The Distillability Conjecture for bipartite NPT states

Let $\rho$ be a bipartite quantum state. It is NPT if its partial transpose is not positive semidefinite, and indistillable if no tensor power of $\rho$ is $1$-distillable. Distillability Conjecture. There exist indistillable bipartite NPT states.

This is the problem of whether bound NPT entangled states exist; it is known to have an affirmative answer in local dimension $2$ only for the complementary question of distillability, while the conjectured existence of such states remains open in dimensions at least $3$.