1210.0111 (Lin Chen et al.)

Qubit-qudit states with positive partial transpose    [PDF]

Lin Chen, Dragomir Z. Djokovic

We show that the length of a qubit-qutrit separable state is equal to the max(r,s), where r is the rank of the state and s is the rank of its partial transpose. We refer to the ordered pair (r,s) as the birank of this state. We also construct examples of qubit-qutrit separable states of any feasible birank (r,s). We determine the closure of the set of normalized two-qutrit entangled states of rank four having positive partial transpose (PPT). The boundary of this set consists of all separable states of length at most four. We prove that the length of any qubit-qudit separable state of birank (d+1,d+1) is d+1. We also show that all qubit-qudit PPT entangled states of birank (d+1,d+1) can be built in a simple way from edge states. If V is a subspace of dimension kView original: http://arxiv.org/abs/1210.0111