Partially Coherent Direct Sum Channels

TL;DR

This paper introduces Partially Coherent Direct Sum (PCDS) quantum channels, providing conditions for degradability and extending quantum capacity calculations to non-degradable channels, with applications to common quantum noise models.

Contribution

It generalizes direct sum channels to PCDS channels, derives degradability conditions, and extends quantum capacity formulas to non-degradable channels.

Findings

Derived necessary and sufficient conditions for degradability of PCDS channels.

Provided simplified quantum capacity expressions for PCDS channels.

Applied results to dephasing, amplitude damping, and their combinations.

Abstract

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.