Monogamy relation of multi-qubit systems for squared Tsallis-\emph{q} entanglement

TL;DR

This paper extends the analytical range of Tsallis-q entanglement, proves monogamy relations for multi-qubit systems within this range, and demonstrates the robustness of the entanglement indicator based on squared Tsallis-q entanglement.

Contribution

It generalizes the analytic formula of Tsallis-q entanglement and establishes monogamy relations for multi-qubit systems in a broader parameter range.

Findings

Monogamy relation holds for rac{5-sqrt{13}}{2}  rac{5+sqrt{13}}{2} range of q.

Multipartite entanglement indicator based on squared Tsallis-q entanglement remains effective.

eyond concurrence, Tsallis-q based measures show robustness in entanglement monogamy.

Abstract

Tsallis-$q$ entanglement is a bipartite entanglement measure which is the generalization of entanglement of formation for $q$ tending to 1. We first expand the range of $q$ for the analytic formula of Tsallis-\emph{q} entanglement. For $\frac{5-\sqrt{13}}{2} \leq \emph{q} \leq \frac{5+\sqrt{13}}{2}$, we prove the monogamy relation in terms of the squared Tsallis-$q$ entanglement for an arbitrary multi-qubit systems. It is shown that the multipartite entanglement indicator based on squared Tsallis-$q$ entanglement still works well even when the indicator based on the squared concurrence loses its efficacy. We also show that the $\mu$-th power of Tsallis-\emph{q} entanglement satisfies the monogamy or polygamy inequalities for any three-qubit state.