Introduction to Optical Quantum Information Processing

by Pieter Kok , Brendon W. Lovett

• ISBN13: 9780521519144
• ISBN10: 0521519144
• Format: Hardcover
• Copyright: 2010-05-31
• Publisher: Cambridge University Press

Summary

Quantum information processing offers fundamental improvements over classical information processing, such as computing power, secure communication, and high-precision measurements. However, the best way to create practical devices is not yet known. This textbook describes the techniques that are likely to be used in implementing optical quantum information processors. After developing the fundamental concepts in quantum optics and quantum information theory, the book shows how optical systems can be used to build quantum computers according to the most recent ideas. It discusses implementations based on single photons and linear optics, optically controlled atoms and solid-state systems, atomic ensembles, and optical continuous variables. This book is ideal for graduate students beginning research in optical quantum information processing. It presents the most important techniques of the field using worked examples and over 120 exercises.

Author Biography

Pieter Kok is a Lecturer in Theoretical Physics in the Department of Physics and Astronomy, the University of Sheffield. He is a member of the Institute of Physics and the American Physical Society, and his Ph.D. thesis won the Institute of Physics Quantum Electronics and Photonics thesis award in 2001.
Brendon W. Lovett is a Royal Society University Research Fellow in the Department of Materials and a Fellow of St Anne's College at the University of Oxford. He is a member of the Institute of Physics. He has been a visiting Fellow at the University of Queensland, Australia, and is an Academic Visitor at the National University of Singapore.

Table of Contents

Preface	p. xi
Quantum optics and quantum information
The quantum theory of light	p. 3
The classical electromagnetic field	p. 3
Quantization of the electromagnetic field	p. 6
Mode functions and polarization	p. 16
Evolution of the field operators	p. 25
Quantum states of the electromagnetic field	p. 37
References and further reading	p. 46
Quantum information processing	p. 48
Quantum information	p. 48
Quantum communication	p. 57
Quantum computation with qubits	p. 62
Quantum computation with continuous variables	p. 80
References and further reading	p. 89
Figures of merit	p. 90
Density operators and superoperators	p. 90
The fidelity	p. 100
Entropy, information, and entanglement measures	p. 101
Correlation functions and interference of light	p. 105
Photon correlation measurements	p. 108
References and further reading	p. 110
Quantum information in photons and atoms
Photon sources and detectors	p. 113
A mathematical model of photodetectors	p. 113
Physical implementations of photodetectors	p. 121
Single-photon sources	p. 129
Entangled photon sources	p. 139
Quantum non-demolition photon detectors	p. 142
References and further reading	p. 144
Quantum communication with single photons	p. 145
Photons as information carriers	p. 145
Quantum teleportation and entanglement swapping	p. 162
Decoherence-free subspaces for communication	p. 170
Quantum cryptography	p. 172
References and further reading	p. 177
Quantum computation with single photons	p. 179
Optical N-port interferometers and scalability	p. 179
Post-selection and feed-forward gates	p. 181
Building quantum computers with probabilistic gates	p. 192
Photon counting and quantum memories	p. 202
Threshold theorem for linear-optical quantum computing	p. 207
References and further reading	p. 209
Atomic quantum information carriers	p. 210
Atomic systems as qubits	p. 210
The Jaynes-Cummings Hamiltonian	p. 222
The optical master equation and quantum jumps	p. 227
Entangling operations via path erasure	p. 236
Other entangling gates	p. 245
References and further reading	p. 251
Quantum information in many-body systems
Quantum communication with continuous variables	p. 255
Phase space in quantum optics	p. 255
Continuous-variable entanglement	p. 267
Teleportation and entanglement swapping	p. 272
Entanglement distillation	p. 280
Quantum cryptography	p. 281
References and further reading	p. 293
Quantum computation with continuous variables	p. 294
Single-mode optical qunat gates	p. 294
Two-mode Gaussian qunat operations	p. 299
The Gottesman-Knill theorem for qunats	p. 303
Nonlinear optical qunat gates	p. 307
The one-way model for qunats	p. 309
Quantum error correction for qunats	p. 318
References and further reading	p. 326
Atomic ensembles in quantum information processing	p. 327
An ensemble of identical two-level atoms	p. 327
Electromagnetically induced transparency	p. 337
Quantum memories and quantum repeaters	p. 344
The atomic ensemble as a single qubit	p. 352
Photon-photon interactions via atomic ensembles	p. 355
References and further reading	p. 360
Solid-state quantum information carriers	p. 361
Basic concepts of solid-state systems	p. 361
Definition and optical manipulation of solid-state qubits	p. 375
Interactions in solid-state qubit systems	p. 381
Entangling two-qubit operations	p. 384
Scalability of solid-state devices	p. 393
References and further reading	p. 395
Decoherence of solid-state qubits	p. 397
Phonons	p. 397
Electron-phonon coupling	p. 400
The master equation for electrons and phonons	p. 403
Overcoming decoherence	p. 406
Strong coupling effects	p. 412
References and further reading	p. 419
Quantum metrology	p. 421
Parameter estimation and Fisher information	p. 421
The statistical distance	p. 425
The dynamical evolution of states	p. 433
Entanglement-assisted parameter estimation	p. 437
Optical quantum metrology	p. 440
References and further reading	p. 452
Baker-Campbell-Haussdorff relations	p. 454
The Knill-Laflamme-Milburn protocol	p. 457
Cross-Kerr nonlinearities for single photons	p. 462
References	p. 465
Index	p. 477
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