Separability Of The Mixed State Of2×5-dimensional Bipartite System

The problem of judging whether a quantum state is separable or not is one of thebasic problems of quantum information theory. quantum nonseparable states (entangledstates)was is proposed first by Einstein, Podolsky, Rosen and Schr dinger. This is one ofthe most fascinating feature of quantum mechanics. Now, quantum nonseparable states(entangled states)has been widely used in different physical environments. Currently, withthe development of experimental methods, quantum nonseparable states (entangled states)already have many practical applications in quantum computation and quantum detection.In particular, for2×2and2×3systems the effective separability criterion of separality ofquantum states have been found. However, only some necessary conditions has beenreached.This paper first introduces positive partial transposition (PPT) and rearrangementcriterion to determine whether the quantum state is separable or not. Then we construct thequantum state of a2×5system and study the quantum state using PPT criterion andrearrangement criterion. The results show that this state is a PPT entangled states.