Necessary and sufficient condition for quantum state-independent contextuality

TL;DR

This paper establishes the necessary and sufficient conditions for quantum state-independent contextuality, identifying minimal sets of tests and clarifying the limitations of existing graph-based methods.

Contribution

It provides a complete characterization of when quantum tests exhibit state-independent contextuality and demonstrates that certain graph-based criteria are insufficient.

Findings

Derived the necessary and sufficient conditions for state-independent contextuality.

Identified the simplest minimal sets of tests in the lowest dimension.

Showed that graph-based criteria alone cannot determine state-independent contextuality.

Abstract

We solve the problem of whether a set of quantum tests reveals state-independent contextuality and use this result to identify the simplest set of the minimal dimension. We also show that identifying state-independent contextuality graphs [R. Ramanathan and P. Horodecki, Phys. Rev. Lett. 112, 040404 (2014)] is not sufficient for revealing state-independent contextuality.