Covariance Decomposition as a Universal Limit on Correlations in Networks

TL;DR

This paper establishes a universal covariance matrix decomposition that bounds the correlations achievable in any network, regardless of the underlying physical theory, including classical and quantum.

Contribution

It introduces a universal covariance decomposition framework that applies across all physical theories to constrain network correlations.

Findings

Covariance matrices of feasible correlations can be decomposed into source-specific positive semidefinite matrices.

The decomposition applies universally to classical, quantum, and generalized probabilistic theories.

Provides a fundamental limit on correlations in networks based on covariance structure.

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.