A general scheme for construction of bound entangled states by convex linear combination

To characterize bound entangled states is one of the most challenging problems in quantum information theory. In this paper, we look from a new different angle to find bound entangled states. In particularly, we give a general scheme for construction of new bound entangled states from known bound entangled states by convex linear combination. This is achieved by quantitatively characterizing entanglement of quantum states via the positive partial transpose (PPT) criterion and the computable cross-norm or realignment (CCNR) criterion. The obtained results are illustrated through an explicit example.