Complementarity of genuine multipartite non-locality

TL;DR

This paper introduces the concept of complementarity of genuine multipartite non-locality, showing that high non-locality in a system limits non-locality in its subsets, with tighter constraints under quantum conditions.

Contribution

It defines and explores the complementarity of genuine multipartite non-locality, deriving new relations and comparing them with monogamy of non-locality, supported by numerical evidence.

Findings

Complementarity relations are derived under no-signaling constraints.

Quantum constraints tighten the complementarity relations.

Numerical evidence supports the complementarity feature.

Abstract

We introduce a new feature of no-signaling (Bell) non-local theories, namely, when a system of multiple parties manifests genuine non-local correlation, then there cannot be arbitrarily high non-local correlation among any subset of the parties. We call this feature, \textit{complementarity of genuine multipartite non-locality}. We use Svetlichny's criterion for genuine multipartite non-locality and non-local games to derive the complementarity relations under no-signaling constraints. We find that the complementarity relations are tightened for the much stricter quantum constraints. We compare this notion with the well-known notion of \textit{monogamy of non-locality}. As a consequence, we obtain tighter non-trivial monogamy relations that take into account genuine multipartite non-locality. Furthermore, we provide numerical evidence showcasing this feature using a bipartite measure and several other well-known tripartite measures of non-locality.