Post-quantum nonlocality in the minimal triangle scenario

Abstract

We investigate network nonlocality in the triangle scenario when all three parties have no input and binary outputs. Through an explicit example, we prove that this minimal scenario supports nonlocal correlations compatible with no-signaling and independence of the three sources, but not with realisations based on independent quantum or classical sources. This nonlocality is robust to noise. Moreover, we identify the equivalent to a Popescu-Rohrlich box in the minimal triangle scenario.

arXiv comment7 pages, 5+1 figures, RevTeX 4.2. The computational appendix is available at https://www.github.com/apozas/minimal-triangle V3: Updated to match published version

References in corpus (33)

• A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
• 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
• Guess your neighbour's input: a multipartite non-local game with no quantum advantage
• Genuine quantum nonlocality in the triangle network
• Nonlocal correlations in the star-network configuration
• Nonlinear Bell inequalities tailored for quantum networks
• Polynomial Bell inequalities
• Ruling out real-valued standard formalism of quantum theory
• The Inflation Technique for Causal Inference with Latent Variables
• Computationally Efficient Nonlinear Bell Inequalities for General Quantum Networks
• Bilocal Bell inequalities violated by the quantum Elegant Joint Measurement
• Causal Compatibility Inequalities Admitting Quantum Violations in the Triangle Structure
• Constraints on nonlocality in networks from no-signaling and independence
• Quantum Inflation: A General Approach to Quantum Causal Compatibility
• A neural network oracle for quantum nonlocality problems in networks
• Bounding the sets of classical and quantum correlations in networks
• Bell-type Inequalities for Arbitrary Non-Cyclic Networks
• Correlations in star networks: from Bell inequalities to network inequalities
• Correlations In n-local Scenario
• Quantum Correlations in Connected Multipartite Bell Experiments
• Single-photon nonlocality in quantum networks
• Nonlocality for Generic Networks
• Proofs of network quantum nonlocality in continuous families of distributions
• Self-testing of physical theories, or, is quantum theory optimal with respect to some information-processing task?
• Nonlocality of All Quantum Networks
• Characterizing Quantum Correlations In Fixed Input $n$-Local Network Scenario
• Towards a minimal example of quantum nonlocality without inputs
• Partial self-testing and randomness certification in the triangle network
• Inflation: a Python library for classical and quantum causal compatibility
• Numerically assisted determination of local models in network scenarios

Cited by in corpus (6)

• Semidefinite programming relaxations for quantum correlations
• Hierarchical certification of nonclassical network correlations
• Local models and Bell inequalities for the minimal triangle network
• Symmetric observations without symmetric causal explanations
• A minimal example of quantum non-classicality without freedom of choice
• Guarantees on the structure of experimental quantum networks