Comment on "Quantum discord through the generalized entropy in bipartite quantum states"

TL;DR

This paper critically examines generalized quantum discord measures based on Tsallis and Rényi entropies, revealing conditions under which these measures can be negative and identifying regions of non-negativity in two-qubit systems.

Contribution

It clarifies the properties of generalized quantum discord measures, showing their potential negativity and providing conditions for non-negativity in specific quantum states.

Findings

Quantum discord can be negative with Tsallis and Rényi entropies.

Identified regions where quantum discord remains non-negative in two-qubit states.

Compared different entropy-based generalizations of quantum discord.

Abstract

In [X.-W. Hou, Z.-P. Huang, S. Chen, Eur. Phys. J. D 68, 1 (2014)], Hou et al. present, using Tsallis' entropy, possible generalizations of the quantum discord measure, finding original results. As for the mutual informations and discord, we show here that these two types of quantifiers can take negative values. In the two qubits instance we further determine in which regions they are non-negative. Additionally, we study alternative generalizations on the basis of R\'enyi entropies.