Almost Quantum Correlations are Inconsistent with Specker's Principle

Abstract

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 (https://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.

17 pages + appendix. 5 colour figures. Comments welcome

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Cited by in corpus (13)

• Postquantum common-cause channels: the resource theory of local operations and shared entanglement
• Beyond the Cabello-Severini-Winter framework: Making sense of contextuality without sharpness of measurements
• Kirkwood-Dirac representations beyond quantum states (and their relation to noncontextuality)
• Hypergraph framework for irreducible noncontextuality inequalities from logical proofs of the Kochen-Specker theorem
• Naturally restricted subsets of nonsignaling correlations: typicality and convergence
• Contextuality in composite systems: the role of entanglement in the Kochen-Specker theorem
• Joint measurability structures realizable with qubit measurements: incompatibility via marginal surgery
• Shadows and subsystems of generalized probabilistic theories: when tomographic incompleteness is not a loophole for contextuality proofs
• All two-party facet Bell inequalities are violated by Almost Quantum correlations
• Constrained Measurement Incompatibility from Generalised Contextuality of Steered Preparation
• Unexpected consequences of Post-Quantum theories in the graph-theoretical approach to correlations
• Decoupling local classicality from classical explainability: A noncontextual model for bilocal classical theory and a locally-classical but contextual theory
• Contextuality and Expressivity of Non-locality