Mixed State Entanglement Measures for Intermediate Separability

TL;DR

This paper introduces a new family of entanglement measures, R_m, for multipartite quantum states, providing analytical bounds and analyzing the impact of noise on four-qubit states.

Contribution

It develops a novel set of entanglement measures based on generalized concurrences for intermediate separability detection.

Findings

Derived an analytically computable lower bound for R_m

Applied measures to analyze noise effects on four-qubit states

Demonstrated effectiveness in identifying bipartition separability

Abstract

To determine whether a given multipartite quantum state is separable with respect to some partition we construct a family of entanglement measures R_m. This is done utilizing generalized concurrences as building blocks which are defined by flipping of M constituents and indicate states that are separable with regard to bipartitions when vanishing. Further, we provide an analytically computable lower bound for R_m via a simple ordering relation of the convex roof extension. Using the derived lower bound, we illustrate the effect of the isotropic noise on a family of four-qubit mixed states for each intermediate separability.