Comment on "Contextuality and quantum discord"

TL;DR

This paper critiques a proposed criterion for quantum contextuality in two-qubit systems, clarifies its relation to nonclassicality beyond contextuality, and refines the understanding of quantum correlations versus discordant features.

Contribution

It demonstrates that Al-Qasimi's criterion does not generally imply contextuality and clarifies its relation to a different form of nonclassicality, refining the interpretation of quantum discord.

Findings

Al-Qasimi's criterion does not imply contextuality in general

The criterion relates to a different nonclassicality notion, not contextuality

Quantum correlation and discordant features are not equivalent

Abstract

In a paper, Al-Qasimi [Physics Letters A 449 (2022) 128347] proposed a criterion for contextuality of two-qubit systems extending Peres' proof of contextuality [Phys. Lett. A 151 (1990) 107]. Using this criterion, Al-Qasimi argued that certain discordant states can be contextual even if they are not entangled. Here I demonstrate that Al-Qasimi's criterion does not, in general, imply contextuality of two-qubit system. However, I point out that Al-Qasimi's criterion is related to a different notion of operational nonclassicality of discordant feature, which is inequivalent to contextuality. This nonclassicality beyond contextuality has been formalized in C. Jebarathinam and R. Srikanth [Int. J. Quantum Inf. 23 (2025) 2550037]. Identifying Al-Qasimi's criterion as demonstration of quantum correlation beyond contextuality, it then follows that Al-Qasimi's main conclusion that one cannot equate quantum correlation and discordant feature is made precise.