Quantum Processes Systems, and Information 1st Edition by Benjamin Schumacher (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review “This is a fantastic book, with one of the authors no less than the very inventor of the word and idea of a qubit. When I opened the book for the first time, I found I couldn’t stop reading through it and working out some of the problems. I should be ashamed to admit, but after 15 years as a professional quantum information theorist, I was still learning some elementary aspects of quantum mechanics. There’s no book out there I would recommend more for learning the mechanics of this quantum world.” Chris Fuchs, Perimeter Institute for Theoretical Physics”One of the most original and insightful introductions to quantum mechanics ever written, this book is also an excellent introduction to the emerging field of quantum information science.” Michael Nielsen, co-author of Quantum Computation and Quantum Information”Though the pioneers of quantum mechanics recognized that information encoded in quantum systems has counter-intuitive properties, the systematic development of quantum information theory began only relatively recently. Many quantum information concepts are both mathematically accessible and physically illuminating, yet until now have been omitted from introductory quantum mechanics textbooks. This superb new book by Ben Schumacher and Mike Westmoreland is perfectly suited for a modern undergraduate course on quantum mechanics that emphasizes fundamental notions from quantum information science, such as entanglement, Bell’s theorem, quantum teleportation, quantum cryptography, and quantum error correction. The authors, who are themselves important contributors to the subject, have complete mastery of the material, and they write clearly and engagingly. Schumacher and Westmoreland are equally effective at covering the more standard material included in other texts. Indeed, this book could be used successfully in a traditional quantum mechanics that shuns the rich insights quantum information theory can provide. But that would be a terrible shame.” John Preskill, California Institute of Technology”This is a wonderful book! It covers the usual topics of a first course in quantum mechanics and much more, and it does so with an unusual conceptual depth. The inclusion of information theoretic ideas not only enriches the presentation of the basic theory–for example in helping to articulate the conditions under which quantum coherence is lost–it also opens up the large area of physics in which both quantum mechanical and information theoretic concepts play central roles. On the basis of such concepts, the authors develop, for example, enough thermodynamics to derive the minimum thermodynamic cost of communication. Throughout the book, the writing is clear and engaging and the mathematics is treated carefully. Original insights abound.” William K Wootters, Williams College”With its comprehensive presentation of both quantum mechanics and QIC, this book, written by two pioneers of this emerging new approach to computing, is really one of a kind, something that the glowing editorial reviews on the book’s back cover, written by well-known experts, are eager to point out. Most concepts that one would find in traditional nonrelativistic quantum mechanics physics books are presented in a clear and well thought-out manner (but be prepared for a bit more work when dealing with subtle notions such as quantum relative entropy or mutual information). Quantum mechanics concepts introduced in traditional physics books that have been left out here, such as particle scattering, S-matrix, and Heisenberg’s formalism, are indeed less relevant in an introduction to QIC. The brilliant pedagogical approach taken by the authors, who are able to present quite abstract notions using a clear and sprightly style, together with the quality of the editing (I found very few typographical errors), will provide both students and researchers interested in the growing field of QIC with a pleasant and informative read. A final note, relevant in these days of e-reading craze: the quality of the paper chosen by the publisher for the hardcover edition of this book is a real visual and tactile treat.” P. Jouvelot, Computing Reviews”This textbook is, on the whole, a very impressive piece of work. It has clearly been refined over some time; the explanations and proofs that are scattered throughout the text are clearly written and elegant, and common themes are picked up repeatedly with increasing sophistication as the book goes along, without the earlier explanations seeming dumbed-down or inadequate. The exercises and problems are well-chosen to illustrate the ideas being explained. Overall, I found this book very impressive, and I think it could be adapted for a variety of undergraduate classes on quantum mechanics and quantum information. Moreover, I think it strongly shows that the case for teaching quantum mechanics by starting with simple, finite-dimensional systems is both practical and compelling. This book may well be the model for quantum mechanics classes of the future.” Todd A. Brun, Mathematical Reviews Book Description A new and exciting approach to the basics of quantum theory for undergraduate courses. Book Description 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. In addition to the standard topics covered in other textbooks, it covers communication and measurement, quantum entanglement, entropy and thermodynamics, and quantum information processing. About the Author Benjamin Schumacher is Professor of Physics at Kenyon College. He coined the term ‘qubit’ and 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. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Quite frankly, quite simply, this text remains a favorite–of the more recent publications, this text and the one written by Mark Beck (Quantum Mechanics, OUP, 2012)– battle for my attention. A cursory look at Fall 2022 undergraduate quantum physics courses offered at USA Universities shows that this text is not nearly well-enough known or utilized. What a pity ! This circumstance in 2022 ! Why so ?(1) Textbooks seem to come in two sizes: they are either too big or too small. Happily, not so here.You get twenty chapters spanning some 435 pages (excepting appendices). You get exercises (within sections) and you get problems (at the ends-of-chapters). That is excellent pedagogy (yes, I realize, Griffiths sort of does that too).(2) Happily, you will not get a mess of ambiguity focusing on linguistics. Read section #10.6 : “the wave-function is not a physical field like the air pressure…neither a field nor a probability distribution… it is a creature of a new and different sort.” (page 220).(3) While this book is not explicitly advertised for self-study, I feel that a student embarking on a program of study would be well-advised to study it. So, if this text is not required in your course, get it anyhow !If you can multiply 2X2 matrices and are familiar with the log function (in any base), then initial chapters will pose no issues (exercise 2.13, page 25, will ask you to verify through matrix multiplication). Read: “The particle can carry a ‘secret message’ encoded in its spin state. If we read the particle in the right way, the message is revealed.” (page 36). Information and Q-bits, these terms are introduced early and often.(4) Chapter three, that is the obligatory, compulsory, abstract mathematics (of Hilbert space). Amusingly, chapter three of Griffiths (1995, first edition) gets there too, around the same time (Linear Algebra). There is more pedagogy: “…the easiest way to prove a fact about abstract operators is to work with their matrix representations.” (page 64). More pedagogy: revisit spin one-half (pages 28-36) with more “justification.”(see, page 73). Chapter one started with information, chapter four continues that theme (pages 79-97).(5) Read: “In a measurement process, we extract information from a quantum system. But, what sort of information is it ? Exactly what does a measurement tell us ? Uncertainty relations are better thought of as “indeterminacy relations.” (page 96). Learn why the authors say that in chapter four. Pedagogy again is displayed page 103: utilize dimensional analysis (exercise 5.6). Now, read: “It is a curious thing that time is not itself an observable quantity in quantum theory. Find a nice discussion here (pages 105-107).(6) A problem introduces the so-called Baker-Campbell-Hausdorff identity (5.8, page 116). An excursion to entanglement is offered chapter six: “entanglement is generally the result of dynamical interaction.” (page 121). Bell’s theorem introduced: “we must either give up the idea that determinate hidden variables underlie the indeterminacy of quantum systems, or we must give up the idea that widely separated parts of the Universe act independently.” (page 133-135).(7) Chapter seven continues the theme of “information.” No-cloning theorem and teleportation are here.(8) I like exercise 8.17 (page 167). You are asked to compare the proof here to the previous encounter of the same proof ! That is, chapter eight will refer you back to chapter 4, basic de-coding theorem(page 82).Excellent pedagogy ! Ninth chapter, Open Systems. Read: “…we can often ignore the rest of the world..” (page 182). Here is wisdom: “The signs in equation 9.36 are a customary, if slightly confusing convention.”That is a recap of the ‘first law of thermodynamics.’ Section 9.4 (heat and work) is a thoughtful prelude.(9) Previous to chapter ten, we have been “discrete.” Time to get “continuous.” Reading: “….Infinity is just a simplified way of describing a quantity that is immense, but still finite.” (page 202). Herein Schrodinger equation and probability “flow.” (page 226). Problem 11.13 revisits your vector identities for the goal of showing a relation for “total probability.” (page 246). That is excellent pedagogy !(10) Generalizing spin is chapter 12: “…reverse our logic…” Here: elaboration of spin-angular- momentum. Brief introduction to isospin concludes the chapter. Learning a “conceptual puzzle” regards electrons and entanglement: “we have permission to think of two identical particles as distinct subsystems, provided that there is some physical observable that can be used as an effective label. (page 303). There is more of Schrodinger (in one-dimension) next (revisiting chapter 10 and 11). This material is situated later than is usual in many textbooks at undergraduate-level (for example: Griffiths chapter two). Three-dimensions, that means Hydrogen atom, up next (here page 342; Griffiths gets there early, page 134). Revisit quantum information in chapter 18 (pay close attention to figure 18.1, is there an error in the figure ?). A focus will be an introduction to dynamics, that is, quantum computing (information processing). Excellent !(11) Concluding: After an all too- lengthy review (I got excited all over again), I can only say, get the book and study it. Exposition is lucid. Exercises and problems are invaluable. The textbook is pedagogic and highly recommended !

⭐Best quantum mechanics textbook I have ever come across. This is a great introduction to quantum mechanics because of the way it addresses all of quantum theory through the lens of quantum information. Thinking from this point of view helps demystify concepts such as wave particle duality and the uncertainty principle which really helps beginners better understand quantum mechanics and gain intuition for quantum phenomena. This book is also great for someone who already knows a good deal of quantum mechanics, but don’t expect to find too much hardcore phenomenology. This book is really heavily invested in concepts rather than surveying and explaining in detail a great deal of complicated quantum mechanics experiments. I was into my fourth semester of quantum mechanics courses when I read this and I was struck by all the profound insights and exercises in this book. I have never before seen such a clear and compact look at thermodynamics and quantum information elsewhere. I have personally recommended this book to several of my peers.

⭐The only book you will need on quantum systems

⭐Excellent book with a number of fantastic exercises that support the material.

⭐Excellent introduction to the quantum theory for first acquaintace, but more, it goes deeply into the notions of information and information transfer. Very useful for entering the subject.

⭐Why isn’t this astonishingly beautiful book better known? It has a conceptual clarity that makes it deeper than any book I’ve seen on this level. And it includes modern ideas about quantum information. A superb book!

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