Separable states with infinitely many separable decompositions

Despite intense effort in the past decades, developing a general criterion for identifying separable mixed states is still an open problem. In this context, the Positive Partial Transpose (PPT) criterion constituted an important first step towards practical entanglement detection techniques and was later used to investigate the auxiliary problem of finding separable decompositions for separable states. In this poster, we use the rank diminishing method proposed by B. Kraus et al. [PRA 61, 062302 (2000)], that exploits the PPT property to reconstruct separable decompositions, to study the separable decompositions of symmetric PPT states of 3 qubits. We show that any 3-qubit symmetric product states always belong to an optimal separable decomposition of a PPT symmetric 3-qubit state with maximal birank.