发表机构
Simula UiB; Department of Informatics, University of Bergen（Simula UiB; 卑尔根大学信息系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于谱的量子态区分逆界，用于有限块长经典-量子信道编码，在低噪声下优于现有逆界，并应用于振幅阻尼信道二元码。
AI 中文摘要
我们研究了有限块长经典-量子信道编码中平均解码错误概率的逆界。首先，我们基于成对迹距离提出了多重量子假设检验的下界，并推导了相应的保真度界。随后，我们获得了一个仅依赖于先验概率和态谱的基于谱的逆界。我们证明，在适当条件下，该逆界对量子退极化信道保持紧致。对于乘积态输出的码，该逆界具有涉及输出态特征值乘积的显式形式。我们将其应用于使用输入态 $\vert+\rangle$ 和 $\vert-\rangle$ 的量子振幅阻尼信道上的二元码。对于该设置，我们还讨论了在大块长区域内基于谱的逆界的正态近似。在所有考虑的数值示例中，在低噪声水平下，基于谱的逆界比其他逆界更紧。
英文摘要
We investigate converse bounds on the average decoding error probability in finite-blocklength classical-quantum channel coding. We first present a lower bound for multiple quantum hypothesis testing in terms of pairwise trace distances and derive a corresponding fidelity bound. We then obtain a spectrum-based converse that depends only on the a priori probabilities and spectra of the states. We show that the converse bound remains tight for the quantum depolarizing channel under suitable conditions. For codes with product-state outputs, this converse takes an explicit form involving products of output-state eigenvalues. We apply it to binary codes over the quantum amplitude damping channel using the input states $\vert+\rangle$ and $\vert-\rangle$. For this setting, we also discuss a normal approximation to the spectrum-based converse in the large blocklength regime. In all numerical examples considered, the spectrum-based converse is tighter than the other converse bounds at low noise levels.
