Generalized Choi states and 2-distillability of quantum states

We investigate the distillability of bipartite quantum states in terms of positive and completely positive maps. We construct the so-called generalized Choi states and show that it is distillable when it has negative partial transpose. We convert the distillability problem of 2-copy $n\times n$ Werner states into the determination of the positivity of an Hermitian matrix. We obtain several sufficient conditions by which the positivity holds. Further, we investigate the case $n=3$ by the classification of $2\times 3\times 3$ pure states.