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Classical and 3d Quantum Information | |
Classical information | p. 3 |
Information and physics | p. 3 |
Quantifying information | p. 4 |
Data compression | p. 7 |
Related measures of information | p. 8 |
Relative entropy | p. 9 |
Joint entropy | p. 10 |
Conditional entropy | p. 10 |
Mutual information | p. 10 |
Capacity of a noisy channel | p. 11 |
Summary | p. 12 |
Quantum mechanics | p. 14 |
Dirac notation | p. 14 |
The qubit, higher dimensions, and the inner product | p. 16 |
Hilbert spaces | p. 17 |
Projective measurements and operations | p. 19 |
Unitary operations | p. 20 |
Eigenvectors and eigenvalues | p. 21 |
Spectral decomposition | p. 22 |
Applications of the spectral theorem | p. 23 |
Dirac notation shorthands | p. 24 |
The Mach-Zehnder interferometer | p. 25 |
The postulates of quantum mechanics | p. 27 |
Mixed states | p. 28 |
Entanglement | p. 29 |
Summary | p. 30 |
Quantum information-the basics | p. 31 |
No cloning of quantum bits | p. 31 |
Quantum cryptography | p. 33 |
The trace and partial-trace operations | p. 35 |
Hilbert space extension | p. 37 |
The Schmidt decomposition | p. 38 |
Generalized measurements | p. 40 |
CP-maps and positive operator-valued measurements | p. 41 |
The postulates of quantum mechanics revisited | p. 42 |
Summary | p. 42 |
Quantum communication with entanglement | p. 44 |
Pure state entanglement and Pauli matrices | p. 44 |
Dense coding | p. 45 |
Teleportation | p. 46 |
Entanglement swapping | p. 48 |
No instantaneous transfer of information | p. 49 |
The extended-Hilbert-space view | p. 50 |
Summary | p. 50 |
Quantum information I | p. 52 |
Fidelity | p. 53 |
Helstrom's discrimination | p. 54 |
Quantum data compression | p. 55 |
Entropy of observation | p. 58 |
Conditional entropy and mutual information | p. 59 |
Relative entropy | p. 61 |
Statistical interpretation of relative entropy | p. 62 |
Summary | p. 66 |
Quantum information II | p. 68 |
Equalities and inequalities related to entropy | p. 68 |
The Holevo bound | p. 71 |
Capacity of a bosonic channel | p. 73 |
Information gained through measurements | p. 75 |
Relative entropy and thermodynamics | p. 76 |
Entropy increase due to erasure | p. 77 |
Landauer's erasure and data compression | p. 78 |
Summary | p. 78 |
Quantum Entanglement | |
Quantum entanglement-introduction | p. 81 |
The historical background of entanglement | p. 81 |
Bell's inequalities | p. 83 |
Separable states | p. 85 |
Pure states and Bell's inequalities | p. 86 |
Mixed states and Bell's inequalities | p. 87 |
Entanglement in second quantization | p. 87 |
Summary | p. 91 |
Witnessing quantum entanglement | p. 92 |
Entanglement witnesses | p. 93 |
The Jamiolkowski isomorphism | p. 95 |
The Peres-Horodecki criterion | p. 97 |
More examples of entanglement witnesses | p. 99 |
Summary | p. 100 |
Quantum entanglement in practice | p. 102 |
Measurements with a Mach-Zehnder interferometer | p. 102 |
Interferometric implementation of Peres-Horodecki criterion | p. 104 |
Measuring tr <$$$>2? | p. 104 |
Generalization to tr <$$$>k | p. 105 |
Measuring tr (<$$$>T2)k | p. 106 |
Measuring the fidelity between <$$$> and ¿ | p. 106 |
Summary | p. 107 |
Measures of entanglement | p. 108 |
Distillation of multiple copies of a pure state | p. 108 |
Analogy with the Carnot Cycle | p. 110 |
Properties of entanglement measures | p. 111 |
Entanglement of pure states | p. 113 |
Entanglement of mixed states | p. 113 |
Measures of entanglement derived from relative entropy | p. 117 |
Classical information and entanglement | p. 121 |
Entanglement and thermodynamics | p. 123 |
Summary | p. 128 |
Quantum Computation | |
Quantum algorithms | p. 131 |
Computational complexity | p. 131 |
Deutsch's algorithm | p. 133 |
Deutsch's algorithm and the Holevo bound | p. 135 |
Oracles | p. 136 |
Grover's search algorithm | p. 137 |
Quantum factorization | p. 140 |
Factorization | p. 141 |
The quantum Fourier transform | p. 142 |
Phase estimation | p. 144 |
Summary | p. 145 |
Entanglement, computation and quantum measurements | p. 146 |
Optimization of searches using entanglement | p. 147 |
Model for quantum measurement | p. 149 |
Correlations and quantum measurement | p. 151 |
The ultimate limits of computation: the Bekenstein bound | p. 157 |
Summary | p. 158 |
Quantum error correction | p. 160 |
Introduction | p. 160 |
A simple example | p. 160 |
General conditions | p. 162 |
Reliable quantum cumputation | p. 165 |
Quantum error correction considered as a Maxwell's demon | p. 167 |
Pure states | p. 171 |
Mixed states | p. 172 |
Summary | p. 173 |
Outlook | p. 175 |
Bibliography | p. 179 |
Index | p. 181 |
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