Schmidt Number Entanglement Measure for Multipartite k-nonseparable States

In this paper, an entanglement measure for multipartite quantum states with respect to k -partition was introduced, which is called Schmidt number entanglement measure for multipartite k -nonseparable states, it is simply denoted by k -ME SN. We show that this measure is well-defined, i.e., it satisfies some basic properties as an entanglement measure. In addition, we give a super bound and lower bound of k -ME SN for multipartite pure states according to the definition of joint k-Schmidt number with respect to k-partition. Furthermore, we give some examples to show that Schmidt number entanglement measure can quantify the strength of entanglement for multipartite quantum states.