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.

arXiv comment24 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 (31)

• Quantum cryptography: Public key distribution and coin tossing
• Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km
• Bell nonlocality
• Device-independent security of quantum cryptography against collective attacks
• Random Numbers Certified by Bell's Theorem
• Quantum Random Number Generators
• Self-testing of quantum systems: a review
• Characterizing the nonlocal correlations of particles that never interacted
• Bilocal versus non-bilocal correlations in entanglement swapping experiments
• Beyond Bell's Theorem: Correlation Scenarios
• Quantum theory based on real numbers can be experimentally falsified
• Genuine quantum nonlocality in the triangle network
• Analytic and nearly optimal self-testing bounds for the Clauser-Horne-Shimony-Holt and Mermin inequalities
• Nonlinear Bell inequalities tailored for quantum networks
• The Inflation Technique for Causal Inference with Latent Variables
• Genuine Network Multipartite Entanglement
• Computationally Efficient Nonlinear Bell Inequalities for General Quantum Networks
• Efficient exploration of Hamiltonian parameter space for optimal control of non-Markovian open quantum systems
• All entangled pure quantum states violate the bilocality inequality
• Device-independent entanglement certification of all entangled states
• Bilocal Bell inequalities violated by the quantum Elegant Joint Measurement
• Limits on correlations in networks for quantum and no-signaling resources
• Self-testing entangled measurements in quantum networks
• Quantum Inflation: A General Approach to Quantum Causal Compatibility
• A neural network oracle for quantum nonlocality problems in networks
• Quantum entanglement in the triangle network
• Bounding the sets of classical and quantum correlations in networks
• Noise-resistant device-independent certification of Bell state measurements
• Correlations in star networks: from Bell inequalities to network inequalities
• Nonlocality for Generic Networks
• New Genuine Multipartite Entanglement

Cited by in corpus (16)

• Network Quantum Steering
• Nonlocality for Generic Networks
• Proofs of network quantum nonlocality in continuous families of distributions
• Towards a minimal example of quantum nonlocality without inputs
• Partial self-testing and randomness certification in the triangle network
• Covariance Decomposition as a Universal Limit on Correlations in Networks
• Quantum coherence in networks
• 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
• Noise-robust proofs of quantum network nonlocality
• Closing the detection loophole in the triangle network with high-dimensional photonic states
• Bell nonlocality in quantum networks with unreliable sources: Loophole-free postelection via self-testing
• 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