Non-Local Boxes for Networks

Abstract

Nonlocal boxes are conceptual tools that capture the essence of the phenomenon of quantum non-locality, central to modern quantum theory and quantum technologies. We introduce network nonlocal boxes tailored for quantum networks under the natural assumption that these networks connect independent sources and do not allow signaling. Hence, these boxes satisfy the No-Signaling and Independence (NSI) principle. For the case of boxes without inputs, connecting pairs of bipartite sources and producing binary outputs, we prove that the sources and boxes producing local random outputs and maximal 2-box correlations, i.e. $E_2=\sqrt{2}-1$, $E_2^o=1$, are essentially unique.

arXiv comment4 pages + refs and a short appendix

References in corpus (24)

• Information Causality as a Physical Principle
• The lesson of causal discovery algorithms for quantum correlations: Causal explanations of Bell-inequality violations require fine-tuning
• Characterizing the nonlocal correlations of particles that never interacted
• Bilocal versus non-bilocal correlations in entanglement swapping experiments
• Beyond Bell's Theorem: Correlation Scenarios
• Genuine quantum nonlocality in the triangle network
• Nonlocal correlations in the star-network configuration
• Theory-independent limits on correlations from generalised Bayesian networks
• Polynomial Bell inequalities
• Nonlinear Bell inequalities tailored for quantum networks
• A unifying framework for relaxations of the causal assumptions in Bell's theorem
• The Inflation Technique for Causal Inference with Latent Variables
• An entropic approach to local realism and noncontextuality
• Computationally Efficient Nonlinear Bell Inequalities for General Quantum Networks
• Beyond Bell's Theorem II: Scenarios with arbitrary causal structure
• Entanglement 25 years after Quantum Teleportation: testing joint measurements in quantum networks
• Maximal violation of n-locality inequalities in a star-shaped quantum network
• Causal Compatibility Inequalities Admitting Quantum Violations in the Triangle Structure
• Constraints on nonlocality in networks from no-signaling and independence
• Limits on correlations in networks for quantum and no-signaling resources
• Quantum Inflation: A General Approach to Quantum Causal Compatibility
• Bell-type Inequalities for Arbitrary Non-Cyclic Networks
• Correlations in star networks: from Bell inequalities to network inequalities
• Quantum Correlations in Connected Multipartite Bell Experiments

Cited by in corpus (10)

• Bell nonlocality in networks
• Proofs of network quantum nonlocality in continuous families of distributions
• Test of Genuine Multipartite Nonlocality
• Any Physical Theory of Nature Must Be Boundlessly Multipartite Nonlocal
• Quantum information
• Sharing nonlocality in quantum network by unbounded sequential observers
• Experimental Demonstration that No Tripartite-Nonlocal Causal Theory Explains Nature's Correlations
• Covariance Decomposition as a Universal Limit on Correlations in Networks
• Generalized $n$-locality inequalities in linear-chain network for arbitrary inputs scenario and their quantum violations
• No Bipartite-Nonlocal Causal Theory Can Explain Nature's Correlations