General Monogamy of Tsallis $q$-Entropy Entanglement in Multiqubit Systems

TL;DR

This paper investigates the monogamy properties of Tsallis-q entropy entanglement in multiqubit systems, providing analytic formulas, hierarchical relations, and entanglement indicators that detect genuine multiqubit entanglement.

Contribution

It introduces new analytic formulas and hierarchical monogamy relations for Tsallis-q entropy entanglement in multiqubit and higher-dimensional systems.

Findings

Analytic formula for two-qubit Tsallis-q entropy entanglement within specific q range

Hierarchical monogamy equalities for Tsallis-q entropy in multiqubit systems

Multipartite entanglement indicators that detect all genuine multiqubit entangled states

Abstract

In this paper, we study the monogamy inequality of Tsallis-q entropy entanglement. We first provide an analytic formula of Tsallis-q entropy entanglement in two-qubit systems for $\frac{5-\sqrt{13}}{2}\leq q\leq\frac{5+\sqrt{13}}{2}.$ The analytic formula of Tsallis-q entropy entanglement in $2\otimes d$ system is also obtained and we show that Tsallis-q entropy entanglement satisfies a set of hierarchical monogamy equalities. Furthermore, we prove the squared Tsallis-q entropy entanglement follows a general inequality in the qubit systems. Based on the monogamy relations, a set of multipartite entanglement indicators is constructed, which can detect all genuine multiqubit entangled states even in the case of $N$-tangle vanishes. Moreover, we study some examples in multipartite higher-dimensional system for the monogamy inequalities.