  In this work we design a specific simulation tool for quantum channels which
is based on the use of a control system. This allows us to simulate an average
quantum channel which is expressed in terms of an ensemble of channels, even
when these channel-components are not jointly teleportation-covariant. This
design is also extended to asymptotic simulations, continuous ensembles, and
memory channels. As an application, we derive relative-entropy-of-entanglement
upper bounds for private communication over various channels, including
non-Gaussian mixtures of bosonic lossy channels. Among other results, we also
establish the two-way quantum and private capacity of the so-called
`dephrasure' channel.
