Macroscopic non-contextuality as a principle for Almost Quantum Correlations

Abstract

Quantum mechanics allows only certain sets of experimental results (or "probabilistic models") for Bell-type quantum non-locality experiments. A derivation of this set from simple physical or information theoretic principles would represent an important step forward in our understanding of quantum mechanics, and this problem has been intensely investigated in recent years. "Macroscopic locality," which requires the recovery of locality in the limit of large numbers of trials, is one of several principles discussed in the literature that place a bound on the set of quantum probabilistic models. A similar question can also be asked about probabilistic models for the more general class of quantum contextuality experiments. Here, we extend the Macroscopic Locality principle to this more general setting, using the hypergraph approach of Acín, Fritz, Leverrier and Sainz [Comm. Math. Phys. 334(2), 533-628 (2015)], which provides a framework to study both phenomena of nonlocality and contextuality in a unified manner. We find that the set of probabilistic models allowed by our Macroscopic Non-Contextuality principle is equivalent to an important and previously studied set in this formalism, which is slightly larger than the quantum set. In the particular case of Bell Scenarios, this set is equivalent to the set of "Almost Quantum" models, which is of particular interest since the latter was recently shown to satisfy all but one of the principles that have been proposed to bound quantum probabilistic models, without being implied by any of them (or even their conjunction). Our condition is the first characterisation of the almost quantum set from a simple physical principle.

21 pages (main text 12 pages); v2 minor typos corrected, extended presentation and discussion, published version

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Cited by in corpus (14)

• Kochen-Specker Contextuality
• Bridging the gap between general probabilistic theories and the device-independent framework for nonlocality and contextuality
• 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
• Post-quantum steering is a stronger-than-quantum resource for information processing
• Macroscopically nonlocal quantum correlations
• Almost quantum correlations and their refinements in a tripartite Bell scenario
• The resource theory of nonclassicality of channel assemblages
• A Survey of Physical Principles Attempting to Define Quantum Mechanics
• Correlations constrained by composite measurements
• From the problem of Future Contingents to Peres-Mermin square experiments: An introductory review to Contextuality
• On characterising assemblages in Einstein-Podolsky-Rosen scenarios
• Modelling contextuality by probabilistic programs with hypergraph semantics
• Quantum theory at the macroscopic scale