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arXiv:2512.11450

Comment on "Contextuality and quantum discord"

Chellasamy Jebarathinam

quant-phSubmitted Dec 12, 2025• Announced Dec 15, 2025• 0 citations
v1 · Dec 12, 2025v2 · Jan 5, 2026
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Abstract

In a paper, Al-Qasimi [Physics Letters A 449 (2022) 128347] studied contextuality of two-qubit states using an argument by Peres [Phys. Lett. A 151 (1990) 107]. For two-qubit system in the Werner state, Al-Qasimi argued that only when discord is zero, the system is noncontextual. Here I point out that this argument is false and the related work in C. Jebarathinam and R. Srikanth [Int. J. Quantum Inf. https://doi.org/10.1142/S0219749925500376 (arXiv:2403.01762v2)].

Comments
1 page; comment on arXiv:2208.01698

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In a paper, Al-Qasimi [Physics Letters A 449 (2022) 128347] studied contextuality of two-qubit states using an argument by Peres [Phys. Lett. A 151 (1990) 107]. For two-qubit system in the Werner state, Al-Qasimi argued that only when discord is zero, the system is noncontextual. Here I point out that this argument is false and the related work in C. Jebarathinam and R. Srikanth [Int. J. Quantum Inf. https://doi.org/10.1142/S0219749925500376 (arXiv:2403.01762v2)].
Quantum discord, as introduced by Olliver and Zurek [Phys. Rev. Lett. 88, 017901 (2001)], is a measure of the discrepancy between two natural yet different quantum analogs of the classical mutual information. This notion characterizes and quantifies quantumness of correlations in bipartite states from a measurement perspective, and is fundamentally different from the various entanglement measures in the entanglement vs separability paradigm. The phenomenon of nonzero quantum discord is a manifestation of quantum correlations due to noncommutativity rather than due to entanglement, and has interesting and significant applications in revealing the advantage of certain quantum tasks. We will evaluate analytically the quantum discord for a large family of two-qubit states, and make a comparative study of the relationships between classical and quantum correlations in terms of the quantum discord. We furthermore compare the quantum discord with the entanglement of formation, and illustrate that the latter may be larger than the former, although for separable states, the entanglement of formation always vanishes and thus is less than the quantum discord.
Measurements of quantum systems disturb their states. To quantify this nonclassical characteristic, Zurek and Ollivier [Phys. Rev. Lett. 88, 017901 (2001)] introduced the quantum discord, a quantum correlation that can be nonzero even when entanglement in the system is zero. Discord has aroused great interest as a resource that is more robust against the effects of decoherence and offers the exponential speed-up of certain computational algorithms. Here, we study general two-level bipartite systems and give general results on the relationship between discord, entanglement, and linear entropy. We also identify the states for which discord takes a maximal value for a given entropy or entanglement, thus placing strong bounds on entanglement-discord and entropy-discord relations. We find out that although discord and entanglement are identical for pure states, they differ when generalized to mixed states as a result of the difference in the method of generalization.
Quantum discord quantifies nonclassical correlations beyond the standard classification of quantum states into entangled and unentangled. Although it has received considerable attention, it still lacks any precise interpretation in terms of some protocol in which quantum features are relevant. Here we give quantum discord its first information-theoretic operational meaning in terms of entanglement consumption in an extended quantum-state-merging protocol. We further relate the asymmetry of quantum discord with the performance imbalance in quantum state merging and dense coding.
Quantum discord quantifies nonclassical correlations beyond the standard classification of quantum states into entangled and unentangled. Although it has received considerable attention, it still lacks any precise interpretation in terms of some protocol in which quantum features are relevant. Here we give quantum discord its first information-theoretic operational meaning in terms of entanglement consumption in an extended quantum-state-merging protocol. We further relate the asymmetry of quantum discord with the performance imbalance in quantum state merging and dense coding.