Contents

Introduction page 1

Part I Quantum information 3

1 Quantum bits and quantum gates 51.1 The Bloch sphere 61.2 Density matrices and Pauli matrices 81.3 Quantum logic gates 101.4 Quantum networks 131.5 Initialization and measurement 151.6 Experimental methods 17Further reading 17Exercises 17

2 An atom in a laser field 192.1 Time-dependent systems 192.2 Sudden jumps 202.3 Oscillating fields 222.4 Time-dependent perturbation theory 242.5 Rabi flopping and Fermi’s Golden Rule 252.6 Raman transitions 272.7 Rabi flopping and Ramsey fringes 292.8 Measurement and initialization 31Further reading 31Exercises 31

3 Spins in magnetic fields 333.1 The nuclear spin Hamiltonian 333.2 The rotating frame 353.3 On- and off-resonance excitation 373.4 The vector model 383.5 Spin echoes 393.6 Measurement and initialization 40Further reading 40Exercises 41

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4 Photon techniques 424.1 Spatial encoding 424.2 Polarization encoding 444.3 Single-photon sources and detectors 454.4 Conventions 46Further reading 46Exercises 47

5 Two qubits and beyond 485.1 Direct products 485.2 Matrix forms 495.3 Two-qubit gates 505.4 Networks and circuits 515.5 Entangled states 52Further reading 53Exercises 53

6 Measurement and entanglement 556.1 Measuring a single qubit 556.2 Ensembles and the no-cloning theorem 586.3 Fidelity 596.4 Local operations and classical communication 61Further reading 63Exercises 63

Part II Quantum computation 65

7 Principles of quantum computing 677.1 Reversible computing 677.2 Quantum parallelism 697.3 Getting the answer out 707.4 The DiVincenzo criteria 70Further reading 71Exercises 72

8 Elementary quantum algorithms 738.1 Deutsch’s algorithm 738.2 Why it works 758.3 Circuit identities 778.4 Deutsch’s algorithm and interferometry 788.5 Grover’s algorithm 788.6 Error correction 808.7 Decoherence-free subspaces 82Further reading 83Exercises 83

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9 More advanced quantum algorithms 859.1 The Deutsch–Jozsa algorithm 859.2 The Bernstein–Vazirani algorithm 879.3 Deutsch–Jozsa and period finding 889.4 Fourier transforms and quantum factoring 909.5 Grover’s algorithm 919.6 Generalizing Grover’s algorithm 949.7 Quantum simulation 969.8 Experimental implementations 97Further reading 97Exercises 98

10 Trapped atoms and ions 9910.1 Ion traps 9910.2 Atom traps and optical lattices 10010.3 Initialization 10210.4 Decoherence 10310.5 Universal logic 10410.6 Two-qubit gates with ions 10510.7 Two-qubit gates with atoms 10610.8 Massive entanglement 10910.9 Readout 110Further reading 111Exercises 111

11 Nuclear magnetic resonance 11311.1 Qubits 11311.2 Initialization 11511.3 Decoherence 11611.4 Universal logic 11611.5 Readout 119Further reading 122Exercises 122

12 Large-scale quantum computers 12412.1 Trapped ions 12412.2 Optical lattices 12512.3 NMR 12612.4 Other approaches 126Further reading 128

Part III Quantum communication 129

13 Basics of information theory 13113.1 Classical information 132

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13.2 Mutual information 13513.3 The communication channel 13713.4 Connection to statistical physics 138Further reading 139Exercises 139

14 Quantum information 14014.1 The density operator 14014.2 Global and local measurements 14214.3 Information content of a density operator 14414.4 Joint entropy and mutual information 14514.5 Quantum channels 146Further reading 150Exercises 151

15 Quantum communication 15215.1 Parametric down-conversion 15215.2 Quantum dense coding 15415.3 Quantum teleportation 15615.4 Entanglement swapping 159Further reading 161Exercises 161

16 Testing EPR 16316.1 Bell inequalities 16316.2 GHZ states 167Further reading 170Exercises 170

17 Quantum cryptography 17117.1 One-time pads and the Vernam cipher 17117.2 The BB84 protocol 17217.3 The Ekert91 protocol 17417.4 Experimental setups 175Further reading 177Exercises 178

Appendix: Quantummechanics 179

References 192Index 196

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Cambridge University Press978-1-107-01446-6 - Quantum Information, Computation and CommunicationJonathan A. Jones and Dieter JakschTable of ContentsMore information