Conditional channel simulation

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, from the amplitude damping channel to 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.