Exact Quantum Capacity of Decohering Channels in Arbitrary Dimensions

TL;DR

This paper derives exact formulas for the quantum capacity of a wide class of decohering channels in any dimension, revealing how residual coherence can preserve quantum information even under strong noise.

Contribution

It provides the first exact, single-letter quantum capacity formulas for generalized dephasing channels in arbitrary dimensions, including fully and partially decohering cases.

Findings

Channels are degradable for all noise levels and dimensions.

Nonzero capacity can persist even under maximal decoherence.

Residual coherence structures influence quantum information preservation.

Abstract

We derive exact analytical expressions for the quantum capacity of a broad subclasses of generalized dephasing channels of the form $\Lambda(\rho)=(1-x)\rho + x D(\rho)$, where $D(\rho)$ represents a structured decoherence process. These channels are degradable for all noise parameters and in arbitrary dimensions, yielding closed-form, single-letter capacity formulas. Our analysis includes fully decohering, block-decohering, and weakly decohering channels, the latter involving coherence preservation within overlapping subspaces. Surprisingly, even under maximal decoherence, the channel may retain nonzero capacity due to residual coherence structure. These results provide quantitative role for decoherence-free and partially coherent subspaces in preserving quantum information, offering guidance for encoding strategies in quantum memories and fault-tolerant quantum communication systems.