Nonlinear Bell inequalities tailored for quantum networks

Abstract

In a quantum network, distant observers sharing physical resources emitted by independent sources can establish strong correlations, which defy any classical explanation in terms of local variables. We discuss the characterization of nonlocal correlations in such a situation, when compared to those that can be generated in networks distributing independent local variables. We present an iterative procedure for constructing Bell inequalities tailored for networks: starting from a given network, and a corresponding Bell inequality, our technique provides new Bell inequalities for a more complex network, involving one additional source and one additional observer. The relevance of our method is illustrated on a variety of networks, for which we demonstrate significant quantum violations.

8 pages, 2 figures. Comments welcome

References in corpus (10)

• The Quantum Internet
• Device-independent security of quantum cryptography against collective attacks
• Beyond Bell's Theorem: Correlation Scenarios
• Information-Theoretic Implications of Quantum Causal Structures
• Theory-independent limits on correlations from generalised Bayesian networks
• Nonlocal correlations in the star-network configuration
• Polynomial Bell inequalities
• A unifying framework for relaxations of the causal assumptions in Bell's theorem
• Classifying 50 years of Bell inequalities
• Classical simulation of entanglement swapping with bounded communication

Cited by in corpus (86)

• Bell nonlocality in networks
• Quantum common causes and quantum causal models
• Polynomial Bell inequalities
• The Inflation Technique for Causal Inference with Latent Variables
• Computationally Efficient Nonlinear Bell Inequalities for General Quantum Networks
• Entanglement 25 years after Quantum Teleportation: testing joint measurements in quantum networks
• All entangled pure quantum states violate the bilocality inequality
• Experimental demonstration of non-bilocal quantum correlations
• Bilocal Bell inequalities violated by the quantum Elegant Joint Measurement
• Maximal violation of n-locality inequalities in a star-shaped quantum network
• Experimental non-locality in a quantum network
• Quantifying Bell: the Resource Theory of Nonclassicality of Common-Cause Boxes
• Constraints on nonlocality in networks from no-signaling and independence
• Limits on correlations in networks for quantum and no-signaling resources
• Machine learning non-local correlations
• Towards device-independent information processing on general quantum networks
• A neural network oracle for quantum nonlocality problems in networks
• Quantum entanglement in the triangle network
• Network Quantum Steering
• Experimental demonstration of nonbilocality with truly independent sources and strict locality constraints
• Bell-type Inequalities for Arbitrary Non-Cyclic Networks
• Entanglement without hidden nonlocality
• Correlations in star networks: from Bell inequalities to network inequalities
• Experimental bilocality violation without shared reference frames
• Causal inference via algebraic geometry: feasibility tests for functional causal structures with two binary observed variables
• Symmetries in quantum networks lead to no-go theorems for entanglement distribution and to verification techniques
• Quantum Correlations in Connected Multipartite Bell Experiments
• Concentration phenomena in the geometry of Bell correlations
• Maximal qubit violation of n-local inequalities in quantum network
• The Inflation Technique Completely Solves the Causal Compatibility Problem
• Nonlocality for Generic Networks
• Entropic nonsignaling correlations
• Quantifying causal influences in the presence of a quantum common cause
• Feedback through graph motifs relates structure and function in complex networks
• Generalized $n$-locality inequalities in star-network configuration and their optimal quantum violations
• Analysing causal structures with entropy
• Covariance Bell inequalities
• Full multipartite steering inseparability, genuine multipartite steering and monogamy for continuous variable systems
• Nonlocality of All Quantum Networks
• Characterizing nonlocal correlations through various $n$-locality inequlities in quantum network
• Non-Local Boxes for Networks
• Sharing nonlocality in quantum network by unbounded sequential observers
• Network Nonlocality via Rigidity of Token-Counting and Color-Matching
• Semidefinite tests for latent causal structures
• Variational Quantum Optimization of Nonlocality in Noisy Quantum Networks
• Indistinguishability of causal relations from limited marginals
• Nontrilocality: Exploiting nonlocality from three particle systems
• Quantum violation of local causality in urban network with hybrid photonic technologies
• Hierarchical certification of nonclassical network correlations
• Quantum steering beyond instrumental causal networks
• A convergent inflation hierarchy for quantum causal structures
• Non-signaling Causal Hierarchy of General Multisource Networks
• Regarding the Maximal Qubit Violations of n-Locality in Star and Chain Networks
• The inflation hierarchy and the polarization hierarchy are complete for the quantum bilocal scenario
• Inability of the entropy vector method to certify nonclassicality in linelike causal structures
• Inferring Quantum Network Topology using Local Measurements
• Discriminating Quantum Correlations with Networking Quantum Teleportation
• From Quantum Foundations to Applications and Back
• Post-quantum nonlocality in the minimal triangle scenario
• State polynomials: positivity, optimization and nonlinear Bell inequalities
• Topologically Robust Quantum Network Nonlocality
• New Genuine Multipartite Entanglement
• Detection of Network and Genuine Network Quantum Steering
• Mesoscopic and macroscopic quantum correlations in photonic, atomic and optomechanical systems
• Detection loophole in quantum causality and its countermeasures
• Generalized $n$-locality inequalities in linear-chain network for arbitrary inputs scenario and their quantum violations
• Quantum Causal Structure and Quantum Thermodynamics
• No nonlocal advantage of quantum coherence beyond quantum instrumentality
• Noise-robust proofs of quantum network nonlocality
• Bell non-locality using tensor networks and sparse recovery
• Sharing nonlocality in a network using the quantum violation of chain network inequality
• Optimal quantum violations of n-locality inequalities with conditional dependence on inputs
• Study of entanglement via a multi-agent dynamical quantum game
• Nonlocal correlations in an asymmetric quantum network
• Characterizing nonbilocal correlation: A geometric perspective
• Reality, Causality, and Quantum Theory
• Experimental test of quantum causal influences
• Causal Networks and Freedom of Choice in Bell's Theorem
• Characterizing nonclassical correlations of tensorizing states in a bilocal scenario
• The genuinely multipartite nonlocality of graph states is model-dependent
• Guarantees on the structure of experimental quantum networks
• Experimental genuine quantum nonlocality in the triangle network
• Error-mitigated inference of quantum network topology
• Robust Multipartite Entanglement Without Entanglement Breaking
• Quantifying measurement-induced nonbilocal correlation
• Features of preparable entangled states in Gaussian quantum networks