Discord Derived from Tsallis Entropy

TL;DR

This paper explores the generalization of quantum discord using Tsallis entropy, introduces two types of q-discords, and calculates their values for specific quantum states, revealing positivity properties.

Contribution

It defines two new types of quantum discord based on Tsallis entropy and provides analytical and numerical results for specific quantum states.

Findings

One q-discord is positive for all q>0 in studied states

Analytical expression derived for q-discord of two-qubit X states

Numerical calculations for Werner and isotropic states

Abstract

Due to some ambiguity in defining mutual Tsallis entropy in the classical probability theory, its generalization to quantum theory is discussed and, as a consequence, two types of generalized quantum discord, called $q$-discords, are defined in terms of quantum Tsallis entropy. $q$-discords for two-qubit Werner and isotropic states are calculated and it is shown that one of them is positive, at least for states under investigation, for all $q>0$. Finally, an analytical expression for $q$-discord of certain family of two-qubit X states is presented.