Quantum contextuality from a simple principle?

Abstract

In a recent article entitled "A simple explanation of the quantum violation of a fundamental inequality," Cabello proposes a condition on a class of probabilistic models that, he claims, gives the same bound on contextuality for the KCBS inequality as quantum mechanics, and also rules out PR-box nonlocality. He conjectures that the condition will also reproduce quantum limits on contextuality in other scenarios. Here we show that the proposed principle is actually too weak to derive these results. Cabello has implicitly assumed in the proofs that if all pairs in a set of events are pairwise exclusive (so that their probabilities must sum to less than 1), the set can itself be considered exclusive. Perhaps surprisingly, this is not in general true in the general probabilistic framework under discussion. We call this hidden assumption "Consistent Exclusivity" or CE. With this extra assumption Cabello's proofs are sound. Furthermore, it is established that CE holds in quantum mechanics, providing a reasonable and simple new principle that may characterise quantum non-contextuality in many scenarios.

9 pages, 2 figures. Version 2: note added to acknowledge the previously overlooked work of Fritz, Sainz, Augusiak, Brask, Chaves, Leverrier, and Acín, which gives results and arguments essentially the same as some of those given here. Some references added. v3: comment altered for various reasons, particularly to correct a mistaken labeling of a result

References in corpus (9)

• Information Causality as a Physical Principle
• A simple test for hidden variables in spin-1 system
• The uncertainty principle determines the non-locality of quantum mechanics
• Specker's Parable of the Over-protective Seer: A Road to Contextuality, Nonlocality and Complementarity (PLUS AN ERRATUM)
• Local orthogonality as a multipartite principle for quantum correlations
• Simple explanation of the quantum violation of a fundamental inequality
• Reformulating and Reconstructing Quantum Theory
• (Non-)Contextuality of Physical Theories as an Axiom
• Pentagrams and paradoxes

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• Probabilistic models on contextuality scenarios
• Contextuality, Witness of Quantum Weirdness