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Bibliographic Guide to the Foundations of Quantum Mechanics and Quantum Information

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Bibliographic Guide to the Foundations of Quantum Mechanics and Quantum Information Bibliographic guide to the foundations of quantum mechanics and quantum information Ad´an Cabello∗ Departamento de F´ısica Aplicada II, Universidad de Sevilla, 41012 Sevilla, Spain (May 16, 2001) subjects. This work was partially supported by the Uni- PACS numbers: 03.65.-w, 03.65.Ca, 03.65.Ta, 03.65.Ud, versidad de Sevilla grant OGICYT-191-97, the Junta de 03.65.Wj, 03.65.Xp, 03.65.Yz, 03.67.-a, 03.67.Dd, 03.67.Hk, Andaluc´ıa grant FQM-239, and the Spanish Ministerio 03.67.Lx de Ciencia y Tecnolog´ıa grant BFM2000-0529. INTRODUCTION Contents This is a collection of references (papers, books, preprints, book reviews, Ph. D. thesis, patents, etc.), I Hidden variables 2 sorted alphabetically and (some of them) classified A Von Neumann’s impossibility proof . 2 by subject, on foundations of quantum mechanics B Einstein-Podolsky-Rosen’s argument of and quantum information. Specifically, it covers hid- incompletenessofQM.......... 2 den variables (“no-go” theorems, experiments), in- 1 General................ 2 terpretations of quantum mechanics, entanglement, 2 Bohr’sreplytoEPR......... 3 quantum effects (quantum Zeno effect, quantum era- C Gleasontheorem............. 3 sure, “interaction-free” measurements, quantum “non- D Other proofs of impossibility of hidden demolition” measurements), quantum information (cryp- variables................. 3 tography, cloning, dense coding, teleportation), and E Bell-Kochen-Specker theorem . 3 quantum computation. For a more detailed account of 1 TheBKStheorem.......... 3 the subjects covered, please see the table of contents. 2 From the BKS theorem to the BKS Most of this work was developed for personal use, and with locality theorem . 4 is therefore biased towards my own preferences, tastes 3 The BKS with locality theorem . 4 and phobias. This means that the selection is incom- 4 Probabilistic versions of the BKS plete, although some effort has been made to cover some theorem................ 4 gaps. Some closely related subjects such as quantum 5 The BKS theorem and the existence chaos, geometrical phases, relativistic quantum mechan- of dense “KS-colourable” subsets of ics, or Bose-Einstein condensates have been deliberately projectors............... 4 excluded. 6 The BKS theorem in real experiments 4 Please e-mail corrections to adan@cica (under subject: F Bellinequalities............. 4 error). Indicate the references as, for instance, [von 1 Firstworks.............. 4 Neumann 31], not by its number (since this number 2 Bell inequalities for two spin-s par- may have been changed in a later version). Suggestions ticles................. 4 for additional (essential) references which ought to be in- 3 Bell inequalities for two particles cluded are welcome (please e-mail to [email protected] under and more than two observables per subject: suggestion). particle................ 4 4 Bell inequalities for n particles . 4 5 Which states violate Bell’s inequal- ACKNOWLEDGMENTS ities?................. 4 6 Otherinequalities.......... 5 The author thanks J. L. Cereceda, R. Onofrio, A. 7 Herbert’s proof of Bell theorem . 5 Peres, C. Serra, M. Simonius, R. Stomphorst, and A. Y. 8 Mermin’s statistical proof of Bell Vlasov for their help on the improvement of this bibliog- theorem................ 5 raphy. Additional thanks to those who have pointed out G Bell theorem without inequalities . 5 errors, made suggestions, and sent copies of papers, lists 1 Greenberger-Horne-Zeilinger’s proof 5 of personal publications, and lists of references on specific 2 Peres’ proof of impossibility of re- cursive elements of reality . 5 3 Hardy’sproof............ 5 4 Bell theorem without inequalities ∗Electronic address: [email protected] for EPR-Bohm-Bell states . 5 1 5 Other algebraic proofs of no-local 6 Entanglement concentration (distil- hidden variables . 6 lation, purification) . 12 6 Classical limits of no-local hidden 7 Disentanglement........... 13 variables proofs . 6 8 Boundentanglement......... 13 H Other “nonlocalities” . 6 B State determination, state discrimina- 1 “Nonlocality” of a single particle . 6 tion, and measurement of arbitrary ob- 2 Violations of local realism exhibited servables................. 13 in sequences of measurements (“hid- 1 State determination, discrimination dennonlocality”).......... 6 between non-orthogonal states, gen- 3 Local immeasurability (“nonlocality eralized measurements, positive op- without entanglement”) . 6 erator valued measurements (POVMs) 13 I Experiments on Bell theorem . 6 2 State preparation and measurement 1 Real experiments . 6 of arbitrary observables . 13 2 Proposed gedanken experiments . 6 3 Stern-Gerlach experiment and its 3 EPR with kaons . 7 successors............... 14 4 Reviews................ 7 4 Bell operator measurements . 14 5 Experimental proposals on GHZ proof, preparation of GHZ states . 7 IV Quantum effects 14 6 Experimental proposals on Hardy’s 5 Quantum Zeno and anti-Zeno effects 14 proof................. 7 6 Reversible measurements, delayed 7 Some criticisms of the experiments choice and quantum erasure . 15 on Bell inequalities . 8 7 Quantum nondemolition measure- ments................. 15 II Interpretations 8 8 Interaction-free measurements . 15 A Copenhagen interpretation . 8 B De Broglie’s “pilot wave” and Bohm’s V Quantum information 16 “causal” interpretations . 8 A Quantum crytography . 16 1 General................ 8 1 General................ 16 2 Tunneling times in Bohmian me- 2 Proofsofsecurity.......... 16 chanics................ 9 3 Quantum eavesdropping . 16 C “Relative state”, “many worlds”, and 4 Experiments............. 17 “many minds” interpretations . 9 5 Quantum cryptography with or- D Interpretations with explicit collapse or thogonal states . 17 dynamical reduction theories (sponta- B Quantum cloning . 17 neous localization, nonlinear terms in C Quantum bit commitment . 17 Schr¨odinger equation, stochastic theo- D Secret sharing and quantum secret ries).................... 9 sharing.................. 18 E Statistical (or ensemble) interpretation 10 E Quantum authentication . 18 F “Modal” interpretations . 10 F Teleportation of quantum states . 18 G “Itfrombit”............... 10 1 General................ 18 H “Consistent histories” (or “decoherent 2 Experiments............. 19 histories”)................ 10 G Dense coding . 19 I Decoherence and environment induced H Classical information capacity of quan- superselection.............. 10 tumchannels............... 19 J Time symetric formalism, pre- and I Quantum coding, quantum data com- post-selected systems, “weak” measure- pression.................. 20 ments................... 11 J Quantum games and quantum strategies 20 K The Ithaca interpretation: Correlations K Quantum clock synchronization . 20 without correlata . 11 VI Quantum computation 20 III Composite systems, preparations, and A General.................. 20 measurements 11 B Quantum algorithms . 21 A States of composite systems . 11 1 Factoring............... 21 1 Schmidt decomposition . 11 2 Searching in a database . 21 2 Entanglement measures . 11 3 Simulating quantum systems . 21 3 Separability criteria . 12 4 General and others . 21 4 Multiparticle entanglement . 12 C Logicgates................ 21 5 Entanglement swapping . 12 D Schemes for reducing decoherence . 22 2 E Quantum error correction . 22 F Experiments and experimental proposals 22 VII Miscellaneous 22 A Textbooks................ 22 B History of quantum mechanics . 22 C Biographs . 22 D Philosophy of the founding fathers . 23 E Quantumlogic.............. 23 F Superselection rules . 23 G Relativity and the instantaneous change of the quantum state by local interventions............... 23 H Quantumcosmology........... 23 3 I. HIDDEN VARIABLES on EPR), [H´ajek-Bub 92] (EPR’s argument is “bet- ter” than later arguments by Einstein, contrary to Fine’s A. Von Neumann’s impossibility proof opinion), [Combourieu 92] (Popper on EPR, including a letter by Einstein from 1935 with containing a brief pre- [von Neumann 31], [von Neumann 32] (Sec. IV. sentation of EPR’s argument), [Bohm-Hiley 93] (Sec. 2), [Hermann 35], [Albertson 61], [Komar 62], [Bell 7. 7, analysis of the EPR experiment according to the 66, 71], [Capasso-Fortunato-Selleri 70], [Wigner “causal” interpretation), [Schatten 93] (hidden-variable 70, 71], [Clauser 71 a, b], [Gudder 80] (includes model for the EPR experiment), [Hong-yi-Klauder 94] an example in two dimensions showing that the expected (common eigenvectors of relative position and total mo- value cannot be additive), [Selleri 90] (Chap. 2), [Peres mentum of a two-particle system, see also [Hong-yi- 90 a] (includes an example in two dimensions showing Xiong 95]), [De la Torre 94 a] (EPR-like argument that the expected value cannot be additive), [Ballen- with two components of position and momentum of a tine 90 a] (in pp. 130-131 includes an example in four single particle), [Dieks 94] (Sec. VII, analysis of the dimensions showing that the expected value cannot be EPR experiment according to the “modal” interpreta- additive), [Zimba-Clifton 98], [Busch 99 b] (resur- tion), [Eberhard-Rosselet 95] (Bell theorem based on rection of the theorem). a generalization of EPR criterion for elements of reality which includes values predicted with almost certainty), [Paty 95] (on Einstein’s objections to QM), [Jack 95] B. Einstein-Podolsky-Rosen’s argument of (easy-reading introduction to the EPR and Bell argu- incompleteness of QM ments, with Sherlock Holmes). 1. General 2. Bohr's reply to EPR [Einstein-Podolsky-Rosen 35], [Bohr 35 a, b] [Bohr 35 a, b], [Hooker
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