Abstract. One makes use of the well-known Schmidt decomposition theorem to determine the entanglement status of a bipartite pure quantum state. For solving this problem in the bipartite case one performs Schmidt decomposition procedure and obtains Schmidt number. The given bipartite state is entangled if Schmidt number is greater than unity and separable if it is equal to unity. In this paper we extend this idea of applying Schmidt decomposition procedure to a multipartite pure quantum state and develop an easy algorithm to perform complete analysis of the given N-partite pure quantum state. We successfully manage the full factorization of the given multipartite pure quantum state and specify the following: Whether the given an N-qubit pure quantum state is completely separable (N factors), or completely entangled (no factors), or partially entangled having entangled factors of different sizes which being entangled cannot be factored further. We have thus completely solved the problem of deciding the entanglement status of multipartite pure quantum states and developed an easy method to find all the separable as well as entangled factors of these multipartite pure quantum states.

Full-text: PDF