Contextuality in Three Types of Quantum-Mechanical Systems

Foundations of Physics

Volumn 45, Issue 7, 2015, Pages 762-782

  Dzhafarov, Ehtibar N ^a   Kujala, Janne V ^b   Larsson, Jan Åke ^c  

^a PURDUE UNIVERSITY   (United States)

^b UNIVERSITY OF JYVÄSKYLÄ   (Finland)

^c LINKÖPING UNIVERSITY   (Sweden)

Author keywords

CHSH inequalities; Contextuality; Klyachko inequalities; Leggett Garg inequalities; Probabilistic couplings; Signaling

Indexed keywords

EID: 84931011435     PISSN: 00159018     EISSN: 15729516     Source Type: Journal    
DOI: 10.1007/s10701-015-9882-9     Document Type: Article

References (31)

1. Bacciagaluppi, G.: Leggett–Garg inequalities, pilot waves and contextuality. Int. J. Quant. Found. 1, 1–17 (2015)
2. Bell, J.: On the Einstein–Podolsky–Rosen paradox. Physics 1, 195–200 (1964)
3. Bell, J.: On the problem of hidden variables in quantum mechanics. Rev. Modern Phys. 38, 447–453 (1966)
4. Cereceda, J.: Quantum mechanical probabilities and general probabilistic constraints for Einstein–Podolsky–Rosen–Bohm experiments. Found. Phys. Lett. 13, 427–442 (2000)
5. Clauser, J.F., Horne, M.A., Shimony, A., Holt, R.A.: Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23, 880–884 (1969)
6. Clauser, J.F., Horne, M.A.: Experimental consequences of objective local theories. Phys. Rev. D 10, 526–535 (1974)
7. de Barros, J.A., Dzhafarov, E.N., Kujala, J.V., Oas, G.: Measuring observable quantum contextuality (2014). arXiv:1406.3088
8. Dzhafarov, E.N., Kujala, J.V.: The joint distribution criterion and the distance tests for selective probabilistic causality. Frontiers Quant. Psychol. Meas. 1, 151 (2010). doi:10.3389/fpsyg.2010.00151
9. Dzhafarov, E.N., Kujala, J.V.: Probability, random variables, and selectivity (2013). arXiv:1312.2239
10. Dzhafarov, E.N., Kujala, J.V.: All-possible-couplings approach to measuring probabilistic context. PLoS ONE 8(5), e61712 (2013). doi:10.1371/journal.pone.0061712
11. Dzhafarov, E.N., Kujala, J.V.: Order-distance and other metric-like functions on jointly distributed random variables. Proc. Am. Math. Soc. 141(9), 3291–3301 (2013)
12. Dzhafarov, E.N., Kujala, J.V.: Generalizing Bell-type and Leggett–Garg-type inequalities to systems with signaling (2014). arXiv:1407.2886
13. Dzhafarov, E.N., Kujala, J.V.: Probabilistic contextuality in EPR/Bohm-type systems with signaling allowed (2014). arXiv:1406.0243
14. Dzhafarov, E.N., Kujala, J.V.: No-forcing and no-matching theorems for classical probability applied to quantum mechanics. Found. Phys. 44, 248–265 (2014)
15. Dzhafarov, E.N., Kujala, J.V.: Embedding quantum into classical: contextualization vs conditionalization. PLoS One 9(3), e92818 (2014). doi:10.1371/journal.pone.0092818
16. Dzhafarov, E.N., Kujala, J.V.: A Qualified Kolmogorovian account of probabilistic contextuality. Lect. Not. Comp. Sci. Springer, Berlin (2014)
17. Dzhafarov, E.N., Kujala, J.V.: Contextuality is about identity of random variables. Phys. Scripta. T163, 014009 (2015)
18. Dzhafarov, E.N., Kujala, J.V.: Random variables recorded under mutually exclusive conditions: contextuality-by-default. In: Liljenström, H. (ed.) Advances in Cognitive Neurodynamics IV, pp. 405–410 (2015)
19. Fine, A.: Hidden variables, joint probability, and the Bell inequalities. Phys. Rev. Lett. 48, 291–295 (1982)
20. Khrennikov, A.: The principle of supplementarity: a contextual probabilistic viewpoint to complementarity, the interference of probabilities, and the incompatibility of variables in quantum mechanics. Found. Phys. 35, 1655–1693 (2005)
21. Khrennikov, A.: Bell–Boole inequality: nonlocality or probabilistic incompatibility of random variables? Entropy 10, 19–32 (2008)
22. Khrennikov, A.: Contextual Approach to Quantum Formalism. Springer, Berlin (2009)
23. Klyachko, A.A., Can, M.A., Binicioglu, S., Shumovsky, A.S.: A simple test for hidden variables in spin-1 system. Phys. Rev. Lett. 101, 020403 (2008)
24. Kujala, J.V., Dzhafarov, E.N., Larsson, J.-Å.: Necessary and sufficient conditions for maximal noncontextuality in a broad class of quantum mechanical systems (2014). arXiv:1412.4724
25. Larsson, J.-Å.: A Kochen–Specker inequality. Europhys. Lett. 58, 799–805 (2002)
26. Leggett, A.J., Garg, A.: Quantum mechanics versus macroscopic realism: is the flux there when nobody looks? Phys. Rev. Lett. 54, 857–860 (1985)
27. Masanes, L., Acin, A., Gisin, N.: General properties of nonsignaling theories. Phys. Rev. A 73, 012112 (2006)
28. Popescu, S., Rohrlich, D.: Quantum nonlocality as an axiom. Found. Phys. 24, 379–385 (1994)
29. Specker, E.: Die Logik Nicht Gleichzeitig Entscheidbarer Aussagen. Dialectica 14, 239–246 (1960). (English translation by Seevinck, M.P., available as arXiv:1103.4537.)
30. Suppes, P., Zanotti, M.: When are probabilistic explanations possible? Synthese 48, 191–199 (1981)
31. Svozil, K.: How much contextuality? Nat. Comput. 11, 261–265 (2012)