A Simple and Tighter Derivation of Achievability for Classical-Quantum Channel Coding

In this paper, we propose an elegant and simple one-shot achievability proof for classical-quantum channel coding. The established one-shot bound admits a closed-form expression as in the celebrated Holevo–Helstrom Theorem. Namely, the average error probability of sending M messages through a classical-quantum channel is upper bounded by the minimum error of distinguishing the joint state between channel input and output against (M−1)-many products of its marginals. Our result provides the tightest achievable one-shot capacity for classical-quantum channel coding, and it improves the third-order coding rate in the asymptotic scenario. Moreover, the derived bound directly leads to asymptotic achievability results in the large deviation, small deviation, and moderate deviation regimes in a unified manner.The full version of the manuscript can be found at [arXiv:2208.02132] [1].