Linear Program Witness for Network Nonlocality in Arbitrary Networks

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.

14 pages, 5 figures

References in corpus (18)

• The Quantum Internet
• Bell nonlocality
• Device-independent security of quantum cryptography against collective attacks
• Random Numbers Certified by Bell's Theorem
• No Signalling and Quantum Key Distribution
• Characterizing the nonlocal correlations of particles that never interacted
• Bilocal versus non-bilocal correlations in entanglement swapping experiments
• Beyond Bell's Theorem: Correlation Scenarios
• Geometry of the set of quantum correlations
• Quantum Inflation: A General Approach to Quantum Causal Compatibility
• Bounding the sets of classical and quantum correlations in networks
• Quantifying Bell non-locality with the trace distance
• Two-Party Bell Inequalities Derived from Combinatorics via Triangular Elimination
• Single-photon nonlocality in quantum networks
• The Inflation Technique Completely Solves the Causal Compatibility Problem
• Network Nonlocality via Rigidity of Token-Counting and Color-Matching
• Memory attacks in network nonlocality and self-testing
• Bell nonlocality in quantum networks with unreliable sources: Loophole-free postelection via self-testing