Reformulating noncontextuality inequalities in an operational approach

TL;DR

This paper introduces a new, theory-independent approach to noncontextuality inequalities that generalizes previous results from Kochen-Specker sets to both state-independent and state-dependent scenarios, using novel inequalities and examples.

Contribution

It reformulates noncontextuality inequalities in an operational framework without assuming determinism, extending their applicability to broader scenarios.

Findings

New noncontextuality inequalities are derived.

The approach applies to both state-independent and state-dependent cases.

Examples include YO-13 ray and n-cycle ray.

Abstract

A new theory-independent noncontextuality inequality is presented [Phys. Rev. Lett. 115, 110403 (2015)] based on Kochen-Specker (KS) set without imposing the assumption of determinism. By proposing novel noncontextuality inequalities, we show that such result can be generalized from KS set to the noncontextuality inequalities not only for state-independent but also for state-dependent scenario. The YO-13 ray and $n$ cycle ray are considered as examples.