  The ability to transfer coherent quantum information between systems is a
fundamental component of quantum technologies and leads to coherent
correlations within the global quantum process. However correlation structures
in quantum channels are less studied than those in quantum states. Motivated by
recent techniques in randomized benchmarking, we develop a range of results for
efficient estimation of correlations within a bipartite quantum channel. We
introduce sub-unitarity measures that are invariant under local changes of
basis, generalize the unitarity of a channel, and allow for the analysis of
coherent information exchange within channels. Using these, we show that
unitarity is monogamous, and provide a novel information-disturbance relation.
We then define a notion of correlated unitarity that quantifies the
correlations within a given channel. Crucially, we show that this measure is
strictly bounded on the set of separable channels and therefore provides a
witness of non-separability. Finally, we describe how such measures for
effective noise channels can be efficiently estimated within different
randomized benchmarking protocols. We find that the correlated unitarity can be
estimated in a SPAM-robust manner for any separable quantum channel, and show
that a benchmarking/tomography protocol with mid-circuit resets can reliably
witness non-separability for sufficiently small reset errors. The tools we
develop provide information beyond that obtained via simultaneous randomized
benchmarking and so could find application in the analysis of cross-talk and
coherent errors in quantum devices.
