Connection between the contextuality breaking and incompatibility breaking qubit channels

TL;DR

This paper explores the relationship between channels that break quantum contextuality and incompatibility, showing that breaking certain contextuality implies breaking nonlocality, with specific results on depolarising channels and inequalities.

Contribution

It establishes a connection between channels that break contextuality and those that break measurement incompatibility and nonlocality in bipartite Bell scenarios.

Findings

Channels breaking EBI contextuality also break CHSH nonlocality.

Depolarising channels breaking N-wise incompatibility can break certain contextual inequalities.

Breaking EBI contextuality implies breaking CHSH nonlocality, but not vice versa.

Abstract

Contextuality and measurement incompatibility are two fundamental aspects of nonclassicality, and their manifestations in observed quantum correlations are often deeply interconnected. Recently, measurement incompatibility has been studied in connection with nonlocality, particularly in terms of their robustness under various quantum channels. This line of investigation helps establish a connection between the channels that break nonlocality and those that break incompatibility. In this study, we focus on an asymmetric bipartite Bell scenario involving three and four inputs on Alice and Bob sides, respectively, with each of these inputs having dichotomous outcomes. Under the assumption of locality, the observed statistics in this asymmetric scenario obeys the Elegant Bell inequality (EBI). Here, we use a different version of the EBI that relies on the assumption of the preparation noncontextuality. By taking the violation of this noncontextual version of EBI as a witness of preparation contextuality we establish a connection between the channels that break contextuality and the channels that break triple-wise measurement incompatibility. Our results suggest that any channel which breaks EBI contextuality will also break Clauser-Horne-Shimony-Holt (CHSH) nonlocality; however, the reverse does not hold. We also show that a depolarising channel that breaks N-wise incompatibility can also break a certain form of contextuality, witnessed by a generalised inequality involving N measurements on one wing of a bipartite Bell scenario.