Incompatible quantum measurements admitting a local hidden variable model

TL;DR

This paper constructs a local hidden variable model for incompatible qubit measurements, demonstrating that measurement incompatibility alone does not necessarily lead to Bell inequality violations.

Contribution

It provides a counterexample showing incompatible measurements can admit a local hidden variable model, challenging assumptions about their role in quantum nonlocality.

Findings

Constructed a local hidden variable model for incompatible measurements

Showed that incompatibility does not imply Bell nonlocality in general

Progressed understanding of the relationship between measurement incompatibility and nonlocality

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.