Measure of multipartite entanglement with computable lower bounds

TL;DR

This paper introduces a new multipartite entanglement measure called $k$-ME concurrence that detects all $k$-nonseparable states in any dimension, with experimentally feasible lower bounds that outperform existing criteria.

Contribution

The paper proposes a novel $k$-ME concurrence measure for multipartite entanglement with computable lower bounds that do not require optimization or eigenvalue calculations.

Findings

Lower bounds are experimentally implementable.

Bounds outperform other detection criteria in examples.

Measure detects all $k$-nonseparable states.

Abstract

In this paper, we present a measure of multipartite entanglement ($k$-nonseparable), $k$-ME concurrence $C_{k-\mathrm{ME}}(\rho)$ that unambiguously detects all $k$-nonseparable states in arbitrary dimensions, where the special case, 2-ME concurrence $C_{2-\mathrm{ME}}(\rho)$, is a measure of genuine multipartite entanglement. The new measure $k$-ME concurrence satisfies important characteristics of an entanglement measure including entanglement monotone, vanishing on $k$-separable states, convexity, subadditivity and strictly greater than zero for all $k$-nonseparable states. Two powerful lower bounds on this measure are given. These lower bounds are experimentally implementable without quantum state tomography and are easily computable as no optimization or eigenvalue evaluation is needed. We illustrate detailed examples in which the given bounds perform better than other known detection criteria.