The non-distillation conjecture for noisy Popescu–Rohrlich boxes

For $1/2<\eta_1<\eta_2<1$, let $\operatorname{PR}_{\eta_1}$ and $\operatorname{PR}_{\eta_2}$ denote the corresponding noisy Popescu–Rohrlich boxes. Non-distillation conjecture. Two parties cannot use common randomness and an arbitrary number of copies of $\operatorname{PR}_{\eta_1}$ to generate a single copy of $\operatorname{PR}_{\eta_2}$ with wirings.

This conjecture concerns whether wirings can increase the non-locality of noisy Popescu–Rohrlich boxes. It is presented as part of the question of whether there exists a continuum of sets of non-local boxes closed under wirings; the source gives no resolution, so its status remains open.