Quantum Processes Systems, and Information

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Cambridge University Press, Mar 25, 2010 - Science
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A new and exciting approach to the basics of quantum theory, this undergraduate textbook contains extensive discussions of conceptual puzzles and over 800 exercises and problems. Beginning with three elementary 'qubit' systems, the book develops the formalism of quantum theory, addresses questions of measurement and distinguishability, and explores the dynamics of quantum systems. In addition to the standard topics covered in other textbooks, it also covers communication and measurement, quantum entanglement, entropy and thermodynamics, and quantum information processing. This textbook gives a broad view of quantum theory by emphasizing dynamical evolution, and exploring conceptual and foundational issues. It focuses on contemporary topics, including measurement, time evolution, open systems, quantum entanglement, and the role of information.
 

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Howard M. Wiseman,
“Benjamin Schumacher and Michael Westmoreland: Quantum Processes, Systems, & Information”
Quantum Information Processing 9, 749–751 (2010).
This book promotes information as
the core concept underlying a proper appreci- ation of quantum theory. Given this, it is ironic that the authors’ perpetuate, on page 2, one of the great myths in information transmission: that Paul Revere cried, on his midnight ride of 18th April 1775, “the British are coming!” (The American colonists at this time still considered themselves to be British. According to eyewitness accounts of the ride and Revere’s own descriptions, his cry was “The Regulars are coming out.” [1]) This historical slip aside, choosing such a dramatic illustration of the nature of information — a message (that the Regulars were staying put in Boston, that they were marching down the Neck, or that they were crossing the harbour by boat) that can be encoded into a signal (zero, one, or two lamps hung in a Boston church steeple), and that it can be transformed (into the thoughts and actions of Revere and others that night) – is an inspired start to an inspiring book.
Schumacher and Westmoreland are both eminent researchers in quantum informa- tion theory. The former has the distinction of having coined the term qubit [2] (only 15 years ago!) in the same paper that introduced quantum data compression. This book however is not a research monograph in quantum information. Rather it is, as the authors say, “designed to be both an undergraduate textbook on quantum mechanicsand an exploration of the physical meaning and significance of information.” Having read the book, I have to agree with them that “attention to both subjects can lead to a deeper understanding of both.” A bright undergraduate would get a tremendous grounding in modern quantum theory from reading this book, and solving the problems therein. So would many postgraduate students and academics wanting to get into the heart of quantum information research. Whether it can be easily used, in its entirety, as the basis for a first serious undergraduate course in quantum mechanics, remains to be tested.
The authors are well aware that working through the whole book would be a formidable task at an undergraduate level. For this reason, there is a clear delineation into three divisions. The first, which the authors call Part I (chapters 1-5), is the basic theory. As noted above, this begins with information, and only then moves on to quanta, qubits, and the formalism of finite Hilbert spaces. From the basic theory, the course could then take two possible directions: the “upper track” (the quantum information track) or the “lower track” (a more-or-less conventional quantum mechanics course). The authors divide the “upper track” into Part II (chapters 6-9) — the extension of the theory to entangled states, ebits, open systems and thermodynamics — and Part V (chapters 18-20) — advanced quantum information, including gates, data compression, and error correction. Similarly they divide the “lower track” into Part III (chapters 10- 14) — the infinite dimensional systems that are traditionally introduced very early (i.e. wavefunctions), plus angular momentum, harmonic oscillators and identical particles — and Part IV (chapters 15-17) — stationary states, including the Hydrogen atom and perturbation theory.
Perhaps it is just because my undergraduate quantum mechanics education (which predated the quantum information revolution of the mid-90s) was firmly on the “lower track”, but it seems to me that the level of mathematical sophistication and abstract thought required to tackle Part V was considerably above that of the rest of the book. While coherent information and the quantum Fano inequality are doubtless the most general way to approach quantum error correction (section 20.3), an undergraduate course instructor would probably have more success starting with the simple 3-qubit code, which is introduced (eventually) in section 20.4
 

Contents

2Qubits
15
States and observables
47
Distinguishability and information
79
Quantum dynamics
98
Information and ebits
140
Density operators
158
9Opensystems
182
A particle in space
202
Stationary states in 1D
306
Bound states in 3D
335
Perturbation theory
349
Quantum information processing
366
Classical and quantum entropy
392
Error correction
419
Appendix A Probability
437
Appendix B Fourier facts
444

Dynamics of a free particle
224
Spin and rotation
247
Ladder systems
268
Many particles
282
Gaussian functions
451
Index
463
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About the author (2010)

Benjamin Schumacher is Professor of Physics at Kenyon College. He coined the term ubitand invented quantum data compression, among other contributions to quantum information theory.

Michael D. Westmoreland is Professor of Mathematics at Denison University. Trained as an algebraist, for many years he has researched nonstandard logics, models of computation, and quantum information theory.

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