Tsallis entropy and general polygamy of multi-party quantum entanglement in arbitrary dimensions

TL;DR

This paper introduces a unified framework for understanding multi-party quantum entanglement polygamy using Tsallis-$q$ entropy, generalizing existing inequalities and correlations across arbitrary dimensions.

Contribution

It develops a one-parameter class of polygamy inequalities based on Tsallis-$q$ entropy, unifying and extending previous results in quantum entanglement theory.

Findings

Derived a unified polygamy inequality framework

Reduced to known inequalities for specific parameter choices

Established conditions for the validity of Tsallis-$q$ inequalities

Abstract

We establish a unified view to the polygamy of multi-party quantum entanglement in arbitrary dimensions. Using quantum Tsallis-$q$ entropy, we provide a one-parameter class of polygamy inequalities of multi-party quantum entanglement. This class of polygamy inequalities reduces to the known polygamy inequalities based on tangle and entanglement of assistance for a selective choice of the parameter $q$. We further provide one-parameter generalizations of various quantum correlations based on Tsallis-$q$ entropy. By investigating the properties of the generalized quantum correlations, we provide a sufficient condition, on which the Tsallis-$q$ polygamy inequalities hold in multi-party quantum systems of arbitrary dimensions.