Publication: Observers of quantum systems cannot agree to disagree
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Is the world quantum? An active research line in quantum foundations is devoted to exploring what constraints can rule out the postquantum theories that are consistent with experimentally observed results. We explore this question in the context of epistemics, and ask whether agreement between observers can serve as a physical principle that must hold for any theory of the world. Aumann’s seminal Agreement Theorem states that two observers (of classical systems) cannot agree to disagree. We propose an extension of this theorem to no-signaling settings. In particular, we establish an Agreement Theorem for observers of quantum systems, while we construct examples of (postquantum) no-signaling boxes where observers can agree to disagree. The PR box is an extremal instance of this phenomenon. These results make it plausible that agreement between observers might be a physical principle, while they also establish links between the fields of epistemics and quantum information that seem worthy of further exploration.
1. Spekkens, R. W. Evidence for the epistemic view of quantum states: a toy theory. Phys. Rev. A 75(March), 032110 (2007). 2. Larsson, J.-Å A contextual extension of Spekkens’ toy model. AIP Conf. Proc. 1424, 211–220 (2012). 3. Popescu, S. & Rohrlich, D. Quantum nonlocality as an axiom. Found. Phys. 24 (March), 379–385 (1994). 4. Clifton, R., Bub, J. & Halvorson, H. Characterizing quantum theory in terms of information-theoretic constraints. Found. Phys. 33, 1561–1591 (2003). 5. Pawlowski, M. et al. Information causality as a physical principle. Nature 461 (October), 1101–1104 (2009). 6. Sun, L.-L., Zhou, X. & Yu, S. No disturbance without uncertainty as a physical principle. Preprint at https://arxiv.org/abs/1906.11807 (2019). 7. Yan, B. Quantum correlations are tightly bound by the exclusivity principle. Phys. Rev. Lett. 110(June), 260406 (2013). 8. Aumann, R. J. Agreeing to disagree. Ann. Stat. 4, 1236–1239 (1976). 9. Sebenius, J. K. & Geanakoplos, J. Don’t bet on it: contingent agreements with asymmetric information. J. Am. Stat. Assoc. 78, 424–426 (1983). 10. Milgrom, P. & Stokey, N. Information, trade and common knowledge. J. Economic Theory 26, 17–27 (1982). 11. Aumann, R. J. & Brandenburger, A. Epistemic conditions for nash equilibrium. Econometrica 63, 1161–1180 (1995). 12. Bell, J. On the Einstein Podolsky Rosen paradox. Phys. Phys. Fiz. 1 (November), 195–200 (1964). 13. Barrett, J. et al. Nonlocal correlations as an information-theoretic resource. Phys. Rev. A 71(Feb), 022101 (2005). 14. Ferrie, C. Quasi-probability representations of quantum theory with applications to quantum information science. Rep. Prog. Phys. 74, 116001 (2011). 15. Aaronson, S. The complexity of agreement. In Proceedings of the Thirty-Seventh Annual ACM Symposium on Theory of Computing, STOC ’05, pages 634–643, New York, NY, USA, 2005. Association for Computing Machinery. 16. Abramsky, S. & Brandenburger, A. The sheaf-theoretic structure of nonlocality and contextuality. N. J. Phys. 13(November), 113036 (2011). 17. Abramsky, S. and Brandenburger, A. In Horizons of the Mind. A Tribute to Prakash Panangaden (eds van Breugel, F., Kashefi, E., Palamidessi, C. & Rutten, J.) (Springer International Publishing, 2014). 18. Frauchiger, D. & Renner, R. Quantum theory cannot consistently describe the use of itself. Nat. Commun. 9, 3711 (2018). 19. Cirel’son, B. S. Quantum generalizations of Bell’s inequality. Lett. Math. Phys. 4, 93–100 (1980). 20. Geanakoplos, J. D. & Polemarchakis, H. M. We can’t disagree forever. J. Econ. Theory 28, 192–200 (1982). 21. Hardy, L. Quantum mechanics, local realistic theories, and Lorentz-invariant realistic theories. Phys. Rev. Lett. 68(May), 2981–2984 (1992). 22. Rai, A., Duarte, C., Brito, S. & Chaves, R. Geometry of the quantum set on nosignaling faces. Phys. Rev. A 99(March), 032106 (2019). 23. Fagin, R., Halpern, J., Moses, Y. & Vardi, M. Reasoning About Knowledge (MIT Press, 2003). 24. Goh, K. T. et al. Geometry of the set of quantum correlations. Phys. Rev. A 97(Feb), 022104 (2018). 25. Navascués, M., Guryanova, Y., Hoban, M. J. & Acín, A. Almost quantum correlations. Nat. Commun. 6, (2015). 26. Navascués, M., Pironio, S. & Acín, A. A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations. N. J. Phys. 10(jul), 073013 (2008). 27. Gallego, R., Würflinger, L. E., Acín, A. & Navascués, M. Quantum correlations require multipartite information principles. Phys. Rev. Lett. 107(Nov), 210403 (2011). 28. Parikh, R. & Krasucki, P. Communication, consensus, and knowledge. J. Econ. Theory 52, 178–189 (1990). 29. Khrennikov, A. Quantum version of Aumann’s approach to common knowledge: Sufficient conditions of impossibility to agree on disagree. J. Math. Econ. 60(October), 89–104 (2015). 30. Khrennikov, A. & Basieva, I. Possibility to agree on disagree from quantum information and decision making. J. Math. Psychol. 62-63(October), 1–15 (2014). 31. Abramsky, S. & Carù, G. Non-locality, contextuality and valuation algebras: a general theory of disagreement. Philos. Trans. R. Soc. A 377(November), 20190036 (2019).