×

How much contextuality? (English) Zbl 1339.81013

Summary: The amount of contextuality is quantified in terms of the probability of the necessary violations of noncontextual assignments to counterfactual elements of physical reality.

MSC:

81P13 Contextuality in quantum theory
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Amselem E, Rådmark M, Bourennane M, Cabello A (2009) State-independent quantum contextuality with single photons. Phys Rev Lett 103:160405 · doi:10.1103/PhysRevLett.103.160405
[2] Barrett J, Linden N, Massar S, Pironio S, Popescu S, Roberts D (2005) Nonlocal correlations as an information-theoretic resource. Phys Rev A 71:022101 · doi:10.1103/PhysRevA.71.022101
[3] Bartosik H, Klepp J, Schmitzer C, Sponar S, Cabello A, Rauch H, Hasegawa Y (2009) Experimental test of quantum contextuality in neutron interferometry. Phys Rev Lett 103:040403, arXiv:0904.4576
[4] Bell JS (1966) On the problem of hidden variables in quantum mechanics. Rev Mod Phys 38:447–452 · Zbl 0152.23605 · doi:10.1103/RevModPhys.38.447
[5] Bohr N (1949) Discussion with Einstein on epistemological problems in atomic physics. In: Schilpp PA (ed) Albert Einstein: Philosopher-Scientist. The Library of Living Philosophers, Evanston, Ill, pp. 200–241
[6] Boole G (1862) On the theory of probabilities. Philos Trans R Soc Lond 152:225–252 · Zbl 1319.60004 · doi:10.1098/rstl.1862.0015
[7] Cabello A (2008) Experimentally testable state independent quantum contextuality. Phys Rev Lett 101:210401 · doi:10.1103/PhysRevLett.101.210401
[8] Cabello A, Estebaranz JM, García-Alcaine G (1996) Bell–Kochen–Specker theorem: a proof with 18 vectors. Phys Lett A 212:183–187 · Zbl 1073.81515 · doi:10.1016/0375-9601(96)00134-X
[9] Calude CS, Svozil K (2008) Quantum randomness and value indefiniteness. Adv Sci Lett 1:165–168, eprint arXiv:quant-ph/0611029, arXiv:quant-ph/0611029
[10] Calude C, Hertling P, Svozil K (1999) Embedding quantum universes into classical ones. Found Phys 29:349–379 · doi:10.1023/A:1018862730956
[11] Calude CS, Dinneen MJ, Dumitrescu M, Svozil K (2010) Experimental evidence of quantum randomness incomputability. Phys Rev A 82:022102 · doi:10.1103/PhysRevA.82.022102
[12] Cirel’son BS (1980) Quantum generalizations of Bell’s inequality. Lett Math Phys 4:93–100 · doi:10.1007/BF00417500
[13] Cirel’son BS (1993) Some results and problems on quantum Bell-type inequalities. Hadronic J Suppl 8:329–345
[14] Clauser JF, Shimony A (1978) Bell’s theorem: experimental tests and implications. Rep Prog Phys 41:1881–1926 · doi:10.1088/0034-4885/41/12/002
[15] Clauser JF, Horne MA, Shimony A, Holt RA (1969) Proposed experiment to test local hidden-variable theories. Phys Rev Lett 23:880–884 · Zbl 1371.81014 · doi:10.1103/PhysRevLett.23.880
[16] Einstein A, Podolsky B, Rosen N (1935) Can quantum-mechanical description of physical reality be considered complete?. Phys Rev 47:777–780 · Zbl 0012.04201 · doi:10.1103/PhysRev.47.777
[17] Filipp S, Svozil K (2004) Generalizing Tsirelson’s bound on Bell inequalities using a min-max principle. Phys Rev Lett 93:130407 quantph/ 0403175
[18] Froissart M (1981) Constructive generalization of Bell’s inequalities. Il Nuovo Cimento B (1971–1996) 64:241–251. doi: 10.1007/BF02903286 · doi:10.1007/BF02903286
[19] Hasegawa Y, Loidl R, Badurek G, Baron M, Rauch H (2006) Quantum contextuality in a single-neutron optical experiment. Phys Rev Lett 97:230401 · Zbl 1068.81517 · doi:10.1103/PhysRevLett.97.230401
[20] Kirchmair G, Zähringer F, Gerritsma R, Kleinmann M, Gühne O, Cabello A, Blatt R, Roos CF (2009) State-independent experimental test of quantum contextuality. Nature 460:494–497 arXiv:0904.1655
[21] Kochen S, Specker EP (1967) The problem of hidden variables in quantum mechanics. J Math Mech (now Indiana University Mathematics Journal) 17:59–87 · Zbl 0156.23302
[22] Krenn G, Svozil K (1998) Stronger-thanquantum correlations. Found Phys 28:971–984 · doi:10.1023/A:1018821314465
[23] Meyer DA (1999) Finite precision measurement nullifies the Kochen–Specker theorem. Phys Rev Lett 83:3751–3754, quant-ph/9905080 · Zbl 0946.81009
[24] Peres A (1978) Unperformed experiments have no results. Am J Phys 46:745–747 · doi:10.1119/1.11393
[25] Pitowsky I (1982) Resolution of the Einstein–Podolsky–Rosen and Bell paradoxes. Phys Rev Lett 48:1299–1302 · doi:10.1103/PhysRevLett.48.1299
[26] Pitowsky I (1989) Quantum probability–quantum logic. Springer, Berlin · Zbl 0668.60096
[27] Popescu S, Rohrlich D (1994) Quantum nonlocality as an axiom. Found Phys 24:379–358 · doi:10.1007/BF02058098
[28] Popescu S, Rohrlich D (1997) Action and passion at a distance. In: Cohen RS, Horne MA, Stachel J (eds) Potentiality, entanglement and passion-at-a-distance: quantum mechanical studies for Abner Shimony, Volume Two (Boston Studies in the Philosophy of Science. Kluwer Academic publishers, Dordrecht, pp. 197–206, quant-ph/9605004 · Zbl 1211.81015
[29] Svozil K (1998) Quantum logic. Springer, Singapore · Zbl 0922.03084
[30] Svozil K (2004) Quantum information via state partitions and the context translation principle. J Mod Opt 51:811–819 quant-ph/0308110 · Zbl 1070.81506
[31] Svozil K (2005a) Communication cost of breaking the Bell barrier. Phys Rev A 72:050302(R) physics/0510050
[32] Svozil K (2005b) Noncontextuality in multipartite entanglement. J Phys A Math Gen 38:5781–5798 quant-ph/0401113 · Zbl 1084.81010
[33] Svozil K (2009a) Quantum scholasticism: on quantum contexts, counterfactuals, and the absurdities of quantum omniscience. Inf Sci 179:535–541 · Zbl 1162.81322 · doi:10.1016/j.ins.2008.06.012
[34] Svozil K (2009b) Proposed direct test of a certain type of noncontextuality in quantum mechanics. Phys Rev A 80:040102 · doi:10.1103/PhysRevA.80.040102
[35] Svozil K (2009c) Contexts in quantum, classical and partition logic. In: Engesser K, Gabbay DM, Lehmann D (eds) Handbook of quantum logic and quantum structures. Elsevier, Amsterdam, pp 551–586. arXiv:quant-ph/0609209 · Zbl 1273.03175
[36] Svozil K (2010) Quantum value indefiniteness. Nat Comput online first 1–12, arXiv:1001.1436 · Zbl 1251.81030
[37] Vaidman L (2007) Counterfactuals in quantum mechanics. In: Greenberger D, Hentschel K, Weinert F (eds) Compendium of quantum physics. Springer, Berlin, pp 132–136, arXiv:0709.0340
[38] Zeilinger A (1999) A foundational principle for quantum mechanics. Found Phys 29:631–643 · doi:10.1023/A:1018820410908
[39] Zeilinger A (2005) The message of the quantum. Nature 438:743 · doi:10.1038/438743a
[40] Ziegler GM (1994) Lectures on polytopes. Springer, New York
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.