Quantum measurement incompatibility does not imply Bell nonlocality

Abstract

We discuss the connection between the incompatibility of quantum measurements, as captured by the notion of joint measurability, and the violation of Bell inequalities. Specifically, we present explicitly a given a set of non jointly measurable POVMs ${\mathcal{M}}_A$ with the following property. Considering a bipartite Bell test where Alice uses ${\mathcal{M}}_A$, then for any possible shared entangled state $\rho$ and any set of (possibly infinitely many) POVMs ${\mathcal{N}}_B$ performed by Bob, the resulting statistics admits a local model, and can thus never violate any Bell inequality. This shows that quantum measurement incompatibility does not imply Bell nonlocality in general.

See also arXiv:1705.10069 for a related work Small changes on the main text. Some typos were fixed

References in corpus (11)

• Quantum steering: a review with focus on semidefinite programming
• Joint measurability of generalized measurements implies classicality
• Simulating positive-operator-valued measures with projective measurements
• Local hidden--variable models for entangled quantum states
• Notes on Joint Measurability of Quantum Observables
• Better local hidden variable models for two-qubit Werner states and an upper bound on the Grothendieck constant $K_G(3)$
• All quantum states useful for teleportation are nonlocal resources
• Measurement incompatibility does not give rise to Bell violation in general
• Operational framework for quantum measurement simulability
• Most incompatible measurements for robust steering tests
• Convex separation from convex optimization for large-scale problems

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