Optimal Protocols for Nonlocality Distillation

TL;DR

This paper analyzes and compares various protocols for nonlocality distillation, demonstrating their optimality under different conditions and introducing a new protocol that extends the distillable region.

Contribution

It proves the optimality of a known protocol among non-adaptive methods, improves adaptive protocols, and introduces a new depth 3 protocol for better distillation.

Findings

The non-adaptive protocol by Forster et al. is optimal among all non-adaptive protocols.

The depth 2 adaptive protocol by Allcock et al. outperforms previous methods for symmetric NLBs.

A new depth 3 protocol extends the region of distillable nonlocal boxes.

Abstract

Forster, Winkler, and Wolf 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 non-adaptive 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 new depth 3 protocol that extends the known region of distillable NLBs. We give examples of NLBs for which each of Forster et al.'s, Allcock et al.'s, and our protocol performs best. The new 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.