Multi-User Non-Locality Amplification

Abstract

Non-local correlations are among the most fascinating features of quantum theory 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 -- in terms of classical information. In these contexts, the question is crucial whether such correlations can be amplified or distilled, i.e., whether and how 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 introduce a general framework of reductions between multi-party input-output systems. Within this formalism, we show that a natural n-party generalization of the well-known Popescu-Rohrlich box can be distilled, by an adaptive protocol, to the algebraic maximum.We use this result further to show that a much broader class of correlations, including all purely threepartite correlations, can be distilled from arbitrarily weak to almost maximal strength with partial communication, i.e., using only a subset of the channels required for the creation of the same correlation from scratch. Alternatively, this means that arbitrarily weak non-local correlations can have a "communication value" in the context of the generation of maximal non-locality.