Unified entropy, entanglement measures and monogamy of multi-party entanglement

TL;DR

This paper introduces a new two-parameter class of entanglement measures based on unified-$(q,s)$ entropy, which characterizes multi-qubit entanglement shareability and establishes monogamy inequalities.

Contribution

It develops a novel bipartite entanglement measure using unified-$(q,s)$ entropy with an analytic formula for two-qubit systems and broadens the scope of monogamy inequalities for multi-qubit entanglement.

Findings

Unified-$(q,s)$ entanglement fully characterizes multi-qubit entanglement shareability.

Analytic formula for unified-$(q,s)$ entanglement in two-qubit systems.

Established a broad class of monogamy inequalities for multi-qubit entanglement.

Abstract

We show that restricted shareability of multi-qubit entanglement can be fully characterized by unified-$(q,s)$ entropy. We provide a two-parameter class of bipartite entanglement measures, namely unified-$(q,s)$ entanglement with its analytic formula in two-qubit systems for $q\geq 1$, $0\leq s \leq1$ and $qs\leq3$. Using unified-$(q,s)$ entanglement, we establish a broad class of the monogamy inequalities of multi-qubit entanglement for $q\geq2$, $0\leq s \leq1$ and $qs\leq3$.