{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,4]],"date-time":"2026-04-04T03:21:16Z","timestamp":1775272876664,"version":"3.50.1"},"reference-count":68,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2019,9,9]],"date-time":"2019-09-09T00:00:00Z","timestamp":1567987200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"<jats:p>Entanglement is of paramount importance in quantum information theory. Its supremacy over classical correlations has been demonstrated in a numerous information theoretic protocols. Here we study possible adequacy of quantum entanglement in Bayesian game theory, particularly in social welfare solution (SWS), a strategy which the players follow to maximize sum of their payoffs. Given a multi-partite quantum state as an advice, players can come up with several correlated strategies by performing local measurements on their parts of the quantum state. A quantum strategy is called quantum-SWS if it is advantageous over a classical equilibrium (CE) strategy in the sense that none of the players has to sacrifice their CE-payoff rather some have incentive and at the same time it maximizes sum of all players' payoffs over all possible quantum advantageous strategies. Quantum state yielding such a quantum-SWS is called a quantum social welfare advice (SWA). We show that any two-qubit pure entangled state, even if it is arbitrarily close to a product state, can serve as quantum-SWA in some Bayesian game. Our result, thus, gives cognizance to the fact that every two-qubit pure entanglement is the best resource for some operational task.<\/jats:p>","DOI":"10.22331\/q-2019-09-09-185","type":"journal-article","created":{"date-parts":[[2019,9,9]],"date-time":"2019-09-09T11:12:08Z","timestamp":1568027528000},"page":"185","source":"Crossref","is-referenced-by-count":21,"title":["Two-Qubit Pure Entanglement as Optimal Social Welfare Resource in Bayesian Game"],"prefix":"10.22331","volume":"3","author":[{"given":"Manik","family":"Banik","sequence":"first","affiliation":[{"name":"S.N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700098, India."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Some Sankar","family":"Bhattacharya","sequence":"additional","affiliation":[{"name":"Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nirman","family":"Ganguly","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Birla Institute of Technology and Science Pilani, Hyderabad campus, Telengana 500078,India."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tamal","family":"Guha","sequence":"additional","affiliation":[{"name":"Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Amit","family":"Mukherjee","sequence":"additional","affiliation":[{"name":"Optics and Quantum Information Group, The Institute of Mathematical Sciences, HBNI, CIT Campus, Taramani, Chennai 600113, India."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ashutosh","family":"Rai","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Korea Advanced Institute of Science and Technology (KAIST), 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Republic of Korea."},{"name":"International Institute of Physics, Federal University of Rio Grande do Norte, 59070-405 Natal, Brazil."},{"name":"Centre for Quantum Computer Science, University of Latvia, Raina Bulv. 19, Riga, LV-1586, Latvia."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Arup","family":"Roy","sequence":"additional","affiliation":[{"name":"S.N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700098, India."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2019,9,9]]},"reference":[{"key":"0","unstructured":"R. Gibbons. Game Theory for Applied Economists. Princeton University Press, Princeton, NJ, 1992. URL https:\/\/press.princeton.edu\/titles\/4993.html."},{"key":"1","doi-asserted-by":"crossref","unstructured":"P. Ordeshook. Game Theory and Political Theory: An Introduction. Cambridge University Press, 1986.","DOI":"10.1017\/CBO9780511666742"},{"key":"2","unstructured":"A. M. Colman. Game Theory and its Applications: In the Social and Biological Sciences. Routledge, Taylor & Francis group, 1995."},{"key":"3","unstructured":"M. J. Osborne. An Introduction to Game Theory. Oxford University Press, New York, 2003."},{"key":"4","unstructured":"J. Von Neumann and O. Morgenstern. Theory of Games and Economic Behavior. Princeton University Press, 1944. URL https:\/\/press.princeton.edu\/titles\/7802.html."},{"key":"5","doi-asserted-by":"publisher","unstructured":"John F. Nash. Equilibrium points in n-person games. PNAS, 36: 48, 1950. URL https:\/\/doi.org\/10.1073\/pnas.36.1.48.","DOI":"10.1073\/pnas.36.1.48"},{"key":"6","doi-asserted-by":"publisher","unstructured":"John F. Nash. Non-cooperative games. The Annals of Mathematics, 54: 286295, 1951. URL https:\/\/doi.org\/10.2307\/1969529.","DOI":"10.2307\/1969529"},{"key":"7","doi-asserted-by":"publisher","unstructured":"John C. Harsanyi. Games with Incomplete Information Played by \u201cBayesian\u201d Players, I-III Part I. The Basic Model. Management Science, 14 (3): 159-182, 1967. 10.1287\/mnsc.14.3.159. URL https:\/\/doi.org\/10.1287\/mnsc.14.3.159.","DOI":"10.1287\/mnsc.14.3.159"},{"key":"8","doi-asserted-by":"publisher","unstructured":"John C. Harsanyi. Games with Incomplete Information Played by \u201cBayesian\u201d Players Part II. Bayesian Equilibrium Points. Management Science, 14 (5): 320-334, 1968a. 10.1287\/mnsc.14.5.320. URL https:\/\/doi.org\/10.1287\/mnsc.14.5.320.","DOI":"10.1287\/mnsc.14.5.320"},{"key":"9","doi-asserted-by":"publisher","unstructured":"John C. Harsanyi. Games with Incomplete Information Played by \u2018Bayesian\u2019 Players, Part III. The Basic Probability Distribution of the Game. Management Science, 14 (7): 486-502, 1968b. 10.1287\/mnsc.14.7.486. URL https:\/\/doi.org\/10.1287\/mnsc.14.7.486.","DOI":"10.1287\/mnsc.14.7.486"},{"key":"10","doi-asserted-by":"publisher","unstructured":"R. J. Aumann. Subjectivity and correlation in randomized strategies. Journal of mathematical economics, 1: 67, 1974. URL https:\/\/doi.org\/10.1016\/0304-4068(74)90037-8.","DOI":"10.1016\/0304-4068(74)90037-8"},{"key":"11","unstructured":"M. Rabin. Incorporating Fairness Into Game Theory. UC Berkeley: Department of Economics, UCB, 1991. URL https:\/\/escholarship.org\/uc\/item\/3s87d1tm."},{"key":"12","unstructured":"K. Binmore. Game Theory and the Social Contract, Vol. 2: Just Playing (Economic Learning and Social Evolution). MIT Press, Cambridge, MA, 1998."},{"key":"13","doi-asserted-by":"publisher","unstructured":"J. G. March. Bounded rationality, ambiguity, and the engineering of choice. The Bell Journal of Economics, 9: 587, 1978. URL https:\/\/doi.org\/10.2307\/3003600.","DOI":"10.2307\/3003600"},{"key":"14","unstructured":"W. B. Arthur. Inductive reasoning and bounded rationality. The American Economic Review, 48: 406, 1994. URL https:\/\/www.jstor.org\/stable\/2117868?seq=1#page_scan_tab_content."},{"key":"15","unstructured":"Vincenzo Auletta, Diodato Ferraioli, Ashutosh Rai, Giannicola Scarpa, and Andreas Winter. Belief-Invariant and Quantum Equilibria in Games of Incomplete Information. arXiv:1605.07896, 2016. URL https:\/\/arxiv.org\/abs\/1605.07896."},{"key":"16","doi-asserted-by":"publisher","unstructured":"R. J. Aumann. Correlated equilibrium as an expression of bayesian rationality. Econometrica, 55: 1, 1987. URL https:\/\/doi.org\/10.2307\/1911154.","DOI":"10.2307\/1911154"},{"key":"17","doi-asserted-by":"publisher","unstructured":"Christos H. Papadimitriou and Tim Roughgarden. Computing correlated equilibria in multi-player games. J. ACM, 55 (3): 14:1-14:29, August 2008. ISSN 0004-5411. 10.1145\/1379759.1379762. URL https:\/\/doi.org\/10.1145\/1379759.1379762.","DOI":"10.1145\/1379759.1379762"},{"key":"18","unstructured":"A. Blaquiere. Necessary and sufficiency conditions for optimal strategies in impulsive control. In Differential Games and Control Theory III, 1979."},{"key":"19","doi-asserted-by":"publisher","unstructured":"A. Blaquiere. Wave mechanics as a two-player game. In Dynamical Systems and Microphysics, pages 33-69. Springer Vienna, 1980. 10.1007\/978-3-7091-4330-8_2. URL https:\/\/doi.org\/10.1007\/978-3-7091-4330-8_2.","DOI":"10.1007\/978-3-7091-4330-8_2"},{"key":"20","doi-asserted-by":"publisher","unstructured":"David A. Meyer. Quantum strategies. Phys. Rev. Lett., 82: 1052-1055, Feb 1999. 10.1103\/PhysRevLett.82.1052. URL https:\/\/doi.org\/10.1103\/PhysRevLett.82.1052.","DOI":"10.1103\/PhysRevLett.82.1052"},{"key":"21","doi-asserted-by":"publisher","unstructured":"Jens Eisert, Martin Wilkens, and Maciej Lewenstein. Quantum games and quantum strategies. Physical Review Letters, 83 (15): 3077-3080, October 1999. 10.1103\/physrevlett.83.3077. URL https:\/\/doi.org\/10.1103\/physrevlett.83.3077.","DOI":"10.1103\/physrevlett.83.3077"},{"key":"22","doi-asserted-by":"publisher","unstructured":"A. P. Flitney and D. Abbott. An Introduction to Quantum Game Theory. Fluctuation and Noise Letters, 02 (04): R175-R187, December 2002. 10.1142\/s0219477502000981. URL https:\/\/doi.org\/10.1142\/s0219477502000981.","DOI":"10.1142\/s0219477502000981"},{"key":"23","doi-asserted-by":"publisher","unstructured":"Hong Guo, Juheng Zhang, and Gary J. Koehler. A survey of quantum games. Decision Support Systems, 46 (1): 318-332, December 2008. 10.1016\/j.dss.2008.07.001. URL https:\/\/doi.org\/10.1016\/j.dss.2008.07.001.","DOI":"10.1016\/j.dss.2008.07.001"},{"key":"24","doi-asserted-by":"publisher","unstructured":"Faisal Shah Khan, Neal Solmeyer, Radhakrishnan Balu, and Travis S. Humble. Quantum games: a review of the history, current state, and interpretation. Quantum Information Processing, 17 (11), October 2018. 10.1007\/s11128-018-2082-8. URL https:\/\/doi.org\/10.1007\/s11128-018-2082-8.","DOI":"10.1007\/s11128-018-2082-8"},{"key":"25","doi-asserted-by":"publisher","unstructured":"N. Brunner and N. Linden. Connection between Bell nonlocality and Bayesian game theory. Nat. Comm., 4: 2057, 2013. URL https:\/\/doi.org\/10.1038\/ncomms3057.","DOI":"10.1038\/ncomms3057"},{"key":"26","doi-asserted-by":"publisher","unstructured":"Taksu Cheon and Azhar Iqbal. Bayesian nash equilibria and bell inequalities. Journal of the Physical Society of Japan, 77 (2): 024801, February 2008. 10.1143\/jpsj.77.024801. URL https:\/\/doi.org\/10.1143\/jpsj.77.024801.","DOI":"10.1143\/jpsj.77.024801"},{"key":"27","doi-asserted-by":"publisher","unstructured":"Azhar Iqbal, James M. Chappell, and Derek Abbott. Social optimality in quantum bayesian games. Physica A: Statistical Mechanics and its Applications, 436: 798-805, October 2015. 10.1016\/j.physa.2015.05.020. URL https:\/\/doi.org\/10.1016\/j.physa.2015.05.020.","DOI":"10.1016\/j.physa.2015.05.020"},{"key":"28","doi-asserted-by":"publisher","unstructured":"Ashutosh Rai and Goutam Paul. Strong quantum solutions in conflicting-interest bayesian games. Physical Review A, 96 (4), October 2017. 10.1103\/physreva.96.042340. URL https:\/\/doi.org\/10.1103\/physreva.96.042340.","DOI":"10.1103\/physreva.96.042340"},{"key":"29","doi-asserted-by":"publisher","unstructured":"Faisal Shah Khan and Travis S. Humble. Nash embedding and equilibrium in pure quantum states. In Quantum Technology and Optimization Problems, pages 51-62. Springer International Publishing, 2019, (arXiv:1801.02053). 10.1007\/978-3-030-14082-3_5. URL https:\/\/doi.org\/10.1007\/978-3-030-14082-3_5.","DOI":"10.1007\/978-3-030-14082-3_5"},{"key":"30","doi-asserted-by":"publisher","unstructured":"A. Pappa, N. Kumar, T. Lawson, M. Santha, S. Zhang, E. Diamanti, and I. Kerenidis. Nonlocality and Conflicting Interest Games. Phys. Rev. Lett., 114: 020401, Jan 2015. 10.1103\/PhysRevLett.114.020401. URL https:\/\/doi.org\/10.1103\/PhysRevLett.114.020401.","DOI":"10.1103\/PhysRevLett.114.020401"},{"key":"31","doi-asserted-by":"publisher","unstructured":"Arup Roy, Amit Mukherjee, Tamal Guha, Sibasish Ghosh, Some Sankar Bhattacharya, and Manik Banik. Nonlocal correlations: Fair and unfair strategies in Bayesian games. Phys. Rev. A, 94: 032120, Sep 2016. 10.1103\/PhysRevA.94.032120. URL https:\/\/doi.org\/10.1103\/PhysRevA.94.032120.","DOI":"10.1103\/PhysRevA.94.032120"},{"key":"32","doi-asserted-by":"publisher","unstructured":"N. Gisin. Bell's inequality holds for all non-product states. Physics Letters A, 154 (5-6): 201-202, April 1991. 10.1016\/0375-9601(91)90805-i. URL https:\/\/doi.org\/10.1016\/0375-9601(91)90805-i.","DOI":"10.1016\/0375-9601(91)90805-i"},{"key":"33","doi-asserted-by":"publisher","unstructured":"Francesco Buscemi. All entangled quantum states are nonlocal. Physical Review Letters, 108 (20), May 2012. 10.1103\/physrevlett.108.200401. URL https:\/\/doi.org\/10.1103\/physrevlett.108.200401.","DOI":"10.1103\/physrevlett.108.200401"},{"key":"34","doi-asserted-by":"publisher","unstructured":"Llu\u00eds Masanes. All bipartite entangled states are useful for information processing. Physical Review Letters, 96 (15), April 2006a. 10.1103\/physrevlett.96.150501. URL https:\/\/doi.org\/10.1103\/physrevlett.96.150501.","DOI":"10.1103\/physrevlett.96.150501"},{"key":"35","doi-asserted-by":"publisher","unstructured":"Marco Piani and John Watrous. All entangled states are useful for channel discrimination. Physical Review Letters, 102 (25), June 2009. 10.1103\/physrevlett.102.250501. URL https:\/\/doi.org\/10.1103\/physrevlett.102.250501.","DOI":"10.1103\/physrevlett.102.250501"},{"key":"36","doi-asserted-by":"publisher","unstructured":"Daniel Cavalcanti, Paul Skrzypczyk, and Ivan \u0160upi\u0107. All entangled states can demonstrate nonclassical teleportation. Physical Review Letters, 119 (11), September 2017. 10.1103\/physrevlett.119.110501. URL https:\/\/doi.org\/10.1103\/physrevlett.119.110501.","DOI":"10.1103\/physrevlett.119.110501"},{"key":"37","doi-asserted-by":"publisher","unstructured":"Reinhard F. Werner. Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model. Phys. Rev. A, 40: 4277-4281, Oct 1989. 10.1103\/PhysRevA.40.4277. URL https:\/\/doi.org\/10.1103\/PhysRevA.40.4277.","DOI":"10.1103\/PhysRevA.40.4277"},{"key":"38","doi-asserted-by":"publisher","unstructured":"R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki. Quantum entanglement. Rev. Mod. Phys., 81: 865-942, Jun 2009. 10.1103\/RevModPhys.81.865. URL https:\/\/doi.org\/10.1103\/RevModPhys.81.865.","DOI":"10.1103\/RevModPhys.81.865"},{"key":"39","doi-asserted-by":"publisher","unstructured":"J. S. Bell. On the Einstein Podolsky Rosen Paradox. Physics, 1 (3): 195, 1964. URL https:\/\/doi.org\/10.1103\/PhysicsPhysiqueFizika.1.195.","DOI":"10.1103\/PhysicsPhysiqueFizika.1.195"},{"key":"40","doi-asserted-by":"publisher","unstructured":"J. S. Bell. On the Problem of Hidden Variables in Quantum Mechanics. Rev. Mod. Phys., 38: 447, 1966. URL https:\/\/doi.org\/10.1103\/RevModPhys.38.447.","DOI":"10.1103\/RevModPhys.38.447"},{"key":"41","doi-asserted-by":"publisher","unstructured":"Nicolas Brunner, Daniel Cavalcanti, Stefano Pironio, Valerio Scarani, and Stephanie Wehner. Bell nonlocality. Rev. Mod. Phys., 86: 419-478, Apr 2014. 10.1103\/RevModPhys.86.419. URL https:\/\/doi.org\/10.1103\/RevModPhys.86.419.","DOI":"10.1103\/RevModPhys.86.419"},{"key":"42","unstructured":"edited by, K. Arrow, A. Sen, and K. Suzumura. Handbook of Social Choice and Welfare-Vol.I. 2002. URL https:\/\/www.sciencedirect.com\/handbook\/handbook-of-social-choice-and-welfare\/vol\/1\/suppl\/C."},{"key":"43","unstructured":"edited by, K. Arrow, A. Sen, and K. Suzumura. Handbook of Social Choice and Welfare-Vol.II. 2011. URL https:\/\/www.sciencedirect.com\/handbook\/handbook-of-social-choice-and-welfare\/vol\/2\/suppl\/C."},{"key":"44","doi-asserted-by":"publisher","unstructured":"Jonathan Barrett, Noah Linden, Serge Massar, Stefano Pironio, Sandu Popescu, and David Roberts. Nonlocal correlations as an information-theoretic resource. Phys. Rev. A, 71: 022101, Feb 2005. 10.1103\/PhysRevA.71.022101. URL https:\/\/doi.org\/10.1103\/PhysRevA.71.022101.","DOI":"10.1103\/PhysRevA.71.022101"},{"key":"45","doi-asserted-by":"publisher","unstructured":"Stefano Pironio. Lifting bell inequalities. Journal of Mathematical Physics, 46 (6): 062112, 2005. 10.1063\/1.1928727. URL https:\/\/doi.org\/10.1063\/1.1928727.","DOI":"10.1063\/1.1928727"},{"key":"46","doi-asserted-by":"publisher","unstructured":"Nicolas Brunner, Valerio Scarani, and Nicolas Gisin. Bell-type inequalities for nonlocal resources. Journal of Mathematical Physics, 47 (11): 112101, 2006. 10.1063\/1.2352857. URL https:\/\/doi.org\/10.1063\/1.2352857.","DOI":"10.1063\/1.2352857"},{"key":"47","doi-asserted-by":"publisher","unstructured":"Fr\u00e9d\u00e9ric Dupuis, Nicolas Gisin, Avinatan Hasidim, Andr\u00e9 Allan M\u00e9thot, and Haran Pilpel. No nonlocal box is universal. Journal of Mathematical Physics, 48 (8): 082107, 2007. URL https:\/\/doi.org\/10.1063\/1.2767538.","DOI":"10.1063\/1.2767538"},{"key":"48","doi-asserted-by":"publisher","unstructured":"J. M. M\u00e9ndez and Jes\u00fas Ur\u00edas. On the no-signaling approach to quantum nonlocality. Journal of Mathematical Physics, 56 (3): 032101, 2015. 10.1063\/1.4914336. URL https:\/\/doi.org\/10.1063\/1.4914336.","DOI":"10.1063\/1.4914336"},{"key":"49","doi-asserted-by":"publisher","unstructured":"Antonio Ac\u00edn, Serge Massar, and Stefano Pironio. Randomness versus Nonlocality and Entanglement. Phys. Rev. Lett., 108: 100402, Mar 2012. 10.1103\/PhysRevLett.108.100402. URL https:\/\/doi.org\/10.1103\/PhysRevLett.108.100402.","DOI":"10.1103\/PhysRevLett.108.100402"},{"key":"50","doi-asserted-by":"publisher","unstructured":"Tzyh Haur Yang and Miguel Navascu\u00e9s. Robust self-testing of unknown quantum systems into any entangled two-qubit states. Phys. Rev. A, 87: 050102, May 2013. 10.1103\/PhysRevA.87.050102. URL https:\/\/doi.org\/10.1103\/PhysRevA.87.050102.","DOI":"10.1103\/PhysRevA.87.050102"},{"key":"51","doi-asserted-by":"publisher","unstructured":"C\u00e9dric Bamps and Stefano Pironio. Sum-of-squares decompositions for a family of clauser-horne-shimony-holt-like inequalities and their application to self-testing. Phys. Rev. A, 91: 052111, May 2015. 10.1103\/PhysRevA.91.052111. URL https:\/\/doi.org\/10.1103\/PhysRevA.91.052111.","DOI":"10.1103\/PhysRevA.91.052111"},{"key":"52","doi-asserted-by":"publisher","unstructured":"Artur K. Ekert. Quantum cryptography based on Bell's theorem. Phys. Rev. Lett., 67: 661-663, Aug 1991. 10.1103\/PhysRevLett.67.661. URL https:\/\/doi.org\/10.1103\/PhysRevLett.67.661.","DOI":"10.1103\/PhysRevLett.67.661"},{"key":"53","doi-asserted-by":"publisher","unstructured":"C.H. Bennett and S.J. Wiesner. Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. Phys. Rev. Lett., 69: 2881, 1992. 10.1103\/PhysRevLett.69.2881. URL https:\/\/doi.org\/10.1103\/PhysRevLett.69.2881.","DOI":"10.1103\/PhysRevLett.69.2881"},{"key":"54","doi-asserted-by":"publisher","unstructured":"Charles H. Bennett, Gilles Brassard, and N. David Mermin. Quantum cryptography without Bell's theorem. Phys. Rev. Lett., 68: 557-559, Feb 1992. 10.1103\/PhysRevLett.68.557. URL https:\/\/doi.org\/10.1103\/PhysRevLett.68.557.","DOI":"10.1103\/PhysRevLett.68.557"},{"key":"55","doi-asserted-by":"publisher","unstructured":"C.H. Bennett, G. Brassard, C. Cr\u00e9peau, R. Jozsa, A. Peres, and W.K. Wootters. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett., 70: 1895, 1993. 10.1103\/PhysRevLett.70.1895. URL https:\/\/doi.org\/10.1103\/PhysRevLett.70.1895.","DOI":"10.1103\/PhysRevLett.70.1895"},{"key":"56","doi-asserted-by":"publisher","unstructured":"A. Einstein, B. Podolsky, and N. Rosen. Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Phys. Rev., 47: 777-780, May 1935. 10.1103\/PhysRev.47.777. URL https:\/\/doi.org\/10.1103\/PhysRev.47.777.","DOI":"10.1103\/PhysRev.47.777"},{"key":"57","doi-asserted-by":"publisher","unstructured":"E. Schr\u00f6dinger. Discussion of Probability Relations between Separated Systems. Proc. Cambridge Philos. Soc., 31: 553, 1935. URL https:\/\/doi.org\/10.1017\/S0305004100013554.","DOI":"10.1017\/S0305004100013554"},{"key":"58","doi-asserted-by":"publisher","unstructured":"E. Schr\u00f6dinger. Probability relations between separated systems. Proc. Cambridge Philos. Soc., 32: 446, 1936. URL https:\/\/doi.org\/10.1017\/S0305004100019137.","DOI":"10.1017\/S0305004100019137"},{"key":"59","doi-asserted-by":"publisher","unstructured":"H.M. Wiseman, S.J. Jones, and A.C. Doherty. Steering, Entanglement, Nonlocality, and the Einstein-Podolsky-Rosen Paradox. Phys. Rev. Lett., 98: 140402, 2007. 10.1103\/PhysRevLett.98.140402. URL https:\/\/doi.org\/10.1103\/PhysRevLett.98.140402.","DOI":"10.1103\/PhysRevLett.98.140402"},{"key":"60","doi-asserted-by":"publisher","unstructured":"Llu\u00eds Masanes. Asymptotic violation of bell inequalities and distillability. Phys. Rev. Lett., 97: 050503, Aug 2006b. 10.1103\/PhysRevLett.97.050503. URL https:\/\/doi.org\/10.1103\/PhysRevLett.97.050503.","DOI":"10.1103\/PhysRevLett.97.050503"},{"key":"61","doi-asserted-by":"publisher","unstructured":"Shizuo Kakutani. A generalization of brouwer's fixed point theorem. Duke Mathematical Journal, 8 (3): 457-459, September 1941. 10.1215\/s0012-7094-41-00838-4. URL https:\/\/doi.org\/10.1215\/s0012-7094-41-00838-4.","DOI":"10.1215\/s0012-7094-41-00838-4"},{"key":"62","doi-asserted-by":"publisher","unstructured":"I. L. Glicksberg. A further generalization of the kakutani fixed theorem, with application to nash equilibrium points. Proceedings of the American Mathematical Society, 3 (1): 170-170, January 1952. 10.1090\/s0002-9939-1952-0046638-5. URL https:\/\/doi.org\/10.1090\/s0002-9939-1952-0046638-5.","DOI":"10.1090\/s0002-9939-1952-0046638-5"},{"key":"63","doi-asserted-by":"publisher","unstructured":"John Nash. The imbedding problem for riemannian manifolds. The Annals of Mathematics, 63 (1): 20, January 1956. 10.2307\/1969989. URL https:\/\/doi.org\/10.2307\/1969989.","DOI":"10.2307\/1969989"},{"key":"64","unstructured":"H. Reichenbach. The Direction of Time. University of Los Angeles Press, Berkeley, 1956."},{"key":"65","doi-asserted-by":"publisher","unstructured":"Eric G Cavalcanti and Raymond Lal. On modifications of reichenbach's principle of common cause in light of bell's theorem. J. Phys. A: Math. Theor., 47: 424018, 2014. URL https:\/\/doi.org\/10.1088\/1751-8113\/47\/42\/424018.","DOI":"10.1088\/1751-8113\/47\/42\/424018"},{"key":"66","doi-asserted-by":"publisher","unstructured":"Valerio Scarani, Nicolas Gisin, Nicolas Brunner, Lluis Masanes, Sergi Pino, and Antonio Ac\u00edn. Secrecy extraction from no-signaling correlations. Phys. Rev. A, 74: 042339, Oct 2006. 10.1103\/PhysRevA.74.042339. URL https:\/\/doi.org\/10.1103\/PhysRevA.74.042339.","DOI":"10.1103\/PhysRevA.74.042339"},{"key":"67","doi-asserted-by":"publisher","unstructured":"J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt. Proposed Experiment to Test Local Hidden-Variable Theories. Phys. Rev. Lett., 23: 880-884, Oct 1969. 10.1103\/PhysRevLett.23.880. URL https:\/\/doi.org\/10.1103\/PhysRevLett.23.880.","DOI":"10.1103\/PhysRevLett.23.880"}],"container-title":["Quantum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/quantum-journal.org\/papers\/q-2019-09-09-185\/pdf\/","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,9,9]],"date-time":"2019-09-09T11:12:16Z","timestamp":1568027536000},"score":1,"resource":{"primary":{"URL":"https:\/\/quantum-journal.org\/papers\/q-2019-09-09-185\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,9,9]]},"references-count":68,"URL":"https:\/\/doi.org\/10.22331\/q-2019-09-09-185","archive":["CLOCKSS"],"relation":{},"ISSN":["2521-327X"],"issn-type":[{"value":"2521-327X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,9,9]]},"article-number":"185"}}