Quantum contextuality of a qutrit state

TL;DR

This paper investigates quantum contextuality in qutrit states, revealing differences in measurement strategies for two inequalities and providing spectral methods useful for experimental error analysis.

Contribution

It introduces a spectral approach to analyze quantum contextuality, highlighting a universal measurement set for KK inequality but not for KCBS, with implications for experiments.

Findings

Universal measurement set exists for KK inequality in certain states.

No universal measurement set for KCBS inequality in the same states.

Spectral distribution of measurement matrices reflects contextuality differences.

Abstract

We present a study of quantum contextuality of three-dimensional mixed states for the Klyachko-Can-Binicio\u{g}lu-Shumovsky (KCBS) and the Kurzy\'{n}ski-Kaszlikowski (KK) noncontextuality inequalities. For any class of states whose eigenvalues are arranged in decreasing order, a universal set of measurements always exists for the KK inequality, whereas none does for the KCBS inequality. This difference can be reflected from the spectral distribution of the overall measurement matrix. Our results would facilitate the error analysis for experimental setups, and our spectral method in the paper combined with graph theory could be useful in future studies on quantum contextuality.