Some necessary and sufficient conditions for k-separability of multipartite pure states
The detection of entanglement for quantum states in multipartite systems is very significant. In this paper, we firstly give a necessary and sufficient condition for k-separability\((2\le k\le m)\) of m-partite pure states. Furthermore, we derive some equivalent conditions for k-separability of pure states in any multipartite quantum systems of finite or infinite dimension. Lastly, we give some examples to explain the application of our results.
k-separability multipartite pure states entanglement criterion