Minimal state-dependent proof of measurement contextuality for a qubit

TL;DR

This paper demonstrates that three unsharp binary measurements on a qubit can violate a noncontextuality inequality in a state-dependent way, providing a minimal proof of measurement contextuality that rules out certain classical models.

Contribution

It presents the first minimal state-dependent proof of measurement contextuality for a qubit using three unsharp measurements, extending the understanding of nonclassicality.

Findings

Three unsharp measurements violate the LSW inequality in a state-dependent manner.

Optimal quantum violation is calculated for trine spin axes.

Unsharp measurements do not allow state-independent violation.

Abstract

We show that three unsharp binary qubit measurements are enough to violate a generalized noncontextuality inequality, the LSW inequality, in a state-dependent manner. For the case of trine spin axes we calculate the optimal quantum violation of this inequality. Besides, we show that unsharp qubit measurements do not allow a state-independent violation of this inequality. We thus provide a minimal state-dependent proof of measurement contextuality requiring one qubit and three unsharp measurements. Our result rules out generalized noncontextual models of these measurements which were previously conjectured to exist. More importantly, this class of generalized noncontextual models includes the traditional Kochen-Specker (KS) noncontextual models as a proper subset, so our result rules out a larger class of models than those ruled out by a violation of the corresponding KS-inequality in this scenario.