  We consider bipartite mixed states in a $d\otimes d$ quantum system. We say
that $\rho$ is PPT if its partial transpose $1 \otimes T (\rho)$ is positive
semidefinite, and otherwise $\rho$ is NPT. The well-known Werner states are
divided into three types: (a) the separable states (the same as the PPT
states); (b) the one-distillable states (necessarily NPT); and (c) the NPT
states which are not one-distillable. We give several different formulations
and provide further evidence for validity of the conjecture that the Werner
states of type (c) are not two-distillable.
