Universality reduces reliability in classical quantum communication channels
Universality Sacrifices Reliability in Classical-Quantum Channel Coding
Information Theory
Summary
Sending messages through unknown communication channels is common, and classical coding methods can handle this well while keeping reliability high. This paper shows that for channels involving quantum outputs, such universal methods cannot always reach the best possible reliability. The reason is that ignorance about how quantum outputs might be rotated interferes with decoding. The authors identify precise mathematical limits and construct coding schemes that achieve the best possible reliability allowed without detailed channel knowledge.
What this means in practice
- •For quantum communication engineers: Design error-correcting codes for quantum communication systems that optimally balance reliability and universality when channel details are unknown.
- •For network protocol designers: Develop general-purpose protocols for classical-quantum channels that account for reliability trade-offs caused by unknown quantum output variations.
A theory result. No direct application yet.
Authors
Kaito Watanabe, Masahito Hayashi, Takaya Matsuura, Hao-Chung Cheng
Abstract
Universal channel coding enables communication without a complete description of the channel. For classical channels, universal codes can attain both capacity and the optimal high-rate reliability. We show that this compatibility fails for classical-quantum channels in general; that is, the optimal reliability in the channel-aware scenario is not always achievable with universal coding due to the ignorance of the unitary rotation of the output system. We exhibit a family of classical-quantum channels for which one cannot achieve the channel-aware optimal reliability by a fixed coding scheme. We further derive a converse bound on the reliability for unitary-invariant decoders, a natural assumption for the universal coding scheme, that can be strictly smaller than the optimal channel-aware error exponent. Conversely, we construct a channel-independent encoder-decoder pair and establish a universally achievable bound on the reliability that matches this converse bound in the high-rate regime, thereby characterizing the optimal universal reliability. Specifically, the channel-aware and universal exponents are governed by the Petz and sandwiched Rényi divergences, respectively. These divergences coincide for commuting outputs but differ for noncommuting ones, explaining why universality preserves optimal reliability classically but can reduce it quantumly. Our results showcase the fundamental reliability cost of performing the classical-quantum channel coding task universally.