Generalized entanglement constraints in multi-qubit systems in terms of Tsallis entropy

TL;DR

This paper introduces generalized entanglement constraints in multi-qubit systems using Tsallis entropy, extending existing monogamy and polygamy inequalities to broader parameter ranges.

Contribution

It develops generalized monogamy and polygamy inequalities for multi-qubit entanglement based on Tsallis entropy, unifying and extending previous inequalities.

Findings

Generalized monogamy inequality for q=2 or 3

Generalized polygamy inequality for 1≤q≤2 or 3≤q≤4

Contains standard inequalities as special cases

Abstract

We provide generalized entanglement constraints in multi-qubit systems in terms of Tsallis entropy. Using quantum Tsallis entropy of order $q$, we first provide a generalized monogamy inequality of multi-qubit entanglement for $q=2$ or $3$. This generalization encapsulates multi-qubit CKW-type inequality as a special case. We further provide a generalized polygamy inequality of multi-qubit entanglement in terms of Tsallis-$q$ entropy for $1 \leq q \leq2$ or $3 \leq q \leq 4$, which also contains the multi-qubit polygamy inequality as a special case.