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

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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 ($\href{}{}$). 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.

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[2] Ravi Kunjwal, "Hypergraph framework for irreducible noncontextuality inequalities from logical proofs of the Kochen-Specker theorem", Quantum 4, 219 (2020).

[3] Nikola Andrejic and Ravi Kunjwal, "Joint measurability structures realizable with qubit measurements: Incompatibility via marginal surgery", Physical Review Research 2 4, 043147 (2020).

[4] David Schmid, Haoxing Du, Maryam Mudassar, Ghi Coulter-de Wit, Denis Rosset, and Matty J. Hoban, "Postquantum common-cause channels: the resource theory of local operations and shared entanglement", Quantum 5, 419 (2021).

[5] Ravi Kunjwal, "Beyond the Cabello-Severini-Winter framework: Making sense of contextuality without sharpness of measurements", Quantum 3, 184 (2019).

[6] Sacha Huriot-Tattegrain and Mehdi Mhalla, "Contextuality and Expressivity of Non-locality", Electronic Proceedings in Theoretical Computer Science 340, 160 (2021).

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