Measure of multipartite entanglement with computable lower bounds

In this paper, we present a measure of multipartite entanglement (k-nonseparable), k-ME concurrence Ck-ME(rho), that unambiguously detects all k-nonseparable states in arbitrary dimensions, where the special case 2-ME concurrence C2-ME(rho) is a measure of genuine multipartite entanglement. Themeasure k-MEconcurrence 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. DOI: 10.1103/PhysRevA. 86.062323