A $(k+1)$-partite entanglement measure of $N$-partite quantum states

TL;DR

This paper introduces a new $(k+1)$-partite entanglement measure for $N$-partite quantum states, based on permutational invariance, with properties, bounds, and practical measurement methods demonstrated through examples.

Contribution

The paper proposes a novel $(k+1)$-partite entanglement measure with desirable properties and provides bounds and measurement strategies for multipartite quantum systems.

Findings

Defined a new entanglement measure with desirable properties

Established bounds using permutationally invariant parts

Provided measurement methods and illustrative examples

Abstract

The concept of \textquotedblleft the permutationally invariant part of a density matrx\textquotedblright constitutes an important tool for entanglement characterization of multiqubit systems. In this paper, we first present $(k+1)$-partite entanglement measure of $N$-partite quantum system, which possesses desirable properties of an entanglement measure. Moreover, we give strong bounds on this measure by considering the permutationally invariant part of a multipartite state. We give two definitions of efficient measurable degree of $(k+1)$-partite entanglement. Finally, several concrete examples are given to illustrate the effectiveness of our results.