Polygamy of multi-party $q$-expected quantum entanglement

TL;DR

This paper explores the polygamy properties of multi-party quantum entanglement using a generalized $q$-expectation framework, unifying and extending previous inequalities based on von Neumann entropy.

Contribution

It introduces a class of polygamy inequalities for multi-party quantum entanglement using $q$-expectation values, applicable across all $q \\geq 1$, generalizing prior results.

Findings

Established polygamy inequalities based on $q$-expected entanglement.

Unified previous inequalities as special cases when $q$ approaches 1.

Extended the framework to arbitrary-dimensional quantum systems.

Abstract

We characterize the polygamy nature of quantum entanglement in multi-party systems in terms of $q$-expectation value for the full range of $q\geq 1$. By investigating some properties of generalized quantum correlations in terms of $q$-expectation value and Tsallis $q$-entropy, we establish a class of polygamy inequalities of multi-party quantum entanglement in arbitrary dimensions based on $q$-expected entanglement measure. As Tsallis $q$-entropy is reduced to von Neumann entropy, and $q$-expectation value becomes the ordinary expectation value when $q$ tends to $1$, our results encapsulate previous results of polygamy inequalities based on von Neumann entropy as special cases.