The paper orders all known generalizations of measurement incompatibility in a strict chain of inclusions, with n-wise compatible assemblages as the convex hull of n-simulable ones, strictly inside n-copy jointly measurable ones.
Incompatible quantum measurements admitting a local hidden variable model
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abstract
The observation of quantum nonlocality, i.e. quantum correlations violating a Bell inequality, implies the use of incompatible local quantum measurements. Here we consider the converse question. That is, can any set of incompatible measurements be used in order to demonstrate Bell inequality violation? Our main result is to construct a local hidden variable model for an incompatible set of qubit measurements. Specifically, we show that if Alice uses this set of measurements, then for any possible shared entangled state, and any possible dichotomic measurements performed by Bob, the resulting statistics are local. This represents significant progress towards proving that measurement incompatibility does not imply Bell nonlocality in general.
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quant-ph 1years
2025 1verdicts
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Strict hierarchy between $n$-wise measurement simulability, compatibility structures, and multi-copy compatibility
The paper orders all known generalizations of measurement incompatibility in a strict chain of inclusions, with n-wise compatible assemblages as the convex hull of n-simulable ones, strictly inside n-copy jointly measurable ones.