Quantum information science is a rapidly expanding area of technology. This book offers an overview of this field for practitioners and students of quantum physics and information science. It provides information on quantum information processing and communication, such as definitions, protocols and algorithms.
This book is a comprehensive yet concise overview of quantum information science, which is a rapidly developing area of interdisciplinary investigation that now plays a significant role in physics, information technology and engineering. The most well-known applications of quantum information science are quantum key distribution and quantum computation. This book is a handy reference for practitioners and students covering foundational issues as well as these and other applications. It contains more than 25 illustrations that encapsulate essential ideas and fundamental constructs. It contains a Foreword by Prof. Tommaso Toffoli.
Foreword
vii
Preface
xi
Acknowledgments
xiii
Qubits
1
(28)
Quantum state purity
5
(3)
The representation of qubits
8
(3)
Stokes parameters
11
(3)
Single-qubit gates
14
(4)
The double-slit experiment
18
(5)
The Mach-Zehnder interferometer
23
(2)
Quantum coherence and information processing
25
(4)
Measurements and quantum operations
29
(16)
The von Neumann classification of processes
32
(2)
The Pauli classification of measurements
34
(1)
Expectation values and the von Neumann projection
35
(2)
The Luders rule
37
(1)
Reduced statistical operators
38
(1)
General quantum operations
39
(2)
Positive-operator-valued measures
41
(4)
Quantum nonlocality and interferometry
45
(22)
Hidden variables and state completeness
46
(2)
Von Neumann's ``no-go'' theorem
48
(1)
The Einstein--Podolsky--Rosen argument
49
(2)
Gleason's theorem
51
(1)
Bell inequalities
52
(5)
Interferometric complementarity
57
(4)
The Franson interferometer
61
(2)
Two-qubit quantum gates
63
(4)
Classical information and communication
67
(14)
Communication channels
68
(2)
Shannon entropy
70
(4)
Renyi entropy
74
(1)
Coding
74
(3)
Error correction
77
(1)
Data compression
78
(1)
Communication complexity
79
(2)
Quantum information
81
(10)
Quantum entropy
82
(2)
Quantum relative and conditional entropies
84
(1)
Quantum mutual information
85
(1)
Fidelity and coherent information
86
(2)
Quantum Renyi and Tsallis entropies
88
(3)
Quantum entanglement
91
(30)
Basic definitions
92
(2)
The Schmidt decomposition
94
(1)
Special bases and decompositions
95
(3)
Stokes parameters and entanglement
98
(1)
Partial transpose and reduction criteria
99
(2)
The ``fundamental postulate''
101
(1)
Entanglement monotones
102
(2)
Distillation and bound entanglement
104
(1)
Entanglement and majorization
105
(1)
Concurrence
106
(1)
Entanglement witnesses
107
(1)
Entanglement as a resource
108
(1)
The thermodynamic analogy
109
(3)
Information and the foundations of physics
112
(2)
The geometry of entanglement
114
(1)
Creating entangled photons
115
(6)
Entangled multipartite systems
121
(18)
Stokes and correlation tensors
124
(2)
N-tangle
126
(1)
Generalized Schmidt decomposition
127
(1)
Lorentz-group isometries
127
(2)
Entanglement classes
129
(2)
Algebraic invariants of multipartite systems
131
(2)
Three-qubit states and residual tangle
133
(2)
Three-qubit quantum logic gates
135
(1)
States of higher qubit number
136
(3)
Quantum state and process estimation
139
(8)
Quantum state tomography
140
(3)
Quantum process tomography
143
(1)
Direct estimation methods
144
(3)
Quantum communication
147
(24)
Quantum channels
148
(1)
Quantum channel capacities
149
(2)
Holevo's theorem
151
(2)
Discrimination of quantum states
153
(3)
The no-cloning theorem
156
(1)
Basic quantum channels
157
(2)
The GHJW theorem
159
(1)
Quantum dense coding
160
(2)
Quantum teleportation
162
(2)
Entanglement ``swapping''
164
(1)
Entanglement ``purification''
165
(2)
Quantum data compression
167
(2)
Quantum communication complexity
169
(2)
Quantum decoherence and its mitigation
171
(14)
Quantum decoherence
172
(1)
Decoherence and mixtures
173
(1)
Decoherence-free subspaces
174
(1)
Quantum coding, error detection, and correction
175
(4)
The nine-qubit Shor code
179
(2)
Stabilizer codes
181
(2)
Concatenation of quantum codes
183
(2)
Quantum broadcasting, copying, and deleting
185
(6)
Quantum broadcasting
185
(1)
Quantum copying
186
(3)
Quantum deleting
189
(1)
Landauer's principle
190
(1)
Quantum key distribution
191
(12)
Cryptography and cryptosystems
191
(2)
QKD systems
193
(2)
The BB84 (four-state) protocol
195
(2)
The E91 (Ekert) protocol
197
(1)
The B92 (two-state) protocol
198
(1)
The six-state protocol
199
(1)
Eavesdropping
199
(2)
Security proofs
201
(2)
Classical and quantum computing
203
(16)
Classical computing and computational complexity
204
(2)
Deterministic Turing machines
206
(1)
Probabilistic Turing machines
207
(1)
Multi-tape Turing machines
208
(1)
Quantum Turing machines
209
(2)
Quantum computational complexity
211
(3)
Fault-tolerant quantum computing
214
(1)
Linear optical quantum computation
215
(4)
Quantum algorithms
219
(12)
The Deutsch--Jozsa algorithm
220
(1)
The Grover search algorithm
221
(3)
The Shor factoring algorithm
224
(5)
The Simon algorithm
229
(2)
A. Mathematical elements
231
(14)
Boolean algebra and Galois fields
231
(1)
Random variables
232
(1)
Vector Spaces and Hilbert space
233
(4)
The standard quantum formalism
237
(1)
The Dirac notation
237
(2)
Groups of transformations
239
(1)
Probability, lattices, and posets
240
(2)
Projectors, correlations, and the Kochen--Specker theorem
242
(1)
Traditional quantum logic
243
(2)
B. The quantum postulates
245
(4)
The standard postulates
245
(2)
The Heisenberg--Robertson uncertainty relation
247
(1)
Liouville space and open quantum systems
248
(1)
References
249
(22)
Index
271
Dr. Jaeger is a professor at Boston University, where he earned his Ph.D. in Physics with Abner Shimony in 1995. He has published in a number of areas, including quantum computing, quantum cryptography, foundations of quantum mechanics, quantum metrology, and the history and philosophy of science. He was worked in academia and industry in the United States and Europe as a research director and investigator in quantum information science and quantum metrology. As a member of the Quantum Imaging Laboratory at Boston University's Photonics Center, along with colleagues at Harvard University and BBN Technologies, he helped build the world's first practical metropolitan area quantum cryptographic network, the DARPA Quantum Network Test-bed, serving as principal quantum entanglement theorist.
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