Two-parameter bipartite entanglement measure

TL;DR

This paper introduces a new two-parameter family of bipartite entanglement measures called the unified (q,s)-concurrence, unifying existing measures and exploring their properties, bounds, and applications in quantum systems.

Contribution

It proposes the unified (q,s)-concurrence, deriving bounds, explicit formulas for specific states, and establishing monogamy and polygon inequalities for multipartite systems.

Findings

Derived an analytical lower bound for the measure in mixed states.

Obtained explicit expressions for isotropic and Werner states.

Established monogamy and polygon inequalities for multipartite entanglement.

Abstract

Entanglement concurrence is an important bipartite entanglement measure that has found wide applications in quantum technologies. In this work, inspired by unified entropy, we introduce a two-parameter family of entanglement measures, referred to as the unified $(q,s)$-concurrence. Both the standard entanglement concurrence and the recently proposed $q$-concurrence emerge as special cases within this family. By combining the positive partial transposition and realignment criteria, we derive an analytical lower bound for this measure for arbitrary bipartite mixed states, revealing a connection to strong separability criteria. Explicit expressions are obtained for the unified $(q,s)$-concurrence in the cases of isotropic and Werner states under the constraint $q>1$ and $qs\geq 1$. Furthermore, we explore the monogamy properties of the unified $(q,s)$-concurrence for $q\geq 2$, $0\leq s\leq 1$ and $1\leq qs\leq 3$, in qubit systems. In addition, we derive an entanglement polygon inequality for the unified $(q,s)$-concurrence with $q\geq 1$ and $qs\geq 1$, which manifests the relationship among all the marginal entanglements in any multipartite qudit system.