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.

22 pages

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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