Covariance Decomposition as a Universal Limit on Correlations in Networks

Abstract

Parties connected to independent sources through a network can generate correlations among themselves. Notably, the space of feasible correlations for a given network, depends on the physical nature of the sources and the measurements performed by the parties. In particular, quantum sources give access to nonlocal correlations that cannot be generated classically. In this paper, we derive a universal limit on correlations in networks in terms of their covariance matrix. We show that in a network satisfying a certain condition, the covariance matrix of any feasible correlation can be decomposed as a summation of positive semidefinite matrices each of whose terms corresponds to a source in the network. Our result is universal in the sense that it holds in any physical theory of correlation in networks, including the classical, quantum and all generalized probabilistic theories.

arXiv comment22 pages

References in corpus (22)

• Characterizing the nonlocal correlations of particles that never interacted
• Beyond Bell's Theorem: Correlation Scenarios
• Quantum common causes and quantum causal models
• Theory-independent limits on correlations from generalised Bayesian networks
• Embezzling Entangled Quantum States
• The Inflation Technique for Causal Inference with Latent Variables
• Beyond Bell's Theorem II: Scenarios with arbitrary causal structure
• Generalized Probabilistic Theories Without the No-Restriction Hypothesis
• Certification and Quantification of Multilevel Quantum Coherence
• Limits on correlations in networks for quantum and no-signaling resources
• Constraints on nonlocality in networks from no-signaling and independence
• Semidefinite tests for quantum network topologies
• Strong nonlocality: A trade-off between states and measurements
• The Inflation Technique Completely Solves the Causal Compatibility Problem
• Characterizing Quantum Networks: Insights from Coherence Theory
• Self-testing of physical theories, or, is quantum theory optimal with respect to some information-processing task?
• Non-Local Boxes for Networks
• Network Nonlocality via Rigidity of Token-Counting and Color-Matching
• Semidefinite tests for latent causal structures
• Couplers for Non-Locality Swapping
• The PPT${}^2$ conjecture holds for all Choi-type maps
• Feats, Features and Failures of the PR-box

Cited by in corpus (6)

• Bell nonlocality in networks
• Test of Genuine Multipartite Nonlocality
• Any Physical Theory of Nature Must Be Boundlessly Multipartite Nonlocal
• Experimental Demonstration that No Tripartite-Nonlocal Causal Theory Explains Nature's Correlations
• Witnessing Non-Classicality in a Simple Causal Structure with Three Observable Variables
• No Bipartite-Nonlocal Causal Theory Can Explain Nature's Correlations