Quantum Information, Computation and Communication

✍ Scribed by Jonathan A. Jones, Dieter Jaksch

• Publisher: Cambridge University Press
• Year: 2012
• Tongue: English
• Leaves: 210
• Category: Library

✦ Synopsis

Quantum physics allows entirely new forms of computation and cryptography, which could perform tasks currently impossible on classical devices, leading to an explosion of new algorithms, communications protocols and suggestions for physical implementations of all these ideas. As a result, quantum information has made the transition from an exotic research topic to part of mainstream undergraduate courses in physics. Based on years of teaching experience, this textbook builds from simple fundamental concepts to cover the essentials of the field. Aimed at physics undergraduate students with a basic background in quantum mechanics, it guides readers through theory and experiment, introducing all the central concepts without getting caught up in details. Worked examples and exercises make this useful as a self-study text for those who want a brief introduction before starting on more advanced books. Solutions are available online at www.cambridge.org/9781107014466.

✦ Table of Contents

Cover
......Page 1
Quantum Information, Computation and Communication......Page 3
Title......Page 5
Copyright......Page 6
Contents......Page 7
Introduction......Page 11
PART I: QUANTUM INFORMATION......Page 13
1: Quantum bits and quantum gates......Page 15
1.1 The Bloch sphere......Page 16
1.2 Density matrices and Pauli matrices......Page 18
1.3 Quantum logic gates......Page 20
1.4 Quantum networks......Page 23
1.5 Initialization and measurement......Page 25
Exercises......Page 27
2.1 Time-dependent systems......Page 29
2.2 Sudden jumps......Page 30
2.3 Oscillating fields......Page 32
2.4 Time-dependent perturbation theory......Page 34
2.5 Rabi flopping and Fermi's Golden Rule......Page 35
2.6 Raman transitions......Page 37
2.7 Rabi flopping and Ramsey fringes......Page 39
Exercises......Page 41
3.1 The nuclear spin Hamiltonian......Page 43
3.2 The rotating frame......Page 45
3.3 On- and off-resonance excitation......Page 47
3.4 The vector model......Page 48
3.5 Spin echoes......Page 49
Further reading......Page 50
Exercises......Page 51
4.1 Spatial encoding......Page 52
4.2 Polarization encoding......Page 54
4.3 Single-photon sources and detectors......Page 55
Further reading......Page 56
Exercises......Page 57
5.1 Direct products......Page 58
5.2 Matrix forms......Page 59
5.3 Two-qubit gates......Page 60
5.4 Networks and circuits......Page 61
5.5 Entangled states......Page 62
Exercises......Page 63
6.1 Measuring a single qubit......Page 65
6.2 Ensembles and the no-cloning theorem......Page 68
6.3 Fidelity......Page 69
6.4 Local operations and classical communication......Page 71
Exercises......Page 73
PART II: QUANTUM COMPUTATION......Page 75
7.1 Reversible computing......Page 77
7.2 Quantum parallelism......Page 79
7.4 The DiVincenzo criteria......Page 80
Further reading......Page 81
Exercises......Page 82
8.1 Deutsch's algorithm......Page 83
8.2 Why it works......Page 85
8.3 Circuit identities......Page 87
8.5 Grover's algorithm......Page 88
8.6 Error correction......Page 90
8.7 Decoherence-free subspaces......Page 92
Exercises......Page 93
9.1 The Deutsch–Jozsa algorithm......Page 95
9.2 The Bernstein–Vazirani algorithm......Page 97
9.3 Deutsch–Jozsa and period finding......Page 98
9.4 Fourier transforms and quantum factoring......Page 100
9.5 Grover's algorithm......Page 101
9.6 Generalizing Grover's algorithm......Page 104
9.7 Quantum simulation......Page 106
Further reading......Page 107
Exercises......Page 108
10.1 Ion traps......Page 109
10.2 Atom traps and optical lattices......Page 110
10.3 Initialization......Page 112
10.4 Decoherence......Page 113
10.5 Universal logic......Page 114
10.6 Two-qubit gates with ions......Page 115
10.7 Two-qubit gates with atoms......Page 116
10.8 Massive entanglement......Page 119
10.9 Readout......Page 120
Exercises......Page 121
11.1 Qubits......Page 123
11.2 Initialization......Page 125
11.4 Universal logic......Page 126
11.5 Readout......Page 129
Exercises......Page 132
12.1 Trapped ions......Page 134
12.2 Optical lattices......Page 135
12.4 Other approaches......Page 136
Further reading......Page 138
PART III: QUANTUM COMMUNICATION......Page 139
13: Basics of information theory......Page 141
13.1.1 Quantifying classical information......Page 142
13.1.2 Shannon's noiseless coding theorem......Page 143
13.2 Mutual information......Page 145
13.3 The communication channel......Page 147
13.4 Connection to statistical physics......Page 148
Exercises......Page 149
14.1 The density operator......Page 150
14.1.2 Entangled states......Page 151
14.2 Global and local measurements......Page 152
14.3.1 Schumacher's quantum noiseless channel coding theorem......Page 154
14.4 Joint entropy and mutual information......Page 155
14.5.1 Dephasing channel......Page 156
14.5.2 Amplitude damping channel......Page 158
Further reading......Page 160
Exercises......Page 161
15.1.1 Momentum entanglement......Page 162
15.1.2 Polarization entanglement......Page 163
15.2 Quantum dense coding......Page 164
15.2.1 Experimental setup......Page 165
15.3 Quantum teleportation......Page 166
15.3.1 Experimental setup......Page 168
15.4 Entanglement swapping......Page 169
Exercises......Page 171
16.1 Bell inequalities......Page 173
16.1.1 The CHSH inequality......Page 174
16.1.2 The Aspect experiments......Page 175
16.1.3 Loopholes......Page 176
16.2.1 Local realistic analysis......Page 177
16.2.3 Experimental realization......Page 178
Exercises......Page 180
17.1 One-time pads and the Vernam cipher......Page 181
17.2 The BB84 protocol......Page 182
17.2.1 Intercept–resend strategy......Page 183
17.3 The Ekert91 protocol......Page 184
17.4 Experimental setups......Page 185
17.4.1 Phase-encoded fiber systems......Page 186
Further reading......Page 187
Exercises......Page 188
A.1 Hilbert space......Page 189
A.2 Dirac notation......Page 190
A.3 Operators......Page 191
A.4 Vectors and matrices......Page 192
A.5 Eigenvalues and eigenvectors......Page 194
A.6 Operator trace......Page 195
A.7 Hermitian operators......Page 196
A.9 Unitary operators......Page 197
A.10 Operator exponentials......Page 198
A.11 Analytical functions of operators......Page 199
A.13 Time-dependent Hamiltonians......Page 200
Further reading......Page 201
References......Page 202
Index......Page 206