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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¶³sica Aplicada II, Universidad de Sevilla, 41012 Sevilla, Spain (Dated: January 22, 2007) PACS numbers: 01.30.Rr, 01.30.Tt, 03.65.-w, 03.65.Ca, 03.65.Ta, 03.65.Ud, 03.65.Wj, 03.65.Xp, 03.65.Yz, 03.67.-a, 03.67.Dd, 03.67.Hk, 03.67.Lx, 03.67.Mn, 03.67.Pp, 03.75.Gg, 42.50.Dv \[T]here's much more di®erence (. ) be- Most of this work was developed for personal use, and tween a human being who knows quantum is therefore biased towards my own preferences, tastes mechanics and one that doesn't than between and phobias. This means that the selection is incom- one that doesn't and the other great apes." plete, although some e®ort has been made to cover some gaps. Some closely related subjects such as quantum M. Gell-Mann chaos, quantum structures, geometrical phases, relativis- at the annual meeting of the American Association for tic quantum mechanics, or Bose-Einstein condensates the Advancement of Science, Chicago 11 Feb. 1992. have been deliberately excluded. Reported in [Siegfried 00], pp. 177-178. Please note that this guide has been directly written in LaTeX (REVTeX4) and therefore a corresponding Bib- \The Copenhagen interpretation is quan- TeX ¯le does not exist, so do not ask for it. tum mechanics." Please e-mail corrections to [email protected] (under sub- ject: Error). Indicate the references as, for instance, [von R. Peierls. Neumann 31], not by its number (since this number Reported in [Khal¯n 90], p. 477. may have been changed in a later version). Suggestions \Quantum theory needs no `interpreta- for additional (essential) references which ought to be in- tion'." cluded are welcome (please e-mail to [email protected] under subject: Suggestion). C. A. Fuchs and A. Peres. Title of [Fuchs-Peres 00 a]. Acknowledgments \Unperformed experiments have no re- sults." The author thanks those who have pointed out er- rors, made suggestions, and sent copies of papers, lists of A. Peres. personal publications, and lists of references on speci¯c Title of [Peres 78 a]. subjects. Special thanks are given to T. D. Angelidis, J. L. Cereceda, R. Onofrio, A. Peres, E. Santos, C. Serra, M. Simonius, R. G. Stomphorst, and A. Y. Vlasov for Introduction their help on the improvement of this guide. This work was partially supported by the Universidad de Sevilla This is a collection of references (papers, books, grant OGICYT-191-97, the Junta de Andaluc¶³aProjects preprints, book reviews, Ph. D. thesis, patents, web FQM-239 (1998, 2000, 2002, 2004), and the Spanish Min- sites, etc.), sorted alphabetically and (some of them) isterio de Ciencia y Tecnolog¶³aProjects BFM2000-0529, classi¯ed by subject, on foundations of quantum me- BFM2001-3943, and BFM2002-02815. chanics and quantum information. Speci¯cally, it cov- ers hidden variables (\no-go" theorems, experiments), \interpretations" of quantum mechanics, entanglement, quantum e®ects (quantum Zeno e®ect, quantum era- sure, \interaction-free" measurements, quantum \non- demolition" measurements), quantum information (cryp- tography, cloning, dense coding, teleportation), and quantum computation. For a more detailed account of the subjects covered, please see the table of contents in the next pages. ¤Electronic address: [email protected] 2 Contents 3. Local immeasurability or indistinguishability (\nonlocality Introduction 1 without entanglement") 9 I. Experiments on Bell's theorem 9 Acknowledgments 1 1. Real experiments 9 2. Proposed gedanken experiments 9 I. Hidden variables 4 3. EPR with neutral kaons 9 A. Von Neumann's impossibility proof 4 4. Reviews 10 B. Einstein-Podolsky-Rosen's argument of 5. Experimental proposals on GHZ proof, incompleteness of QM 4 preparation of GHZ states 10 1. General 4 6. Experimental proposals on Hardy's 2. Bohr's reply to EPR 4 proof 10 C. Gleason theorem 4 7. Some criticisms of the experiments on D. Other proofs of impossibility of hidden Bell's inequalities. Loopholes 10 variables 5 E. Bell-Kochen-Specker theorem 5 II. \Interpretations" 11 1. The BKS theorem 5 A. Copenhagen interpretation 11 2. From the BKS theorem to the BKS B. De Broglie's \pilot wave" and Bohm's with locality theorem 5 \causal" interpretations 11 3. The BKS with locality theorem 5 1. General 11 2. Tunneling times in Bohmian mechanics 12 4. Probabilistic versions of the BKS theorem 5 C. \Relative state", \many worlds", and \many minds" interpretations 12 5. The BKS theorem and the existence of D. Interpretations with explicit collapse or dense \KS-colourable" subsets of dynamical reduction theories (spontaneous projectors 5 localization, nonlinear terms in SchrÄodinger 6. The BKS theorem in real experiments 6 equation, stochastic theories) 12 7. The BKS theorem for a single qubit 6 E. Statistical (or ensemble) interpretation 13 F. Bell's inequalities 6 F. \Modal" interpretations 13 1. First works 6 G. \It from bit" 13 2. Bell's inequalities for two spin-s H. \Consistent histories" (or \decoherent particles 6 histories") 13 3. Bell's inequalities for two particles and I. Decoherence and environment induced more than two observables per particle 6 superselection 14 4. Bell's inequalities for n particles 6 J. Time symmetric formalism, pre- and 5. Which states violate Bell's inequalities? 7 post-selected systems, \weak" 6. Other inequalities 7 measurements 14 7. Inequalities to detect genuine n-particle K. The transactional interpretation 14 nonseparability 7 L. The Ithaca interpretation (\correlations 8. Herbert's proof of Bell's theorem 7 without correlata") and the observation 9. Mermin's statistical proof of Bell's that correlations cannot be regarded as theorem 7 objective local properties 14 G. Bell's theorem without inequalities 7 1. Greenberger-Horne-Zeilinger's proof 7 III. Composite systems, preparations, and 2. Peres' proof of impossibility of recursive measurements 14 elements of reality 8 A. States of composite systems 14 3. Hardy's proof 8 1. Schmidt decomposition 14 4. Two-observer \all versus nothing" 2. Entanglement measures 15 proof 8 3. Separability criteria 15 5. Other algebraic proofs of no-local 4. Multiparticle entanglement 15 hidden variables 8 5. Entanglement swapping 16 6. Classical limits of no-local hidden 6. Entanglement distillation variables proofs 8 (concentration and puri¯cation) 16 H. Other \nonlocalities" 8 7. Disentanglement 16 1. \Nonlocality" of a single particle 8 8. Bound entanglement 16 2. Violations of local realism exhibited in 9. Entanglement as a catalyst 17 sequences of measurements (\hidden B. State determination, state discrimination, nonlocality") 8 and measurement of arbitrary observables 17 3 1. State determination, quantum 5. Quantum random walks 29 tomography 17 6. General and others 29 2. Generalized measurements, positive C. Quantum logic gates 29 operator-valued measurements D. Schemes for reducing decoherence 29 (POVMs), discrimination between E. Quantum error correction 29 non-orthogonal states 17 F. Decoherence-free subspaces and subsystems 30 3. State preparation and measurement of G. Experiments and experimental proposals 30 arbitrary observables 18 4. Stern-Gerlach experiment and its VII. Miscellaneous 30 successors 18 A. Textbooks 30 5. Bell operator measurements 18 B. History of quantum mechanics 31 C. Biographs 31 IV. Quantum e®ects 18 D. Philosophy of the founding fathers 31 6. Quantum Zeno and anti-Zeno e®ects 18 E. Quantum logic 31 7. Reversible measurements, delayed F. Superselection rules 31 choice and quantum erasure 19 G. Relativity and the instantaneous change of 8. Quantum nondemolition measurements 19 the quantum state by local interventions 32 9. \Interaction-free" measurements 19 H. Quantum cosmology 32 10. Quantum-enhanced measurements 20 VIII. Bibliography 33 V. Quantum information 20 A. 33 A. Quantum cryptography 20 B. 58 1. General 20 C. 115 2. Proofs of security 21 D. 147 3. Quantum eavesdropping 21 E. 166 4. Quantum key distribution with F. 175 orthogonal states 21 G. 194 5. Experiments 21 H. 223 6. Commercial quantum cryptography 22 I. 253 J. 256 7. Quantum detectable Byzantine K. 265 agrement |or broadcast| and liar L. 289 detection 22 M. 310 B. Cloning and deleting quantum states 22 N. 338 C. Quantum bit commitment 23 O. 344 D. Secret sharing and quantum secret sharing 23 P. 352 E. Quantum authentication 23 Q. 380 F. Teleportation of quantum states 23 R. 381 1. General 23 S. 396 2. Experiments 24 T. 437 G. Telecloning 25 U. 449 H. Dense coding 25 V. 451 I. Remote state preparation and measurement25 W. 465 J. Classical information capacity of quantum X. 481 channels 25 Y. 483 K. Quantum coding, quantum data Z. 488 compression 26 L. Reducing the communication complexity with quantum entanglement 26 M. Quantum games and quantum strategies 26 N. Quantum clock synchronization 27 VI. Quantum computation 27 A. General 27 B. Quantum algorithms 28 1. Deutsch-Jozsa's and Simon's 28 2. Factoring 28 3. Searching 28 4. Simulating quantum systems 28 4 I. HIDDEN VARIABLES 91]; [Deltete-Guy 91] (Einstein on EPR), [H¶ajek- Bub 92] (EPR's argument is \better" than later argu- A. Von Neumann's impossibility proof ments by Einstein, contrary to Fine's opinion), [Com- bourieu 92] (Popper on EPR, including a letter by Ein- [von Neumann 31], [von Neumann 32] stein from 1935 with containing a brief presentation of (Sec. IV. 2), [Hermann 35], [Albertson 61], [Komar EPR's argument), [Bohm-Hiley 93] (Sec. 7. 7, analy- 62], [Bell 66, 71], [Capasso-Fortunato-Selleri 70], sis of the EPR experiment according to the \causal" in- [Wigner 70, 71], [Clauser 71 a, b], [Gudder 80] terpretation), [Schatten 93] (hidden-variable model for (includes an example in two dimensions showing that the EPR experiment), [Hong-yi-Klauder 94] (common the expected value cannot be additive), [Selleri 90] eigenvectors of relative position and total momentum of (Chap.
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