplacian......Page 311
References......Page 314
1 Introduction......Page 317
2 An illustrative example Linear functionals of Poisson noise......Page 318
3 Innovation of a linear process......Page 319
4 Determination of kernels......Page 321
References......Page 324
Group Theory of Dynamical Maps......Page 326
2 Quantum Analysis......Page 337
3 Quantum Transfer-Matrix Method based on Exponential Product Formulas and its Connection with Quantum Information......Page 339
4 Effective Information Entropy......Page 341
5 Summary and Discussion......Page 342
References......Page 343
1 Introduction......Page 345
2 Model......Page 346
3 Stochastic Limit Approach......Page 348
4 Nonequilibrium Steady States in C*-algebraic Approach......Page 349
5 Weak coupling limits......Page 355
6 Summary and Discussion......Page 356
References......Page 363
1 Introduction......Page 365
2 Formulation......Page 366
3 Numerical evaluation......Page 368
4 Discussion and Concluding Remarks......Page 370
References......Page 372
1 Entanglement......Page 373
2 Quantum Key Distribution using Polarization Entangled Photons......Page 376
3 Purification of Entanglement......Page 379
References......Page 382
On Quantum Mutual Type Measures and Capacity......Page 383
1 Quantum Channels......Page 384
2 Ohya Mutual Entropy......Page 388
3 Comparison of various quantum mutual type entropies......Page 390
4 Quantum Capacity......Page 392
References......Page 395