发表机构
The University of Tokyo; RIKEN Center for Quantum Computing (RQC); The Chinese University of Hong Kong, Shenzhen; International Quantum Academy; Nagoya University; National Taiwan University; National Center for Theoretical Sciences, Taiwan; Hon Hai (Foxconn) Quantum Computing Center（东京大学; 理化学研究所量子计算中心; 香港中文大学（深圳）; 国际量子学院; 名古屋大学; 台湾大学; 台湾理论科学中心; 鸿海（富士康）量子计算中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究表明，经典-量子信道中普适编码无法达到已知信道的最优可靠性，其最优普适可靠性由夹逼Rényi散度刻画，揭示了普适性的可靠性代价。
AI 中文摘要
普适信道编码使得在没有信道完整描述的情况下也能进行通信。对于经典信道，普适编码能够同时达到容量和最优的高速率可靠性。我们证明，这种兼容性在经典-量子信道中一般是不成立的；也就是说，由于对输出系统酉旋转的无知，在已知信道情形下的最优可靠性并不总能通过普适编码实现。我们展示了一族经典-量子信道，对于这些信道，任何固定的编码方案都无法达到已知信道情形下的最优可靠性。我们进一步推导了酉不变解码器（这是普适编码方案的一个自然假设）的可靠性逆界，该界可以严格小于最优的已知信道误差指数。相反，我们构造了一个与信道无关的编码器-解码器对，并建立了在高速率区域与该逆界匹配的普适可达可靠性界，从而刻画了最优普适可靠性。具体而言，已知信道和普适指数分别由Petz和夹逼Rényi散度控制。这些散度对于交换输出是一致的，但对于非交换输出则不同，这解释了为什么普适性在经典情形下保持最优可靠性但在量子情形下会降低可靠性。我们的结果展示了以普适方式执行经典-量子信道编码任务的根本可靠性代价。
英文摘要
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.
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