Distillation of Multi-Party Non-Locality With and Without Partial Communication

Abstract

Non-local correlations are one of the most fascinating consequences of quantum physics from the point of view of information: Such correlations, although not allowing for signaling, are unexplainable by pre-shared information. The correlations have applications in cryptography, communication complexity, and sit at the very heart of many attempts of understanding quantum theory -- and its limits -- better in terms of classical information. In these contexts, the question is crucial whether such correlations can be distilled, i.e., whether weak correlations can be used for generating (a smaller amount of) stronger. Whereas the question has been studied quite extensively for bipartite correlations (yielding both pessimistic and optimistic results), only little is known in the multi-partite case. We show that a natural generalization of the well-known Popsecu-Rohrlich box can be distilled, by an adaptive protocol, to the algebraic maximum. We use this result further to show that a much bigger class of correlations, including all purely three-partite correlations, can be distilled from arbitrarily weak to maximal strength with partial communication, i.e., using only a subset of the channels required for the creation of the same correlation from scratch. In other words, we show that arbitrarily weak non-local correlations can have a "communication value" in the context of the generation of maximal non-locality.