Unital Qubit Queue-Channels: Classical Capacity and Product Decoding

Quantum queue-channels arise naturally in the context of buffering in quantum networks, wherein the noise suffered by the quantum states depends on the time spent waiting in the buffer. Mandayam (2020) derived a simple upper bound on the classical capacity of an additive queue-channel and showed it to be achievable for the erasure and depolarizing channels. In this article, we characterize the classical capacity for the class of unital qubit queue-channels and show that a simple product (nonentangled) decoding strategy is capacity achieving. As an intermediate step, we present a simpler derivation of an explicit capacity-achieving product decoding strategy for any independent identically distributed unital qubit channel, which may be of interest. As an important special case, we also derive the capacity and optimal decoding strategies for a symmetric generalized amplitude damping queue-channel. Our results provide useful insights toward designing practical quantum communication networks and highlight the need to explicitly model the impact of buffering.