We discuss a connection between the existence of a factorization of a quantum channel $\Phi$ through a von Neumann algebra and the structure of a certain operator system associated with $\Phi$.
This operator system contains information about how the channel $\Phi$ lies in the convex set of quantum channels; in the case of a diagonal channel, it is intimately related with the geometry of correlation matrices. This can be exploited to characterize all rank-two correlation matrices that are factorizable.

This is joint work with Rob Martin, and was supported by NRF grant 105837.