Entanglement Detection for Multipartite States Based on Structural Physical Approximation of Partial Transposition

As an important physical resource, quantum entanglement is widely used in quantum information processing. The positive partial transpose criterion based on partial transpose map is a powerful method for detecting entanglement. Since the partial transpose operation is not a completely positive map, it is not a physical operation and cannot be realized by physical experiments. We approximate partial transposition map by applying structural physical approximation map so that the approximated map are completely positive and thus physically realizable. In this paper, we study the condition that is satisfied when the structural physical approximation is a completely positive map for multipartite states. Then, we give genuine multipartite entanglement criterion for multipartite pure state and full separability criterion for any multipartite quantum states. In addition we derive a generalized method for detecting \((N-1)\) $(N-1)$ -separability of N-partite quantum states. Finally, several examples are used to verify the efficiency of the presented entanglement criteria.