Unified entropy entanglement

TL;DR

This paper introduces new multipartite entanglement measures based on unified entropy, demonstrating their properties like monotonicity and monogamy, and explores their relation to bipartite and global entanglement.

Contribution

It extends the concept of unified entropy entanglement to new parameter ranges, establishing their monotonicity, monogamy, and constructing comprehensive multipartite entanglement measures.

Findings

Unified-($q,s$) entropy entanglement is an entanglement monotone for $q>1$ and $qs extgreater=1$.

One global multipartite entanglement measure is complete and tightly monogamous.

Other proposed measures are not complete.

Abstract

The unified entropy as a promotion of the von Neumann entropy exhibits distinct diversity which contains the Tsallis entropy, the R\'{e}nyi entropy, the von Neumann entropy as special cases. The unified-($r,t$) entropy entanglement with $0<r<1$ and $0< t\leq 1$ was shown to be an entanglement monotone in literature. In this paper, we explore unified-($q,s$) entropy entanglement with $q>1$ and $qs\geq1$ and show that it is also an entanglement monotone and that both of them are monogamous. Going further, we present two kinds of global multipartite entanglement measures (GlMEMs) based on the unified entropy and each kind has two subclasses which are classified by the parameters $(q,s)$ and $(r,t)$. Consequently, from the view of the complete multipartite entanglement measure theory, we show that one of them is a complete multipartite entanglement monotone and is not only completely monogamous but also tightly completely monogamous, but the other three are even not complete. We also explore the genuine entanglement measures induced by the unified entropy and the relations with the bipartite entanglement and the global entanglement are discussed, respectively.