Tsallis entropy and entanglement constraints in multi-qubit systems

TL;DR

This paper introduces Tsallis-$q$ entropy as a tool to characterize the sharing and distribution constraints of entanglement in multi-qubit systems, providing new inequalities and formulas for specific $q$ ranges.

Contribution

It defines Tsallis-$q$ entanglement measures, derives their analytic formulas for two-qubit systems, and establishes monogamy and polygamy inequalities for multi-qubit entanglement.

Findings

Analytic formula for Tsallis-$q$ entanglement in two-qubit systems for $1 \\leq q \\leq 4$

Monogamy inequality of multi-qubit entanglement for $2 \\leq q \\leq 3$

Polygamy inequalities for $1 \\leq q \\leq 2$ and $3 \\leq q \\leq 4$

Abstract

We show that the restricted sharability and distribution of multi-qubit entanglement can be characterized by Tsallis-$q$ entropy. We first provide a class of bipartite entanglement measures named Tsallis-$q$ entanglement, and provide its analytic formula in two-qubit systems for $1 \leq q \leq 4$. For $2 \leq q \leq 3$, we show a monogamy inequality of multi-qubit entanglement in terms of Tsallis-$q$ entanglement, and we also provide a polygamy inequality using Tsallis-$q$ entropy for $1 \leq q \leq 2$ and $3 \leq q \leq 4$.