Partially Coherent Direct Sum Channels

We introduce Partially Coherent Direct Sum (PCDS) quantum channels, as a generalization of the already known Direct Sum quantum channels. We derive necessary and sufficient conditions to identify the subset of those maps which are degradable, and provide a simplified expression for their quantum capacities. Interestingly, the special structure of PCDS allows us to extend the computation of the quantum capacity formula also for quantum channels which are explicitly not degradable (nor antidegradable). We show instances of applications of the results to dephasing channels, amplitude damping channels, and combinations of the two.

Automated summary

In this paper, we introduce the concept of Partially Coherent Direct Sum (PCDS) quantum channels as a generalization of known Direct Sum quantum channels. We provide necessary and sufficient conditions to identify degradable maps and simplify the quantum capacities. Interestingly, the special structure of PCDS allows for extending the computation of quantum capacity even for explicitly non-degradable quantum channels. Applications of the results to dephasing channels, amplitude damping channels, and combinations of the two are demonstrated.