Nonlocality distillation and quantum voids

Abstract

Via nonlocality distillation, a number of copies of a given nonlocal correlation can be turned into a new correlation displaying a higher degree of nonlocality. Apart from its clear relevance in situations where nonlocality is a resource, distillation protocols also play an important role in the understanding of information-theoretical principles for quantum theory. Here, we derive a necessary condition for nonlocality distillation from two copies and apply it, among other results, to show that 1D and 2D quantum voids -faces of the nonlocal simplex set with no quantum realization-can be distilled up to PR-boxes. With that, we generalize previous results in the literature. For instance, showing a broad class of post-quantum correlations that make communication complexity trivial and violate the information causality principle. arXiv:1903.09289v1 [quant-ph]

Advantages of multi-copy nonlocality distillation and its application to minimizing communication complexity

“…We remark here that previously, heuristics to simplify the optimisation over two-copy protocols have been proposed. For instance, the method in [29] suggests to reduce the search over 82 4 protocols to a manageable number of only 3152, by only considering protocols that preserve the PR-box, P NL 1 . Using linear programming, as proposed here, has the advantage that it takes all distillation protocols into account.…”

“…Using linear programming, as proposed here, has the advantage that it takes all distillation protocols into account. In contrast, the heuristic from [29] discards various protocols, e.g., FWW and ABL + 2, that despite not preserving P NL 1 , are useful for non-locality distillation-they are even among the optimal 2-copy distillation protocols in CS I-so this shortcoming is pertinent.…”

Advantages of Multicopy Nonlocality Distillation and Its Application to Minimizing Communication Complexity

“…CHSH value of the distilled box We remark here that previously, heuristics to simplify the optimisation over two-copy protocols have been proposed. For instance, the method in [34] suggests to reduce the search over 82 4 protocols to a manageable number of only 3152, by only considering protocols that preserve the PR-box, P NL 1 . Using linear programming, as proposed here, has the advantage that it takes all distillation protocols into account.…”

“…Using linear programming, as proposed here, has the advantage that it takes all distillation protocols into account. In contrast, the heuristic from [34] discards various protocols, e.g., FWW and ABL + 2, that despite not preserving P NL 1 , are useful for non-locality distillation-they are even among the optimal 2-copy distillation protocols in CS I-so this shortcoming is pertinent.…”