Separable State Decompositions for a Class of Mixed States

We study certain quantum states for which the PPT criterion is both sufficient and necessary for separability. A class of n × n bipartite mixed states is presented and the conditions of PPT for these states are derived. The separable pure state decompositions of these states are explicitly constructed when they are PPT. Quantum entangled states have become one of the key resources in quantum information processing. The study of quantum teleportation, quantum cryptography, quantum dense coding, quantum error correction and parallel computation [1–3] has spurred a flurry of activities in the investigation of quantum entanglement. Despite the potential applications of quantum entangled states, there are many open questions in the theory of quantum entanglement. The separability of quantum mixed states is one of the important problems in the theory of quantum entanglement. Let H be an n-dimensional complex Hilbert space, with |i⟩, i = 1, ..., n the orthonormal basis. A bipartite mixed state in H ⊗H is said to be separable if the density matrix can be