Robust preparation noncontextuality inequalities in the simplest scenario

TL;DR

This paper derives eight necessary and sufficient non-linear inequalities for testing preparation noncontextuality in the simplest scenario, eliminating the need for fixed operational equivalences and facilitating experimental validation.

Contribution

It introduces a set of robust inequalities for preparation noncontextuality that are operationally friendly and directly testable without fixed equivalences, based on a connection to the CHSH scenario.

Findings

Eight non-linear inequalities characterize preparation noncontextuality.

No fixed operational equivalences are needed for testing.

The inequalities are necessary and sufficient for the simplest scenario.

Abstract

Contextuality is the leading notion of nonclassicality for a single system. However, an experimental demonstration requires finding procedures that are operationally equivalent, which might seem impossible to achieve exactly. Here I focus on the simplest non-trivial case, four preparations and two tomographically complete binary measurements. Exploiting a subtle connection to the CHSH scenario gives eight non-linear inequalities which are together necessary and sufficient for the experimental statistics to admit a preparation noncontextual model in such a scenario. No fixed operational equivalences are required, removing a key difficulty with experimental tests of older preparation noncontextuality inequalities.