In this paper, we present a measure of multipartite entanglement ($k$-nonseparable), $k$-ME concurrence $C_{k-\mathrm{ME}}\left(\rho \right)$, that unambiguously detects all $k$-nonseparable states in arbitrary dimensions, where the special case 2-ME concurrence $C_{2-\mathrm{ME}}\left(\rho \right)$ is a measure of genuine multipartite entanglement. The measure $k$-ME concurrence satisfies important characteristics of an entanglement measure, including the entanglement monotone, vanishing on $k$-separable states, convexity, subadditivity, and being 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.

• Received 18 September 2012

DOI:https://doi.org/10.1103/PhysRevA.86.062323