Almost Quantum Correlations are Inconsistent with Specker’s Principle

Tomáš Gonda1,2, Ravi Kunjwal1, David Schmid1,2, Elie Wolfe1, and Ana Belén Sainz1

1Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada, N2L 2Y5
2Dept. of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1

Ernst Specker considered a particular feature of quantum theory to be especially fundamental, namely that pairwise joint measurability of sharp measurements implies their global joint measurability ($\href{https://vimeo.com/52923835}{vimeo.com/52923835}$). To date, Specker's principle seemed incapable of singling out quantum theory from the space of all general probabilistic theories. In particular, its well-known consequence for experimental statistics, the principle of consistent exclusivity, does not rule out the set of correlations known as almost quantum, which is strictly larger than the set of quantum correlations. Here we show that, contrary to the popular belief, Specker's principle cannot be satisfied in any theory that yields almost quantum correlations.

► BibTeX data

► References

[1] G. Bacciagaluppi and A. Valentini, Quantum theory at the crossroads: reconsidering the 1927 Solvay conference (Cambridge University Press, 2009).
https://doi.org/10.1017/cbo9781139194983

[2] A. Einstein, B. Podolsky, and N. Rosen, ``Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?'' Phys. Rev. 47, 777 (1935).
https://doi.org/10.1103/PhysRev.47.777

[3] M. D. Mazurek, M. F. Pusey, K. J. Resch, and R. W. Spekkens, ``Experimentally bounding deviations from quantum theory in the landscape of generalized probabilistic theories,'' arXiv:1710.05948 (2017).
arXiv:1710.05948

[4] J. S. Bell, ``On the Einstein-Podolsky-Rosen paradox,'' Physics 1, 195 (1964).
https://doi.org/10.1103/PhysicsPhysiqueFizika.1.195

[5] S. Kochen and E. P. Specker, ``The problem of hidden variables in quantum mechanics,'' J. Math. Mech. 17, 59 (1967).
https://doi.org/10.1007/978-94-010-1795-4_17

[6] R. W. Spekkens, ``Contextuality for preparations, transformations, and unsharp measurements,'' Phys. Rev. A 71, 052108 (2005).
https://doi.org/10.1103/PhysRevA.71.052108

[7] S. Abramsky and A. Brandenburger, ``The sheaf-theoretic structure of non-locality and contextuality,'' New J. Phys. 13, 113036 (2011).
https://doi.org/10.1088/1367-2630/13/11/113036

[8] A. Acín, T. Fritz, A. Leverrier, and A. B. Sainz, ``A Combinatorial Approach to Nonlocality and Contextuality,'' Comm. Math. Phys. 334, 533 (2015).
https://doi.org/10.1007/s00220-014-2260-1

[9] M. Navascués, Y. Guryanova, M. J. Hoban, and A. Acín, ``Almost quantum correlations,'' Nat. Comm. 6, 6288 (2015).
https://doi.org/10.1038/ncomms7288

[10] L. Hardy, ``Quantum Theory From Five Reasonable Axioms,'' arXiv:quant-ph/​0101012 (2001).
arXiv:quant-ph/0101012

[11] B. Dakić and Č. Brukner, ``Quantum theory and beyond: is entanglement special?'' in Deep Beauty: Understanding the Quantum World through Mathematical Innovation, edited by H. Halvorson (Cambridge University Press, 2011) pp. 365-392.
https://doi.org/10.1017/CBO9780511976971

[12] L. Masanes and M. P. Müller, ``A derivation of quantum theory from physical requirements,'' New Journal of Physics 13, 063001 (2011).
https://doi.org/10.1088/1367-2630/13/6/063001

[13] L. Masanes, M. P. Müller, R. Augusiak, and D. Pérez-García, ``Existence of an information unit as a postulate of quantum theory,'' Proceedings of the National Academy of Sciences 110, 16373 (2013), http:/​/​www.pnas.org/​content/​110/​41/​16373.full.pdf.
https://doi.org/10.1073/pnas.1304884110
arXiv:http://www.pnas.org/content/110/41/16373.full.pdf

[14] M. P. Müller and L. Masanes, ``Information-theoretic postulates for quantum theory,'' in Quantum Theory: Informational Foundations and Foils, edited by G. Chiribella and R. W. Spekkens (Springer Netherlands, Dordrecht, 2016) pp. 139-170.
https://doi.org/10.1007/978-94-017-7303-4_5

[15] G. Chiribella, G. M. D'Ariano, and P. Perinotti, ``Quantum from principles,'' in Quantum Theory: Informational Foundations and Foils, edited by G. Chiribella and R. W. Spekkens (Springer Netherlands, Dordrecht, 2016) pp. 171-221.
https://doi.org/10.1007/978-94-017-7303-4_6

[16] L. Hardy, ``Reconstructing quantum theory,'' in Quantum Theory: Informational Foundations and Foils, edited by G. Chiribella and R. W. Spekkens (Springer Netherlands, Dordrecht, 2016) pp. 223-248.
https://doi.org/10.1007/978-94-017-7303-4_7

[17] B. Dakić and Č. Brukner, ``The classical limit of a physical theory and the dimensionality of space,'' in Quantum Theory: Informational Foundations and Foils, edited by G. Chiribella and R. W. Spekkens (Springer Netherlands, Dordrecht, 2016) pp. 249-282.
https://doi.org/10.1007/978-94-017-7303-4_8

[18] R. Oeckl, ``A local and operational framework for the foundations of physics,'' arXiv:1610.09052 (2016).
arXiv:1610.09052

[19] P. A. Höhn, ``Toolbox for reconstructing quantum theory from rules on information acquisition,'' Quantum 1, 38 (2017).
https://doi.org/10.22331/q-2017-12-14-38

[20] P. A. Höhn and C. S. P. Wever, ``Quantum theory from questions,'' Phys. Rev. A 95, 012102 (2017).
https://doi.org/10.1103/PhysRevA.95.012102

[21] J. Barrett, ``Information processing in generalized probabilistic theories,'' Phys. Rev. A 75, 032304 (2007).
https://doi.org/10.1103/PhysRevA.75.032304

[22] G. Chiribella, G. M. D'Ariano, and P. Perinotti, ``Probabilistic theories with purification,'' Phys. Rev. A 81, 062348 (2010).
https://doi.org/10.1103/PhysRevA.81.062348

[23] A. B. Sainz, Y. Guryanova, A. Acín, and M. Navascués, ``Almost quantum correlations violate the no-restriction hypothesis,'' Phys. Rev. Lett. 120, 200402 (2018).
https://doi.org/10.1103/physrevlett.120.200402

[24] A. Cabello, S. Severini, and A. Winter, ``(Non-)Contextuality of Physical Theories as an Axiom,'' arXiv:1010.2163 (2010).
arXiv:1010.2163

[25] T. Heinosaari, D. Reitzner, and P. Stano, ``Notes on Joint Measurability of Quantum Observables,'' Found. Phys. 38, 1133 (2008).
https://doi.org/10.1007/s10701-008-9256-7

[26] Y.-C. Liang, R. W. Spekkens, and H. M. Wiseman, ``Specker's parable of the overprotective seer: A road to contextuality, nonlocality and complementarity,'' Phys. Rep. 506, 1 (2011).
https://doi.org/10.1016/j.physrep.2011.05.001

[27] S. Mansfield and R. Soares Barbosa, ``Extendability in the Sheaf-theoretic Approach: Construction of Bell Models from Kochen-Specker Models,'' arXiv:1402.4827 (2014).
arXiv:1402.4827

[28] A. B. Sainz and E. Wolfe, ``Multipartite Composition of Contextuality Scenarios,'' Foundations of Physics (2018), 10.1007/​s10701-018-0168-x.
https://doi.org/10.1007/s10701-018-0168-x

[29] A. Cabello, ``Specker's fundamental principle of quantum mechanics,'' arXiv:1212.1756 (2012).
arXiv:1212.1756

[30] R. Ramanathan, M. T. Quintino, A. B. Sainz, G. Murta, and R. Augusiak, ``Tightness of correlation inequalities with no quantum violation,'' Phys. Rev. A 95, 012139 (2017).
https://doi.org/10.1103/PhysRevA.95.012139

[31] G. Chiribella and X. Yuan, ``Measurement sharpness cuts nonlocality and contextuality in every physical theory,'' arXiv:1404.3348 (2014).
arXiv:1404.3348

[32] G. Chiribella and X. Yuan, ``Bridging the gap between general probabilistic theories and the device-independent framework for nonlocality and contextuality,'' Info. & Comp. 250, 15 (2016).
https://doi.org/10.1016/j.ic.2016.02.006

[33] R. Kunjwal, ``Beyond the Cabello-Severini-Winter framework: making sense of contextuality without sharpness of measurements,'' arXiv:1709.01098 (2017).
arXiv:1709.01098

[34] B. Yan, ``Quantum correlations are tightly bound by the exclusivity principle,'' Phys. Rev. Lett. 110, 260406 (2013).
https://doi.org/10.1103/PhysRevLett.110.260406

[35] A. Cabello, ``Exclusivity principle and the quantum bound of the bell inequality,'' Phys. Rev. A 90, 062125 (2014).
https://doi.org/10.1103/PhysRevA.90.062125

[36] B. Amaral, M. T. Cunha, and A. Cabello, ``Exclusivity principle forbids sets of correlations larger than the quantum set,'' Phys. Rev. A 89, 030101 (2014).
https://doi.org/10.1103/PhysRevA.89.030101

[37] F. Dowker, J. Henson, and P. Wallden, ``A histories perspective on characterising quantum non-locality,'' New Journal of Physics 16, 033033 (2014).
https://doi.org/10.1088/1367-2630/16/3/033033

[38] D. Collins and N. Gisin, ``A relevant two qubit Bell inequality inequivalent to the CHSH inequality,'' J. Phys. A 37, 1775 (2004).
https://doi.org/10.1088/0305-4470/37/5/021

[39] P. McMullen, ``The maximum numbers of faces of a convex polytope,'' Mathematika 17, 179 (1970).
https://doi.org/10.1112/S0025579300002850

[40] D. Gale, ``Neighborly and cyclic polytopes,'' in Proc. Sympos. Pure Math, Vol. 7 (1963) pp. 225-232.
https://doi.org/10.1090/pspum/007/0152944

► Cited by (beta)

Crossref's cited-by service has no data on citing works. Unfortunately not all publishers provide suitable citation data.