{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T15:21:08Z","timestamp":1778167268476,"version":"3.51.4"},"reference-count":88,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,2,8]],"date-time":"2019-02-08T00:00:00Z","timestamp":1549584000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We start with a review on classical probability representations of quantum states and observables. We show that the correlations of the observables involved in the Bohm\u2013Bell type experiments can be expressed as correlations of classical random variables. The main part of the paper is devoted to the conditional probability model with conditioning on the selection of the pairs of experimental settings. From the viewpoint of quantum foundations, this is a local contextual hidden-variables model. Following the recent works of Dzhafarov and collaborators, we apply our conditional probability approach to characterize (no-)signaling. Consideration of the Bohm\u2013Bell experimental scheme in the presence of signaling is important for applications outside quantum mechanics, e.g., in psychology and social science. The main message of this paper (rooted to Ballentine) is that quantum probabilities and more generally probabilities related to the Bohm\u2013Bell type experiments (not only in physics, but also in psychology, sociology, game theory, economics, and finances) can be classically represented as conditional probabilities.<\/jats:p>","DOI":"10.3390\/e21020157","type":"journal-article","created":{"date-parts":[[2019,2,11]],"date-time":"2019-02-11T03:26:01Z","timestamp":1549855561000},"page":"157","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":45,"title":["Classical (Local and Contextual) Probability Model for Bohm\u2013Bell Type Experiments: No-Signaling as Independence of Random Variables"],"prefix":"10.3390","volume":"21","author":[{"given":"Andrei","family":"Khrennikov","sequence":"first","affiliation":[{"name":"Mechanics and Optics (ITMO) Department, National Research University for Information Technology, St. Petersburg 197101, Russia"},{"name":"International Center for Mathematical Modeling in Physics and Cognitive Sciences, Linnaeus University, SE-351 95 V\u00e4xj\u00f6, Sweden"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexander","family":"Alodjants","sequence":"additional","affiliation":[{"name":"Mechanics and Optics (ITMO) Department, National Research University for Information Technology, St. Petersburg 197101, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,2,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Man\u2019ko, M.A., and Man\u2019ko, V.I. (2018). New entropic inequalities and hidden correlations in quantum suprematism pictue of qudit states. Entropy, 20.","DOI":"10.3390\/e20090692"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0375-9601(96)00107-7","article-title":"Symplectic tomography as classical approach to quantum systems","volume":"213","author":"Mancini","year":"1996","journal-title":"Phys. Lett. A"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1016\/S0375-9601(97)00199-0","article-title":"Positive distribution description for spin states","volume":"229","author":"Dodonov","year":"1997","journal-title":"Phys. Lett. A"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"430","DOI":"10.1134\/1.558326","article-title":"Spin state tomography","volume":"85","year":"1997","journal-title":"J. Exp. Theor. Phys."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1007\/s10701-009-9402-x","article-title":"Prequantum classical statistical field theory: Schr\u00f6dinger dynamics of entangled systems as a classical stochastic process","volume":"41","author":"Khrennikov","year":"2011","journal-title":"Found. Phys."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"725","DOI":"10.1007\/s10701-011-9611-y","article-title":"Towards a field model of prequantum reality","volume":"42","author":"Khrennikov","year":"2012","journal-title":"Found. Phys."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Khrennikov, A. (2014). Beyond Quantum, Pan Stanford Publishing.","DOI":"10.1201\/b15540"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/j.aop.2016.12.005","article-title":"Quantum epistemology from subquantum ontology: Quantum mechanics from theory of classical random fields","volume":"377","author":"Khrennikov","year":"2017","journal-title":"Ann. Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1143\/PTP.128.31","article-title":"Quantum probabilities and violation of CHSH-inequality from classical random signals and threshold type detection scheme","volume":"128","author":"Khrennikov","year":"2012","journal-title":"Prog. Theor. Phys."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1241014","DOI":"10.1142\/S0219749912410146","article-title":"On an experimental test of prequantum theory of classical random fields: An estimate from above of the coefficient of second-order coherence","volume":"10","author":"Khrennikov","year":"2012","journal-title":"Int. J. Quantum Inf."},{"key":"ref_11","unstructured":"Kolmogorov, A.N. (1956). Foundations of the Theory of Probability, Chelsea Publishing Company."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"749","DOI":"10.1103\/PhysRev.40.749","article-title":"On the quantum correction for thermodynamic equilibrium","volume":"40","author":"Wigner","year":"1932","journal-title":"Phys. Rev."},{"key":"ref_13","unstructured":"Feynman, R.P. The Concept of Probability in Quantum Mechanics. Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability."},{"key":"ref_14","unstructured":"Von Neumann, J. (1955). Mathematical Foundations of Quantum Mechanics, Princeton University Press."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Bell, J.S. (2004). Speakable and Unspeakable in Quantum Mechanics, Cambridge University Press. [2nd ed.].","DOI":"10.1017\/CBO9780511815676"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1103\/PhysicsPhysiqueFizika.1.195","article-title":"On the Einstein Podolsky Rosen paradox","volume":"1","author":"Bell","year":"1964","journal-title":"Physics"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Accardi, L. (2005). Some loopholes to save quantum nonlocality. Foundations of Probability and Physics-3, AIP.","DOI":"10.1063\/1.1874552"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Accardi, L. (2006). Could one now convince Einstein?. Quantum Theory: Reconsideration of Foundations-3, American Institute of Physics.","DOI":"10.1063\/1.2158707"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2016039","DOI":"10.1098\/rsta.2016.0392","article-title":"Can Einstein with Bohr debate on quantum mechanics be closed?","volume":"375","author":"Kupczynski","year":"2017","journal-title":"Phil. Trans. R. Soc. A"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Kupczynski, M. (2018). Closing the door on quantum nonlocality. Entropy, 20.","DOI":"10.20944\/preprints201809.0205.v1"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1600044","DOI":"10.1002\/prop.201600044","article-title":"After bell","volume":"65","author":"Khrennikov","year":"2017","journal-title":"Fortschr. Phys."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"734","DOI":"10.1515\/phys-2017-0086","article-title":"Bohr against Bell: Complementarity versus nonlocality","volume":"15","author":"Khrennikov","year":"2017","journal-title":"Open Phys."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1016\/j.aop.2018.07.014","article-title":"Logical inference derivation of the quantum theoretical description of Stern\u2013Gerlach and Einstein\u2013Podolsky\u2013Rosen\u2013Bohm experiments","volume":"396","author":"Katsnelson","year":"2018","journal-title":"Ann. Phys."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Khrennikov, A., and Basieva, I. (2018). Towards experiments to test violation of the original Bell inequality. Entropy, 20.","DOI":"10.3390\/e20040280"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Khrennikov, A., and Loubnets, E. (2018). Evaluating the maximal violation of the original Bell inequality by two-qudit states exhibiting perfect correlations\/anticorrelations. Entropy, 20.","DOI":"10.3390\/e20110829"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"880","DOI":"10.1103\/PhysRevLett.23.880","article-title":"Proposed experiment to test local hidden-variable theories","volume":"23","author":"Clauser","year":"1969","journal-title":"Phys. Rev. Lett."},{"key":"ref_27","unstructured":"Khrennikov, A. (arXiv, 2018). Has CHSH-inequality any relation to EPR-argument?, arXiv."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1103\/PhysRevLett.48.291","article-title":"Hidden Variables, Joint Probability, and the Bell Inequalities","volume":"48","author":"Fine","year":"1982","journal-title":"Phys. Rev. Lett."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1306","DOI":"10.1063\/1.525514","article-title":"Joint distributions, quantum correlations, and commuting observables","volume":"23","author":"Fine","year":"1982","journal-title":"J. Math. Phys."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Avis, D., Fischer, P., Hilbert, A., and Khrennikov, A. (2009). Single, Complete, Probability Spaces Consistent with EPR-Bohm\u2013Bell Experimental Data. Foundations of Probability and Physics-5, AIP Conference Proceedings.","DOI":"10.1063\/1.3109952"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"711","DOI":"10.1007\/s10701-014-9851-8","article-title":"CHSH inequality: Quantum probabilities as classical conditional probabilities","volume":"45","author":"Khrennikov","year":"2015","journal-title":"Found. Phys."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1016\/j.jmp.2011.12.003","article-title":"Selectivity in probabilistic causality: Where psychology runs into quantum physics","volume":"56","author":"Dzhafarov","year":"2012","journal-title":"J. Math. Psych."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"20150099","DOI":"10.1098\/rsta.2015.0099","article-title":"Is there contextuality in behavioral and social systems?","volume":"374","author":"Dzhafarov","year":"2015","journal-title":"Phil. Trans. R. Soc. A"},{"key":"ref_34","unstructured":"Dzhafarov, E.N., and Kujala, J.V. (2015). Probabilistic contextuality in EPR\/Bohm-type systems with signaling allowed. Contextuality from Quantum Physics to Psychology, WSP."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/j.jmp.2016.04.010","article-title":"Context-content systems of random variables: The contextuality-by default theory","volume":"74","author":"Dzhafarov","year":"2016","journal-title":"J. Math. Psych."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"20150234","DOI":"10.1098\/rsta.2015.0234","article-title":"On contextuality in behavioral data","volume":"374","author":"Dzhafarov","year":"2016","journal-title":"Phil. Trans. R. Soc. A"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Dzhafarov, E.N., and Kujala, J.V. (2018). Contextuality analysis of the double slit experiment (with a glimpse into three slits). Entropy, 20.","DOI":"10.3390\/e20040278"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.jmp.2018.06.001","article-title":"On universality of classical probability with contextually labeled random variables","volume":"85","author":"Dzhafarov","year":"2018","journal-title":"J. Math. Psych."},{"key":"ref_39","unstructured":"Khrennikov, A., and Alodjants, A. (arXiv, 2018). Bohm\u2013Bell type experiments: Classical probability approach to (no-)signaling and applications to quantum physics and psychology, arXiv."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/0375-9601(88)90334-9","article-title":"On some class of random variables leading to violations of the Bell inequality","volume":"129","author":"Czachor","year":"1988","journal-title":"Phys. Lett. A"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Khrennikov, A. (2019). Classical versus quantum probability: Comments on the paper \u201cOn universality of classical probability with contextually labeled random variables\u201d by E. Dzhafarov and M. Kon. J. Math. Psychol., in press.","DOI":"10.1016\/j.jmp.2018.10.005"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1088\/0953-4075\/40\/1\/012","article-title":"Is the fair sampling assumption supported by EPR experiments?","volume":"40","author":"Adenier","year":"2007","journal-title":"J. Phys. B"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"250401","DOI":"10.1103\/PhysRevLett.115.250401","article-title":"A significant-loophole-free test of Bell\u2019s theorem with entangled photons","volume":"115","author":"Giustina","year":"2015","journal-title":"Phys. Rev. Lett."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"250402","DOI":"10.1103\/PhysRevLett.115.250402","article-title":"Strong loophole-free test of local realism","volume":"115","author":"Shalm","year":"2015","journal-title":"Phys. Rev. Lett."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"682","DOI":"10.1038\/nature15759","article-title":"Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km","volume":"526","author":"Hensen","year":"2015","journal-title":"Nature"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1600096","DOI":"10.1002\/prop.201600096","article-title":"Test of the no-signaling principle in the Hensen loophole-free CHSH experiment","volume":"65","author":"Adenier","year":"2016","journal-title":"Fortschritte der Physik (Prog. Phys.)"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"014019","DOI":"10.1088\/0031-8949\/2014\/T163\/014019","article-title":"On the equivalence of the Clauser-Horne and Eberhard inequality based tests","volume":"2014","author":"Khrennikov","year":"2014","journal-title":"Phys. Scr."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"358","DOI":"10.1103\/RevModPhys.42.358","article-title":"The statistical interpretation of quantum mechanics","volume":"42","author":"Ballentine","year":"1989","journal-title":"Rev. Mod. Phys."},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Ballentine, L.E. (1998). Quantum Mechanics: A Modern Development, WSP.","DOI":"10.1142\/3142"},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Ballentine, L.E. (2001). Interpretations of probability and quantum theory. Quantum Probability and White Noise Analysis, WSP.","DOI":"10.1142\/9789812810809_0005"},{"key":"ref_51","unstructured":"Bohr, N. (1987). The Philosophical Writings of Niels Bohr, Ox Bow Press."},{"key":"ref_52","unstructured":"Plotnitsky, A. (2009). Epistemology and Probability: Bohr, Heisenberg, Schr\u00f6dinger and the Nature of Quantum-Theoretical Thinking, Springer."},{"key":"ref_53","doi-asserted-by":"crossref","unstructured":"Plotnitsky, A. (2012). Niels Bohr and Complementarity: An Introduction, Springer.","DOI":"10.1007\/978-1-4614-4517-3"},{"key":"ref_54","unstructured":"Jaeger, G. (2007). Quantum Information: An Overview, Springer."},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Jaeger, G. (2013). Quantum Objects: Non-Local Correlation, Causality and Objective Indefiniteness in the Quantum World, Springer.","DOI":"10.1007\/978-3-642-37629-0"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"1768","DOI":"10.1063\/1.533210","article-title":"Non-Kolmogorov probability models and modified Bell\u2019s inequality","volume":"41","author":"Khrennikov","year":"2000","journal-title":"J. Math. Phys."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1016\/S0375-9601(00)00804-5","article-title":"Contextualist viewpoint to Greenberger-Horne-Zeilinger paradox","volume":"278","author":"Khrennikov","year":"2001","journal-title":"Phys. Lett. A"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"2471","DOI":"10.1063\/1.1570952","article-title":"Contextual viewpoint to quantum stochastics","volume":"44","author":"Khrennikov","year":"2003","journal-title":"J. Math. Phys."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"678","DOI":"10.1209\/epl\/i2004-10425-9","article-title":"Schr\u00f6dinger dynamics as the Hilbert space projection of a realistic contextual probabilistic dynamics","volume":"69","author":"Khrennikov","year":"2005","journal-title":"Europhys. Lett."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"19","DOI":"10.3390\/entropy-e10020019","article-title":"Bell-Boole inequality: Nonlocality or probabilistic incompatibility of random variables?","volume":"10","author":"Khrennikov","year":"2008","journal-title":"Entropy"},{"key":"ref_61","doi-asserted-by":"crossref","unstructured":"Khrennikov, A. (2009). Contextual Approach to Quantum Formalism, Springer.","DOI":"10.1007\/978-1-4020-9593-1"},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"1650008","DOI":"10.1142\/S1230161216500086","article-title":"Bell could become the Copernicus of probability","volume":"23","author":"Khrennikov","year":"2016","journal-title":"Open Syst. Inf. Dyn."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"214","DOI":"10.14704\/nq.2008.6.3.178","article-title":"A preliminary experimental verification on the possibility of Bell inequality violation in mental states","volume":"6","author":"Conte","year":"2008","journal-title":"NeuroQuantology"},{"key":"ref_64","doi-asserted-by":"crossref","unstructured":"Asano, M., Khrennikov, A., Ohya, O., Tanaka, Y., and Yamato, I. (2015). Quantum Adaptivity in Biology: From Genetics to Cognition, Springer.","DOI":"10.1007\/978-94-017-9819-8"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.jmp.2018.06.001","article-title":"Snow queen is evil and beautiful: Experimental evidence for probabilistic contextuality in human choices","volume":"85","author":"Dzhafarov","year":"2018","journal-title":"J. Math. Psych."},{"key":"ref_66","doi-asserted-by":"crossref","unstructured":"Platonov, A.V., Poleshchuk, E.A., Bessmertny, I.A., and Gafurov, N.R. (2018, January 17\u201319). Using quantum mechanical framework for language modeling and information retrieval. Proceedings of the 12th IEEE International Conference on Application of Information and Communication Technologies (AICT 2018), Almaty, Kazakhstan.","DOI":"10.1109\/ICAICT.2018.8747051"},{"key":"ref_67","doi-asserted-by":"crossref","unstructured":"Bell, J.S. (2004). Locality in quantum mechanics: Reply to critics. Speakable and Unspeakable in Quantum Mechanics, Cambridge University Press. [2nd ed.].","DOI":"10.1017\/CBO9780511815676"},{"key":"ref_68","unstructured":"Einstein, A. (1949). Albert Einstein, Philosopher Scientist, Library of Living Philosophers."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"5039","DOI":"10.1103\/PhysRevLett.81.5039","article-title":"Violation of Bell\u2019s inequality under strict Einstein locality conditions","volume":"81","author":"Weihs","year":"1998","journal-title":"Phys. Rev. Lett."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"19708","DOI":"10.1073\/pnas.1002780107","article-title":"Violation of local realism with freedom of choice","volume":"107","author":"Scheidl","year":"2010","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1038\/nphoton.2014.50","article-title":"Experimental three-photon quantum nonlocality under strict locality conditions","volume":"8","author":"Erven","year":"2014","journal-title":"Nat. Photon."},{"key":"ref_72","doi-asserted-by":"crossref","unstructured":"Abellan, C., Amaya, W., Mitrani, D., Pruneri, V., and Mitchell, M.W. (arXiv, 2015). Generation of fresh and pure random numbers for loophole-free Bell tests, arXiv.","DOI":"10.1103\/PhysRevLett.115.250403"},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"110405","DOI":"10.1103\/PhysRevLett.112.110405","article-title":"Testing Bell\u2019s inequality with cosmic photons: Closing the setting-independence loophole","volume":"112","author":"Gallicchio","year":"2014","journal-title":"Phys. Rev. Lett."},{"key":"ref_74","unstructured":"Pironio, S. (arXiv, 2015). Random \u201cchoices\u201d and the locality loophole, arXiv."},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"212","DOI":"10.1038\/s41586-018-0085-3","article-title":"Challenging local realism with human choices","volume":"557","author":"Mitchell","year":"2018","journal-title":"Nature"},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"1179","DOI":"10.1007\/s10701-015-9930-5","article-title":"Unconditional quantum correlations do not violate Bell\u2019s inequality","volume":"45","author":"Khrennikov","year":"2015","journal-title":"Found. Phys."},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"1804","DOI":"10.1103\/PhysRevLett.49.1804","article-title":"Experimental test of Bell\u2019s Inequalities using time-varying analyzers","volume":"49","author":"Aspect","year":"1982","journal-title":"Phys. Rev. Lett."},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"803","DOI":"10.1103\/RevModPhys.65.803","article-title":"Hidden variables and the two theorerns of John Bell","volume":"65","author":"Mermin","year":"1993","journal-title":"Rev. Mod. Phys."},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"450","DOI":"10.1103\/RevModPhys.38.447","article-title":"On the problem of hidden variables in quantum theory","volume":"38","author":"Bell","year":"1966","journal-title":"Rev. Mod. Phys."},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1090\/S0002-9939-1968-0224339-X","article-title":"Dispersion-free states and the exclusion of hidden variables","volume":"19","author":"Gudder","year":"1968","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1103\/RevModPhys.40.229","article-title":"Hidden variables in quantum mechanics reconsidered","volume":"40","author":"Gudder","year":"1968","journal-title":"Rev. Mod. Phys."},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1063\/1.1665156","article-title":"On hidden-variable theories","volume":"11","author":"Gudder","year":"1970","journal-title":"J. Math. Phys"},{"key":"ref_83","doi-asserted-by":"crossref","unstructured":"Shimony, A. (2009). Hidden-variables models of quantum mechanics (Noncontextual and contextual). Compendium of Quantum Physics, Springer.","DOI":"10.1007\/978-3-540-70626-7_89"},{"key":"ref_84","unstructured":"Shimony, A. (1971). Experimental test of local hidden variable theories. Foundations of Quantum Mechanics, Academic."},{"key":"ref_85","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1137\/1025105","article-title":"The logic of quantum mechanics","volume":"25","author":"Beltrametti","year":"1983","journal-title":"SIAM"},{"key":"ref_86","first-page":"325","article-title":"Local realism, contextualism and loopholes in Bell\u2019s experiments","volume":"5","author":"Khrennikov","year":"2002","journal-title":"Found. Prob. Phys. Math. Modell."},{"key":"ref_87","unstructured":"Khrennikov, A., and Volovich, I. Quantum nonlocality, EPR model, and Bell\u2019s theorem. Proceedings of the 3nd Sakharov Conference on Physics (Moscow)."},{"key":"ref_88","doi-asserted-by":"crossref","unstructured":"Khrennikov, A., Nilsson, B., Nordebo, S., and Volovich, I. (2012). Distance dependence of entangled photons in waveguides. Foundations of Probability and Physics 6, AIP.","DOI":"10.1063\/1.3688979"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/2\/157\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:30:42Z","timestamp":1760185842000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/2\/157"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,2,8]]},"references-count":88,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2019,2]]}},"alternative-id":["e21020157"],"URL":"https:\/\/doi.org\/10.3390\/e21020157","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,2,8]]}}}