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{{short description|1993 physics textbook by Asher Peres}}

{{italic title}}

{{Infobox book

'''''Quantum Theory: Concepts and Methods''''' is a 1993 [[quantum physics]] textbook by [[Asher Peres]].

| author = [[Asher Peres]]

| isbn =

| pub_date = 1993

| subject = [[Quantum mechanics]]

| publisher = Kluwer Academic Publishers

| language = English

| image = File:Quantum_Theory,_Concepts_and_Methods.jpeg

}}

'''''Quantum Theory: Concepts and Methods''''' is a 1993 [[quantum physics]] textbook by Israeli physicist [[Asher Peres]]. Well-regarded among the physics community, it is known for unconventional choices of topics to include.

==Contents==

In his preface, Peres summarized his goals as follows:

:<blockquote>The purpose of this book is to clarify the ''conceptual meaning'' of quantum theory, and to explain some of the mathematical methods that it utilizes. This text is not concerned with specialized topics such as atomic structure, or strong or weak interactions, but with the very foundations of the theory. This is not, however, a book on the [[philosophy of science]]. The approach is pragmatic and strictly instrumentalist. This attitude will undoubtedly antagonize some readers, but it has its own logic: quantum phenomena do not occur in a [[Hilbert space]], they occur in a laboratory.{{efn|Preface, p. xi. The last remark is often quoted,<ref>{{Cite journal|last=Gilligan-Lee|first=Ciarán M|date=2021-10-01|title=Computation in a general physical setting|url=https://iopscience.iop.org/article/10.1088/1751-8121/ac2007|journal=[[Journal of Physics A: Mathematical and Theoretical]]|volume=54|issue=39|pages=394001|arxiv=2108.11454|bibcode=2021JPhA...54M4001G|doi=10.1088/1751-8121/ac2007|s2cid=237304127 |issn=1751-8113}}</ref> for example by [[Časlav Brukner|Brukner]] and [[Anton Zeilinger|Zeilinger]]<ref>{{cite book|last1=Brukner|first1=Časlav|chapter=Information and Fundamental Elements of the Structure of Quantum Theory|date=2003|chapter-url=http://link.springer.com/10.1007/978-3-662-10557-3_21|title=Time, Quantum and Information|pages=323–354|editor-last=Castell|editor-first=Lutz|place=Berlin, Heidelberg|publisher=Springer Berlin Heidelberg|language=en|arxiv=quant-ph/0212084|bibcode=2003tqi..conf..323B|doi=10.1007/978-3-662-10557-3_21|isbn=978-3-642-07892-7|access-date=2022-02-19|last2=Zeilinger|first2=Anton|s2cid=16831915 |author-link=Časlav Brukner|author-link2=Anton Zeilinger|editor2-last=Ischebeck|editor2-first=Otfried}}</ref> and by Czartowski and [[Karol Życzkowski|Życzkowski]].<ref>{{Cite journal|last1=Czartowski|first1=Jakub|last2=Życzkowski|first2=Karol|author-link2=Karol Życzkowski|date=2021-04-26|title=Bipartite quantum measurements with optimal single-sided distinguishability|url=https://quantum-journal.org/papers/q-2021-04-26-442/|journal=[[Quantum (journal)|Quantum]]|language=en|volume=5|article-number=442|arxiv=2010.14868|bibcode=2021Quant...5..442C|doi=10.22331/q-2021-04-26-442|s2cid=225094378 |issn=2521-327X}}</ref>}}</blockquote>

The book is divided into three parts. The first, "Gathering the Tools", introduces quantum mechanics as a theory of "preparations" and "tests", and it develops the mathematical formalism of Hilbert spaces, concluding with the [[spectral theory]] used to understand the quantum mechanics of continuous-valued observables. Part II, "Cryptodeterminism and Quantum Inseparability", focuses on [[Bell's theorem]] and other demonstrations that quantum mechanics is incompatible with [[local hidden-variable theory|local hidden-variable theories]]. (AmongWithin its substantial discussion of the failure of [[Hidden variable theory|hidden variable theories]], the book includes a [[FORTRAN]] program for testing whether a list of [[Euclidean vector|vector]]s forms a [[Kochen–Specker theorem|Kochen–Specker configuration]].{{efn|Section 7-5, "Appendix: Computer test for Kochen–Specker contradiction", p. 209}}) Part III, "Quantum Dynamics and Information", covers the role of [[spacetime]] symmetry in quantum physics, the relation of [[quantum information]] to [[thermodynamics]], [[Semiclassical physics|semiclassical approximation]] methods, [[quantum chaos]], and the treatment of [[measurement in quantum mechanics]].

To generate the figures in his chapter on quantum chaos, including plots in [[phase space]] of chaotic motion, Peres wrote [[PostScript]] code that executed simulations in the printer itself.{{efn|Section 11-7, "Appendix: PostScript code for a map", p. 370}}

The book develops the methodology of mathematically representing quantum measurements by [[POVM|POVMs]],<ref name="Mermin" /><ref>{{Cite journal|lastlast1=Flammia|firstfirst1=Steven T.|last2=Silberfarb|first2=Andrew|last3=Caves|first3=Carlton M.|author-link3=Carlton M. Caves|date=2005-12-01|title=Minimal Informationally Complete Measurements for Pure States|journal=[[Foundations of Physics]]|language=en|volume=35|issue=12|pages=1985–2006|arxiv=quant-ph/0404137|bibcode=2005FoPh...35.1985F|doi=10.1007/s10701-005-8658-z|s2cid=119382552|issn=1572-9516|via=}}</ref> and it provided the first pedagogical treatment of how to use a POVM for [[quantum key distribution]].<ref>{{Cite journal|last=Brandt|first=Howard E.|author-link=Howard Brandt|date=May 1999|title=Positive operator valued measure in quantum information processing|journal=[[American Journal of Physics]]|language=en|volume=67|issue=5|pages=434–439|doi=10.1119/1.19280|bibcode=1999AmJPh..67..434B|issn=0002-9505|viadoi-access=free}}</ref> Peres downplayed the importance of the [[uncertainty principle]]; that specific term only appears once in his index, and its entry points to that same page in the index.<ref name="PhysToday">{{cite journal|last1=Terzian |first1=Joseph E.|last2=Bennett |first2=Charles H.|author2-link=Charles H. Bennett (computer scientist)|last3=Mann |first3=Ady|last4=Wootters |first4=William K.|author4-link=William Wootters|title=Obituary: Asher Peres|journal=[[Physics Today]]|date=August 2005|volume=58|issue=8|pages=65–66|doi=10.1063/1.2062925|bibcode = 2005PhT....58h..65A |doi-access=free}}</ref> The text itself does discuss the uncertainty principle, pointing out how an oversimplified "derivation" of it breaks down, and posing as a homework problem the task of finding three quantum-physics textbooks with a demonstrably incorrect uncertainty relation.<ref>{{Cite journal |last=Clifton |first=Rob |date=1995-01-01 |title=none |journal=[[Foundations of Physics]] |language=en |volume=25 |issue=1 |pages=205–209 |doi=10.1007/BF02054666 |s2cid=189837484 |issn=1572-9516}}</ref>

==Reception==

Physicist Leslie E. Ballentine gave the textbook a positive review, declaring it a good introduction to [[quantum foundations]] and ongoing research therein.<ref name="Ballentine">{{Cite journal|last=Ballentine|first=Leslie E.|date=March 1995|title=none|url=|journal=[[American Journal of Physics]]|language=en|volume=63|issue=3|pages=285–286|doi=10.1119/1.17946|issn=0002-9505 }}</ref> [[John C. Baez]] also gave the book a positive assessment, calling it "clear-headed" and finding that it contained "a lot of gems that I hadn't seen", such as the [[Wigner–Araki–Yanase theorem]].<ref name="Baez">{{Cite web|url=http://math.ucr.edu/home/baez/week33.html|title=week33|last=Baez|first=John C.|authorlinkauthor-link=John C. Baez|date=1994-05-10|website=[[This Week's Finds in Mathematical Physics]]|url-status=live|archive-url=|archive-date=|access-date=2020-04-10}}</ref> [[Michael Nielsen]] wrote of the textbook, "Revelation! Suddenly, all the key results of 30 years of work (several of those results due to Asher) were distilled into beautiful and simple explanations."<ref>{{cite web|last=Nielsen|first=Michael A.|author-link=Michael Nielsen|title=Asher Peres|url=http://michaelnielsen.org/blog/asher-peres/|date=2005-01-05|website=michaelnielsen.org|access-date=2018-02-21}}</ref> Nielsen and [[Isaac Chuang]] said in their own influential textbook that Peres' was "superb", providing "an extremely clear exposition of elementary quantum mechanics" as well as an "extensive discussion of the Bell inequalities and related results".<ref>{{Cite book|lastlast1=Nielsen|firstfirst1=Michael A.|title=Quantum Computation and Quantum Information: 10th Anniversary Edition|url=https://archive.org/details/quantumcomputati00niel_720|url-access=limited|last2=Chuang|first2=Isaac L.|date=2010-12-09|publisher=[[Cambridge University Press]]|isbn=9781107002173|___location=|pages=[https://archive.org/details/quantumcomputati00niel_720/page/n151 118]|language=en|oclc=844974180|author-link=Michael Nielsen|author-link2=Isaac Chuang}}</ref> Jochen Rau's introductory textbook on quantum physics described Peres' work as "an excellent place to start" learning about Bell inequalities and related topics like [[Gleason's theorem]].<ref>{{Cite book|last=Rau|first=Jochen|title=Quantum Theory: An information processing approach|date=2021|publisher=Oxford University Press|isbn=978-0-19-265027-6|edition=1st|___location=Oxford|pages=152|oclc=1256446911}}</ref>

[[N. David Mermin]] wrote that Peres had bridged the "textual gap" between conceptually-oriented books, aimed at understanding what quantum physics implies about the nature of the world, and more practical books intended to teach how to apply quantum mechanics. Mermin found the book praiseworthy, noting that he had "only a few complaints". He wrote,:

:<blockquote>Peres is careless in discriminating among the various kinds of assumptions one needs to prove the impossibility of a no-hidden-variables theory that reproduces the statistical predictions of quantum mechanics. I would guess that this is because even though he is a master practitioner of this particular art form, deep in his heart he is so firmly convinced that hidden variables cannot capture the essence of quantum mechanics, that he is simply not interested in precisely what you need to assume to ''prove'' that they cannot.<ref name="Mermin">{{Cite journal|last=Mermin|first=N. David|author-link=N. David Mermin|date=1997-03-01|title=none|journal=[[Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics]]|language=en|volume=28|issue=1|pages=131–135|doi=10.1016/S1355-2198(97)85538-4|issn=1355-2198 |bibcode=1997SHPMP..28..131M }}</ref></blockquote>

[[N. David Mermin]] wrote that Peres had bridged the "textual gap" between conceptually-oriented books, aimed at understanding what quantum physics implies about the nature of the world, and more practical books intended to teach how to apply quantum mechanics. Mermin found the book praiseworthy, noting that he had "only a few complaints". He wrote,

:Peres is careless in discriminating among the various kinds of assumptions one needs to prove the impossibility of a no-hidden-variables theory that reproduces the statistical predictions of quantum mechanics. I would guess that this is because even though he is a master practitioner of this particular art form, deep in his heart he is so firmly convinced that hidden variables cannot capture the essence of quantum mechanics, that he is simply not interested in precisely what you need to assume to ''prove'' that they cannot.<ref name="Mermin">{{Cite journal|last=Mermin|first=N. David|author-link=N. David Mermin|date=1997-03-01|title=none|journal=[[Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics]]|language=en|volume=28|issue=1|pages=131–135|doi=10.1016/S1355-2198(97)85538-4|issn=1355-2198 |bibcode=1997SHPMP..28..131M }}</ref>

Mermin called the book "a treasure trove of novel perspectives on quantum mechanics" and said that Peres' choice of topics is "a catalogue of common omissions" from other approaches.<ref name="Mermin"/>

[[Meinhard E. Mayer]] declared that he would "recommend it to anyone teaching or studying quantum mechanics", finding Part II the most interesting of the book. While he noted some disappointment with Peres' selection of topics to include in the chapter on [[measurement in quantum mechanics|measurement]], he reserved most of his negativity for the publisher, saying (as Ballentine also did<ref name="Ballentine"/>) that they had priced the book beyond the reach of graduate students.:

:<blockquote>Such pricing practices are not justified when one considers that many publishers provide very little copyediting or typesetting any more, as is obvious from the "[[TeX]]"-ish look of most books published recently, this one included.<ref name="Mayer">{{Cite journal|last=Mayer|first=Meinhard E.|author-link=Meinhard E. Mayer|date=2008-01-11|title=none |journal=[[Physics Today]]|language=en|volume=47|issue=12|pages=6565–66|doi=10.1063/1.2808757|issn=0031-9228}}</ref></blockquote>

Mermin, Mayer and Baez noted that Peres briefly dismissed the [[many-worlds interpretation]] of quantum mechanics.<ref name="Mermin" /><ref name="Baez"/><ref name="Mayer"/> Peres argued that all varieties of many-worlds interpretations merely shifted the arbitrariness or vagueness of the [[wavefunction collapse]] idea to the question of when "worlds" can be regarded as separate, and that no objective criterion for that separation can actually be formulated.{{efn|Section 12-1, "The ambivalent observer", p. 374}} Moreover, Peres dismissed "spontaneous collapse" models like [[Ghirardi–Rimini–Weber theory]] in the same brief section, designating them "mutations" of quantum mechanics.<ref name="Mermin"/> In a review that praised the book's thoroughness, Tony Sudbery noted that Peres disparaged the idea that human consciousness plays a special role in quantum mechanics.<ref>{{Cite journal |last=Sudbery |first=Tony |date=April 1994 |title=Ordinary questions, extraordinary answers |url=https://iopscience.iop.org/article/10.1088/2058-7058/7/4/42 |journal=[[Physics World]] |volume=7 |issue=4 |pages=65–68 |doi=10.1088/2058-7058/7/4/42 |issn=0953-8585|url-access=subscription }}</ref>

Manuel Bächtold analyzed Peres' textbook from a standpoint of [[Pragmatism|philosophical pragmatism]].<ref name="Healey">{{Cite book|chapter-url=https://plato.stanford.edu/entries/quantum-bayesian/|title=[[Stanford Encyclopedia of Philosophy]]|last=Healey|first=Richard|publisher=Metaphysics Research Lab, [[Stanford University]]|year=2016|editor-last=Zalta|editor-first=Edward N.|chapter=Quantum-Bayesian and Pragmatist Views of Quantum Theory}}</ref> [[John Horton Conway|John Conway]] and [[Simon B. Kochen|Simon Kochen]] used a Kochen–Specker configuration from the book in order to prove their [[free will theorem]].<ref>{{Cite journal|last1=Conway|first1=John|author-link=John Horton Conway|last2=Kochen|first2=Simon|author-link2=Simon B. Kochen|date=2006-11-22|title=The Free Will Theorem|url=http://link.springer.com/10.1007/s10701-006-9068-6|journal=[[Foundations of Physics]]|language=en|volume=36|issue=10|pages=1441–1473|arxiv=quant-ph/0604079|bibcode=2006FoPh...36.1441C|doi=10.1007/s10701-006-9068-6|s2cid=12999337 |issn=0015-9018}}</ref> Peres' insistence in his textbook that the classical analogue of a [[quantum state]] is a [[Liouville's theorem (Hamiltonian)|Liouville density function]] was influential in the development of [[QBism]].<ref>{{cite encyclopedia|first1=Christopher A. |last1=Fuchs |first2=Blake C. |last2=Stacey |title=QBism: Quantum Theory as a Hero's Handbook |encyclopedia=Proceedings of the International School of Physics "Enrico Fermi": Course 197, "Foundations of Quantum Theory" |editor-first1=E. M. |editor-last1=Rasel |editor-first2=W. P. |editor-last2=Schleich |editor-link2=Wolfgang P. Schleich |editor-first3=S. |editor-last3=Wölk |doi=10.3254/978-1-61499-937-9-133 |arxiv=1612.07308 |year=2019 |volume=197 |issue=Foundations of Quantum Theory |pages=133–202 |publisher=[[IOS Press]] |isbn=9781614999379 |oclc=1086375617}}</ref>

==Related works==

[[John Watrous (computer scientist)|John Watrous]] places Peres' textbook among the "indispensable references", along with [[Michael Nielsen|Nielsen]] and [[Isaac Chuang|Chuang]]'s ''[[Quantum Computation and Quantum Information]]'' and [[Mark Wilde]]'s ''Quantum Information Theory.''<ref>{{cite book|last=Watrous|first=John|title=The Theory of Quantum Information|publisher=[[Cambridge University Press]]|year=2018|isbn=9781316853122|oclc=1034577167|authorlinkauthor-link=John Watrous (computer scientist)}}</ref> In their obituary for Peres, [[William Wootters]], [[Charles H. Bennett (physicist)|Charles Bennett]] and coauthors call ''Quantum Theory: Concepts and Methods'' the "modern successor" to [[John von Neumann]]'s 1955 ''[[Mathematical Foundations of Quantum Mechanics]].''<ref name="PhysToday" />

==Editions==

* {{cite book|first=Asher |last=Peres |title=Quantum Theory: Concepts and Methods |year=1993 |publisher=[[Kluwer]] |isbn=0-7923-2549-4 |oclc=28854083}} Original hardcover.

* {{cite book|first=Asher |last=Peres |title=Quantum Theory: Concepts and Methods |year=1995 |publisher=[[Kluwer]] |isbn=9780792336327 |oclc=901395752}} Paperback reprint.

* {{cite book|first=Asher |last=Peres |title=ペレス量子論の概念と手法―先端研究へのアプローチ |year=2001 |publisher=Maruzen |isbn=9784621049228 |oclc=834645102 |language=Japaneseja |translator-first1=Ichirō |translator-last1=Ōba |translator-first2=Yoshiya |translator-last2=Yamanaka |translator-first3=Hiromichi |translator-last3=Nakazato}}

==Notes==

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{{reflist}}

[[Category:Quantum information science]]

[[Category:Textbooks]]

[[Category:Physics books]]

[[Category:Science textbooks]]

[[Category:1993 non-fiction books]]

[[Category:TextbooksPhysics textbooks]]

[[Category:Quantum information science]]