Optimal protocols for nonlocality distillation

Forster et al. recently showed that weak nonlocality can be amplified by giving the first protocol that distills a class of nonlocal boxes (NLBs) Phys. Rev. Lett. 102, 120401 (2009) We first show that their protocol is optimal among all nonadaptive protocols. We next consider adaptive protocols. We show that the depth-2 protocol of Allcock et al. Phys. Rev. A 80, 062107 (2009) performs better than previously known adaptive depth-2 protocols for all symmetric NLBs. We present a depth-3 protocol that extends the known region of distillable NLBs. We give examples of NLBs for which each of the Forster et al., the Allcock et al., and our protocols perform best. The understanding we develop is that there is no single optimal protocol for NLB distillation. The choice of which protocol to use depends on the noise parameters for the NLB.