Linear Program Witness for Network Nonlocality in Arbitrary Networks

TL;DR

This paper introduces a linear programming-based method to certify network nonlocality in quantum networks, providing a versatile and efficient tool applicable to various network structures.

Contribution

It develops a network-agnostic linear programming witness framework for certifying nonlocality, adaptable to different network topologies and based solely on observed probabilities.

Findings

Constructed nonlocality witnesses for ring networks

Certified network nonlocality in a concrete example

Provided a scalable, efficient certification method

Abstract

Network nonlocality extends Bell nonlocality to settings with multiple independent sources and parties. Certifying it in quantum information processing tasks requires suitable witnesses. However, in contrast to local correlations, the set of network-local correlations is non-convex. This non-convexity makes certifying network nonlocality a highly non-trivial task. Existing approaches involve leveraging network-specific properties, or inflation-based methods whose constraints grow combinatorially in the number of local variables. In this work, we introduce a linear programming witness for network nonlocality built from five classes of linear constraints. These classes are network-agnostic, although the explicit forms of the constraints must be tailored to a specific network's structure. We use the procedure to construct network nonlocality witnesses for a family of ring networks and certify network nonlocality for a concrete example, relying only on observed probabilities and a tunable experimental parameter. Our work advances the search for efficient witnesses to certify network nonlocality across diverse quantum network architectures.