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

Quantum measurement incompatibility does not imply Bell nonlocality