# Tsallis entropy, $q$-expectation and constraints on three-party quantum correlations

## TL;DR

This paper introduces a generalized framework using Tsallis-$q$ entropy and $q$-expectation to characterize and analyze the trade-offs and distribution constraints of classical and quantum correlations in multi-party quantum systems.

## Contribution

It provides new definitions and trade-off relations for correlations in three-party quantum systems based on Tsallis-$q$ entropy, extending understanding of monogamy and polygamy inequalities.

## Key findings

- Generalized definitions of classical and quantum correlations using Tsallis-$q$ entropy.
- Trade-off relations for correlations in three-party systems with respect to $q$-expectation.
- Conditions for monogamy and polygamy inequalities in quantum correlations.

## Abstract

We show that the mutually exclusive nature of classical and quantum correlations distributed in multi-party quantum systems can be characterized in terms of $q$-expectation. Using Tsallis-$q$ entropy and $q$-expectation, we first provide generalized definitions of classical and quantum correlations, and establish their trade-off relations in three-party quantum systems of arbitrary dimension with respect to $q$-expectation for $q\geq 1$. We also provide equivalence conditions for monogamy and polygamy inequalities of quantum entanglement and quantum discord distributed in three-party quantum systems of arbitrary dimension with respect to $q$-expectation for $q\geq 1$.