The Study Of Some Separability Criteria

A new type of resource called entanglement is one of the main research field of the quan-tum information and it essentially surpass the classical resources. But until now, this new re-source has not been well understand and there are a number of unsolved problems for thisseparability of bipartite quantum states. First, we compare∥T_ρ∥criterion, PPT criterion, andrealignment criterion. Besides, we supplement a general proof about this∥T_ρ∥criterion.Then, from the general definition of symmetric quantum state, we prove that the densitymatrices of the 2×2 bipartite real symmetric quantum states consist of only six parameters.that is,We also show for the 2×2 bipartite real symmetric quantum states, the PPT criterion andrealignment criterion are equivalent.Finally, based on the∥T_ρ∥criterion, we give the separability of another important quantumstatethat is,(1) ifρis a separable state, then 2ab + 2|1-2p|ab + |2p-1|≤1.(2) if 2ab + 2|1-2p|ab + |2p-1| > 1, then theρis a entanglement state.But from PPT criterion, ifρis separable, then p = 12 . We also give the separability of thegiven quantum state by the realignment criterion.Key Words: separable state entangled state∥T_ρ∥criterion density matrix...