Lindbladian耗散的最优容忍测试
Optimal Tolerant Testing of Lindbladian Dissipation
- University of Edinburgh（爱丁堡大学）
- Stanford University（斯坦福大学）
- University of Copenhagen（哥本哈根大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究提出一种最优容忍测试算法，用于在给定容差阈值下区分Lindblad耗散强度，通过无记忆前向演化访问，在最优时间内完成，并扩展至更广泛的实验场景。
AI中文摘要：
量化耗散对于控制量子噪声和表征开放系统动力学至关重要。在实际实验环境中，尽管努力抑制残余噪声，但噪声可能仍然存在，因此确定耗散强度是否保持在规定的容差阈值内变得非常重要。我们针对一个未知的、时间无关的、具有有界强度的Lindblad生成器研究此问题，其中跳跃算子是局域的但允许无限制重叠，仅使用无记忆的前向演化访问。任务是区分耗散强度至多为$\varepsilon_1$与强度至少为$\varepsilon_2$的情况，其中$0 \leq \varepsilon_1 < \varepsilon_2$，以规范耗散子的归一化Frobenius范数度量。我们给出一个算法，在总演化时间$O(\varepsilon_2/(\varepsilon_2-\varepsilon_1)^2)$内解决此任务，适用于所有非平凡阈值，具有恒定成功概率，并提供匹配的下界$\Omega(\varepsilon_2/(\varepsilon_2-\varepsilon_1)^2)$，即使在自适应协议下也确立了最优性。这扩展了耗散测试到容忍设置，并消除了有界度的要求，使该框架适用于更广泛的实验相关场景。
英文摘要：
Quantifying dissipation is essential for controlling quantum noise and characterizing open-system dynamics. In practical experimental settings, residual noise may still persist despite efforts to suppress it, making it important to determine whether the dissipative strength remains within a prescribed tolerance threshold. We study this question for an unknown, time-independent Lindblad generator with bounded strength, where the jump operators are local but with unrestricted overlap, using only memoryless forward-evolution access. The task is to distinguish dissipative strength of at most $\varepsilon_1$ from strength of at least $\varepsilon_2$, for $0 \leq \varepsilon_1 < \varepsilon_2$, measured in the canonical dissipator's normalized Frobenius norm. We give an algorithm that solves this task in total evolution time $O(\varepsilon_2/(\varepsilon_2-\varepsilon_1)^2)$ for all nontrivial thresholds, with constant success probability, and provide a matching lower bound $Ω(\varepsilon_2/(\varepsilon_2-\varepsilon_1)^2)$ that establishes optimality even for adaptive protocols. This extends dissipation testing to the tolerant setting and eliminates the bounded-degree requirement, making the framework applicable to a broader range of experimentally relevant settings.
