Abstract
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$$(2\le k\le m)$$(2≤k≤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.
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