On Sufficient and Necessary Criteria of Multipartite Quantum Entanglement

Abstract: Based on the generalized Bloch representation, we study the separability and genuine multipartite entanglement of arbitrary dimensional multipartite quantum states. Some sufficient and some necessary criteria are presented. For certain states, these criteria together are both sufficient and necessary. Detailed examples show that our criteria are better than some existing ones in identifying entanglement. Based on these criteria, the largest separable ball around the maximally mixed state for arbitrary multi-qubit systems is found, and it is proved that its radius is the constant 1. Furthermore, the criteria in this paper can be implemented experimentally.