Tests against noncontextual models with measurement disturbances

TL;DR

This paper explores the challenges of testing noncontextuality in quantum mechanics due to measurement disturbances and proposes a combined approach using Leggett-Garg inequalities to address compatibility issues.

Contribution

It introduces a model showing how measurement disturbances can falsely indicate noncontextuality violations and suggests a method to overcome this using combined inequalities.

Findings

Measurement disturbances can cause false violations of noncontextuality inequalities.

Combining Leggett-Garg and Kochen-Specker ideas helps address compatibility issues.

Proposed approach improves the testability of noncontextuality in experiments.

Abstract

The testability of the Kochen-Specker theorem is a subject of ongoing controversy. A central issue is that experimental implementations relying on sequential measurements cannot achieve perfect compatibility between the measurements and that therefore the notion of noncontextuality is not well defined. We demonstrate by an explicit model that such compatibility violations may yield a violation of noncontextuality inequalities, even if we assume that the incompatibilities merely originate from context-independent noise. We show, however, that this problem can be circumvented by combining the ideas behind Leggett-Garg inequalities with those of the Kochen-Specker theorem.