Adaptivity is not helpful for Pauli channel learning

IF 5.1 2区 物理与天体物理 Q1 PHYSICS, MULTIDISCIPLINARY
Quantum Pub Date : 2025-09-24 DOI:10.22331/q-2025-09-24-1864
Xuan Du Trinh, Nengkun Yu
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引用次数: 0

Abstract

We prove that adaptive strategies offer no advantage over non-adaptive ones for learning and testing Pauli channels using entangled inputs. This key observation allows us to characterize the query complexity for several fundamental tasks by translating optimal classical estimation algorithms into the quantum setting. First, we determine the tight query complexity for learning a Pauli channel under the general $\ell_p$ norm, providing results that improve upon or match the best-known bounds for the $\ell_1, \ell_2,$ and $\ell_\infty$ distances. Second, we resolve the complexity of testing whether a Pauli channel is a white noise source. Finally, we show that the optimal query complexities for estimating the Shannon entropy and support size of the channel's error distribution, and for estimating the diamond distance between two Pauli channels, are all $\Theta\left(\tfrac{4^n}{n\epsilon^2}\right)$.
自适应对泡利通道学习没有帮助
我们证明了自适应策略在使用纠缠输入学习和测试泡利通道方面没有比非自适应策略更有优势。通过将最优的经典估计算法转换为量子设置,这一关键观察使我们能够表征几个基本任务的查询复杂性。首先,我们确定在一般$\ell_p$范数下学习泡利通道的严格查询复杂度,提供改进或匹配最著名的$\ell_1, \ell_2,$和$\ell_\infty$距离界限的结果。其次,我们解决了测试泡利信道是否为白噪声源的复杂性。最后,我们证明了用于估计香农熵和通道误差分布的支持大小以及用于估计两个泡利通道之间的钻石距离的最佳查询复杂性都是$\Theta\left(\tfrac{4^n}{n\epsilon^2}\right)$。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Quantum
Quantum Physics and Astronomy-Physics and Astronomy (miscellaneous)
CiteScore
9.20
自引率
10.90%
发文量
241
审稿时长
16 weeks
期刊介绍: Quantum is an open-access peer-reviewed journal for quantum science and related fields. Quantum is non-profit and community-run: an effort by researchers and for researchers to make science more open and publishing more transparent and efficient.
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