Nonlocality for Generic Networks

Abstract

Bell's theorem shows that correlations created by a single entangled quantum state cannot be reproduced classically. Such correlations are called Nonlocal. They are the elementary manifestation of a broader phenomenon called Network Nonlocality, where several entangled states shared in a network create Network Nonlocal correlations. In this paper, we provide the first class of strategies producing nonlocal correlations in generic networks. In these strategies, called Color-Matching (CM), any source takes a color at random or in superposition, where the colors are labels for a basis of the associated Hilbert space. A party (besides other things) checks if the color of neighboring sources match. We show that in a large class of networks without input, well-chosen quantum CM strategies result in nonlocal correlations that cannot be produced classically. For our construction, we introduce the graph theoretical concept of rigidity of classical strategies in networks, and using the Finner inequality, establish a deep connection between network nonlocality and graph theory. In particular, we establish a link between CM strategies and the graph coloring problem. This work is extended in a longer paper, Network Nonlocality via Rigidity of Token-Counting and Color-Matching, where we introduce a second family of rigid strategies called Token-Counting, leading to network nonlocality.

6 pages. Comments are welcome! The first version of this work was split of for publication, see the extended work arXiv:2202.00905 (Phys. Rev. A 105, 022408, DOI: 10.1103/PhysRevA.105.022408)

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• Network Nonlocality via Rigidity of Token-Counting and Color-Matching
• Quantum Correlation Sharing: A Review On Recent Progress From Nonlocality To Other Non-Classical Correlations
• Sharing nonlocality in quantum network by unbounded sequential observers
• Network nonlocality sharing via weak measurements in the generalized star network configuration
• Sharing Quantum Nonlocality in Star Network Scenarios
• Post-quantum nonlocality in the minimal triangle scenario
• Network quantum steering enables randomness certification without seed randomness
• Topologically Robust Quantum Network Nonlocality
• Generalized $n$-locality inequalities in linear-chain network for arbitrary inputs scenario and their quantum violations
• Multipartite Nonlocality in Clifford Networks
• An Operational Environment for Quantum Self-Testing
• Two convergent NPA-like hierarchies for the quantum bilocal scenario
• Nonlocal correlations in an asymmetric quantum network
• Experimental quantum triangle network nonlocality with an AlGaAs multiplexed entangled photon source
• Closing the detection loophole in the triangle network with high-dimensional photonic states
• Optimal quantum violations of n-locality inequalities with conditional dependence on inputs
• Experimental genuine quantum nonlocality in the triangle network
• The genuinely multipartite nonlocality of graph states is model-dependent