Qualitative equivalence between incompatibility and Bell nonlocality

• URL: http://arxiv.org/abs/2008.10100v3
• Date: Wed, 20 Nov 2024 09:30:03 GMT
• Title: Qualitative equivalence between incompatibility and Bell nonlocality
• Authors: Shiv Akshar Yadavalli, Nikola Andrejic, Ravi Kunjwal,
• Abstract summary: Measurements in quantum theory can fail to be jointly measurable. Incompatibility of measurements is necessary but not sufficient for violating Bell inequalities. A non-trivial joint measurability structure is not only necessary for a Bell violation, but also sufficient.
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• Abstract: Measurements in quantum theory can fail to be jointly measurable. Like entanglement, this incompatibility of measurements is necessary but not sufficient for violating Bell inequalities. The (in)compatibility relations among a set of measurements can be represented by a joint measurability structure, i.e., a hypergraph whose vertices denote measurements and hyperedges denote all and only compatible sets of measurements. Since incompatibility is necessary for a Bell violation, the joint measurability structure on each wing of a Bell experiment must necessarily be non-trivial, i.e., it must admit a subset of incompatible vertices. Here we show that for any non-trivial joint measurability structure with a finite set of vertices, there exists a quantum realization with a set of measurements that enables a Bell violation, i.e., given that Alice has access to this incompatible set of measurements, there exists a set of measurements for Bob and an entangled state shared between them such that they can jointly violate a Bell inequality. Hence, a non-trivial joint measurability structure is not only necessary for a Bell violation, but also sufficient.

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