arXiv:2504.12989quant-phcs.IT2025-04被引 8

量化了区分量子信道所需的最少调用次数,揭示其与错误率和信道相似度的关系。

Query Complexity of Classical and Quantum Channel Discrimination

  • 通过信道保真度和散度分析,建立二元信道区分的查询复杂度模型。
  • 在固定错误率下,查询次数与错误概率的对数成正比,与信道差异的对数成反比。
  • 结果适用于经典、经典-量子及多信道场景,适合量子信息与统计推断研究者。

量子信道区分问题从信息论角度研究错误概率随未知信道调用次数的最优衰减率。本文研究量子信道区分的查询复杂度,即达到指定错误概率所需的最少信道调用次数。我们证明,二元信道区分的查询复杂度关于错误概率的倒数呈对数依赖,且与几何和Holevo信道保真度的负对数成反比。作为特例,精确刻画了两个经典信道和两个经典-量子信道区分的查询复杂度。通过获得包含先验概率的量子假设检验样本复杂度最优表征,进一步精确描述了错误概率不超过固定阈值时的查询复杂度。此外,我们给出了非对称二元信道区分和多量子信道区分的上下界:前者依赖于几何Rényi和Petz Rényi信道散度,后者依赖于几何和Uhlmann信道保真度的负对数;多信道区分的上界随信道数量的对数增长。

原文摘要 · Abstract (English)

Quantum channel discrimination has been studied from an information-theoretic perspective, wherein one is interested in the optimal decay rate of error probabilities as a function of the number of unknown channel accesses. In this paper, we study the query complexity of quantum channel discrimination, wherein the goal is to determine the minimum number of channel uses needed to reach a desired error probability. To this end, we show that the query complexity of binary channel discrimination depends logarithmically on the inverse error probability and inversely on the negative logarithm of the (geometric and Holevo) channel fidelity. As a special case of these findings, we precisely characterize the query complexity of discriminating two classical channels and two classical-quantum channels. Furthermore, by obtaining an optimal characterization of the sample complexity of quantum hypothesis testing, including prior probabilities, we provide a more precise characterization of query complexity when the error probability does not exceed a fixed threshold. We also provide lower and upper bounds on the query complexity of binary asymmetric channel discrimination and multiple quantum channel discrimination. For the former, the query complexity depends on the geometric Rényi and Petz Rényi channel divergences, while for the latter, it depends on the negative logarithm of the (geometric and Uhlmann) channel fidelity. For multiple channel discrimination, the upper bound scales as the logarithm of the number of channels.

量子信息信道区分查询复杂度假设检验

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