Network Nonlocality via Rigidity of Token-Counting and Color-Matching

Abstract

Network Nonlocality is the study of the Network Nonlocal correlations created by several independent entangled states shared in a network. In this paper, we provide the first two generic strategies to produce nonlocal correlations in large classes of networks without input. In the first one, called Token-Counting (TC), each source distributes a fixed number of tokens and each party counts the number of received tokens. In the second one, called Color-Matching (CM), each source takes a color and a party checks if the color of neighboring sources match. Using graph theoretic tools and Finner's inequality, we show that TC and CM distributions are rigid in wide classes of networks, meaning that there is essentially a unique classical strategy to simulate such correlations. Using this rigidity property, we show that certain quantum TC and CM strategies produce correlations that cannot be produced classicality. This leads us to several examples of Network Nonlocality without input. These examples involve creation of coherence throughout the whole network, which we claim to be a fingerprint of genuine forms of Network Nonlocality. This work extends a more compact parallel work [Nonlocality for Generic Networks, arXiv:2011.02769] on the same subject and provides all the required technical proofs.

24 pages (9 of appendices), 8 figures. The original paper was split off for publication, see the more compact parallel work arXiv:2011.02769 (Phys. Rev. Lett. 128, 060401, DOI: 10.1103/PhysRevLett.128.060401)

References in corpus (2)

• Device-independent security of quantum cryptography against collective attacks
• Beyond Bell's Theorem: Correlation Scenarios

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• Towards a minimal example of quantum nonlocality without inputs
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• Topologically Robust Quantum Network Nonlocality
• Generalized $n$-locality inequalities in linear-chain network for arbitrary inputs scenario and their quantum violations
• Noise-robust proofs of quantum network nonlocality
• Multipartite Nonlocality in Clifford Networks
• Bell nonlocality in quantum networks with unreliable sources: Loophole-free postelection via self-testing
• Closing the detection loophole in the triangle network with high-dimensional photonic states
• Violation of the Finner inequality in the four-output triangle network
• Experimental genuine quantum nonlocality in the triangle network
• Linear Program Witness for Network Nonlocality in Arbitrary Networks