Quantum computation and information: From theory to experiment

front-matter......Page 1
Introduction......Page 16
Formalization......Page 18
General Upper Bounds......Page 21
Relation With Learning Theory......Page 24
Tight Upper Bounds for Small M......Page 25
Classical Lower and Upper Bounds......Page 27
Concluding Remarks......Page 28
References......Page 29
Index......Page 31
Introduction......Page 32
Goldreich--Levin Problem and Biased Oracles......Page 34
The Model of Quantum Biased Oracles......Page 39
Basic Tools for Quantum Computation......Page 40
Quantum Biased Oracles With the Same Bias Factor......Page 41
Quantum Biased Oracles With Resettable Condition......Page 46
Lower Bounds of the Query Complexity of Biased Oracles......Page 47
Concluding Remarks......Page 52
References......Page 53
Index......Page 55
Introduction......Page 56
State Estimation in Pure State Family......Page 58
State Estimation for Covariant Pure States Family......Page 59
State Estimation in Gaussian States Family......Page 60
State Estimation in Nonregular Family......Page 62
Estimation of SU(2) Action With Entanglement......Page 63
Three-Parameter Case......Page 64
Hypothesis Testing of Entangled State......Page 65
Application of Quantum Hypothesis Testing......Page 66
Experimental Application of Quantum Statistical Inference......Page 67
Testing of Entangled State in the SPDC System......Page 68
Quantum Universal Compression......Page 69
References......Page 70
Index......Page 72
Buzek and Hillery Universal Quantum Cloning Machine......Page 73
Universal Quantum Cloning Machine for General d-Dimensional System, Werner Cloning Machine......Page 75
A UQCM for d-Dimensional Quantum State Proposed by Fan et al.......Page 76
Further Results About the UQCM......Page 77
UQCM for 2-Level System......Page 78
UQCM for d-Level System......Page 81
UQCM Realized in Real Physical Systems......Page 84
A 2 to 3 Universal Quantum Cloning for Mixed States......Page 89
Phase-Covariant Quantum Cloning Machine......Page 91
Transformation......Page 92
Hilbert--Schmidt Norm......Page 94
Bures Fidelity......Page 98
Quantum Cloning for x-y Equatorial Qubits......Page 100
Quantum Cloning Networks for Equatorial Qubits......Page 101
Separability......Page 103
Optimal Quantum Triplicators......Page 104
Optimal 1 to M Phase-Covariant Quantum Cloning Machines......Page 106
Some Known Results About Phase-Covariant Quantum Cloning Machine for Qubits and Qutrits......Page 108
Phase-Covariant Cloning of Qudits......Page 110
Cerf's Asymmetric Quantum Cloning Machine......Page 113
Duan and Guo Probabilistic Quantum Cloning Machine......Page 116
References......Page 117
Index......Page 119
Entanglement Distillation......Page 121
Exponents of Optimal Concentration......Page 122
Universal Entanglement Concentration......Page 123
Entanglement in Boson--Fock Space......Page 124
Computation of Distillable Entanglement of a Certain Class of Bipartite Mixed States......Page 125
Quantum Error Correction......Page 126
Background of Information Theory and Coding Theory......Page 127
Extensions......Page 128
Relation Between Teleportation and Entanglement Distillation......Page 129
Application to Quantum Key Distribution......Page 130
Concurrence Hierarchy......Page 131
Optimal Compression Rates and Entanglement of Purification......Page 132
Bell-Type Inequalities Via Combinatorial Approach......Page 133
Multipartite Entanglement......Page 134
Bipartite Entanglement in Infinite-Dimensional Space......Page 136
Remote State Preparation of Entangled State......Page 138
References......Page 139
Index......Page 142
Introduction......Page 143
Holevo Capacity, Output Minimum Entropy, and Maximum Output p-Norm......Page 144
Entanglement of Formation......Page 147
Channel States......Page 148
Strong Superadditivity and Additivity of Holevo Capacity......Page 150
Equivalence Theorem by Shor, and One More New Equivalent Additivity Question......Page 151
Group Symmetry......Page 153
Example 1......Page 156
Example 2......Page 157
Example 3......Page 158
Additivity of WH Channel......Page 159
Some Useful Facts......Page 163
Heuristic Construction of a Four-State Channel......Page 164
Approximation Algorithm to Compute the Holevo Capacity......Page 165
Numerical Verification of Four-State Channel......Page 166
Numerical Check of Additivity......Page 167
Strong Superadditivity of EoF of Pure States......Page 169
References......Page 171
Index......Page 174
Introduction......Page 175
Quantum One-Wayness of Permutations......Page 176
Worst-Case Characterization......Page 178
Average-Case Characterization......Page 179
Universal Tests......Page 183
Quantum Public-Key Cryptosystem......Page 184
Cryptographic Properties of QSCDff......Page 185
Reduction From the Worst Case to the Average Case......Page 186
Hardness of QSCDff......Page 187
Construction......Page 188
References......Page 190
Index......Page 192
General Model of Steganography System......Page 193
Model of Quantum Steganography System......Page 195
Comparison Between Classical and Quantum Steganography......Page 196
Index......Page 198
Introduction......Page 199
Cryptography......Page 200
Requirement for Single-Photon Detectors......Page 201
Improved Single-Photon Detector for Fiber Transmission......Page 202
Single-Photon Transmission Over 150 km in a Unidirectional System With Integrated Interferometers......Page 204
Temperature-Insensitive Interferometer......Page 207
High-Speed Operation......Page 209
Implementation and Experimental Results......Page 212
Effects of Imperfection......Page 214
Validity of Majority Voting......Page 216
Toward Quantum Computers......Page 218
Control-Unitary Gates......Page 219
Solid-State Bell State Measurement Devices by Two-Photon Absorption......Page 220
Generation of Entangled Photon Pairs by SPDC......Page 221
SPDC With Two-Crystal Geometry......Page 222
Interferometric Generation of Entangled Photon Pairs......Page 225
A New Material for SPDC: Periodically Poled KTP......Page 226
Conclusion......Page 228
References......Page 229
Index......Page 231
Index......Page 232