Quantum information and computing

Masanori Ohya, N. Watanabe9812566147, 9789812566140, 9789812774491

Table of contents :
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