Mirror Entanglement Measure of Multipartite Quantum States with Respect to k-partitions

In Monras et al. (Phys. Rev. A, 2011, 84(1):012301 2011), the authors presented an entanglement measure for bipartite pure states based on local unitary operations. In this paper, motivated by this idea, we obtained an entanglement measure for multipartite quantum states with respect to k-partitions, which is called mirror entanglement measure for multipartite k-nonseparable states, it is simply denoted by k-MEM. We show that this measure is well-defined, i.e., it satisfies some necessary conditions of entanglement measure including vanishes iff the multipartite quantum states are k-separable, invariance under local unitary operation and monotonicity under local quantum operation and classical communication.