  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.
