We consider bipartite mixed states in a \(d\otimes d\) quantum system. We say that such
a state is PPT if its partial transpose is positive semidefinite, and otherwise that
it is NPT. The well-known Werner states are partitioned into three types: a) the separable
states (same as the PPT states), b) the 1-distillable states (necessarily NPT), and
c) the NPT states which are not 1-distillable. We give several different formulations
and provide further evidence for validity of the conjecture that the type c) Werner
states are not 2-distillable.