The 2-distillability conjecture for Werner states

Fix $d\ge3$ and define the Werner states by

$$\rho_W(t)=1-tF,$$

where $F$ is the flip operator. For $t\in(1/d,1/2]$, these states are NPT. A state is 2-distillable if there exists a Schmidt-rank-at-most-two vector $\psi$ such that the expectation value of the second tensor power of its partial transpose is negative.

2-distillability conjecture for Werner states. None of the Werner states $\rho_W(t)$, $t\in(1/d,1/2]$, is $2$-distillable.

The paper calls this a very weak version of the stronger Werner-state nondistillability conjecture. It remains open in the source and is studied through equivalent positivity formulations.