arXiv:2503.22823quant-phcs.IT2025-03被引 6

量子杜布林系数为量子信道收缩提供可高效计算的上界,助力多个量子信息任务分析。

Quantum Doeblin Coefficients: Interpretations and Applications

  • 定义新量子杜布林系数,具备可乘性与高效计算特性。
  • 揭示其在态排除任务中的错误概率比例关系,具物理直观意义。
  • 适用于量子机器学习、误差缓解等场景,优于已有研究且通用性强。

在经典信息论中,杜布林系数为经典信道提供总变差收缩系数的高效可计算上界,形成强数据处理不等式。本文研究量子杜布林系数作为经典概念的推广,提出多种新定义,其中一种具备连接性与可乘性,并可高效计算。我们发展了两个量子杜布林系数的多重解释:包括最小单态份额、排除值、反向最大互信息与反向鲁棒性等。尤其值得注意的是,它们可解释为有/无纠缠辅助下的态排除任务最优错误概率比例,具有明确物理意义。此外,本文概述了多项应用:包括参数化量子电路的噪声诱导平谷现象限制、误差缓解协议、含噪量子假设检验的样本复杂度,以及随时间变化信道的混合、可区分性与去关联时间。所有应用均基于量子杜布林系数对各类迹距离收缩系数的上界作用,且相比前人工作,在通用性与计算效率上均有提升。

原文摘要 · Abstract (English)

In classical information theory, the Doeblin coefficient of a classical channel provides an efficiently computable upper bound on the total-variation contraction coefficient of the channel, leading to what is known as a strong data-processing inequality. Here, we investigate quantum Doeblin coefficients as a generalization of the classical concept. In particular, we define various new quantum Doeblin coefficients, one of which has several desirable properties, including concatenation and multiplicativity, in addition to being efficiently computable. We also develop various interpretations of two of the quantum Doeblin coefficients, including representations as minimal singlet fractions, exclusion values, reverse max-mutual and oveloH informations, reverse robustnesses, and hypothesis testing reverse mutual and oveloH informations. Our interpretations of quantum Doeblin coefficients as either entanglement-assisted or unassisted exclusion values are particularly appealing, indicating that they are proportional to the best possible error probabilities one could achieve in state-exclusion tasks by making use of the channel. We also outline various applications of quantum Doeblin coefficients, ranging from limitations on quantum machine learning algorithms that use parameterized quantum circuits (noise-induced barren plateaus), on error mitigation protocols, on the sample complexity of noisy quantum hypothesis testing, and on mixing, distinguishability, and decoupling times of time-varying channels. All of these applications make use of the fact that quantum Doeblin coefficients appear in upper bounds on various trace-distance contraction coefficients of a channel. Furthermore, in all of these applications, our analysis using Doeblin coefficients provides improvements of various kinds over contributions from prior literature, both in terms of generality and being efficiently computable.

量子信息信道分析可计算性应用广度

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