Optimal Tolerant Testing of Lindbladian Dissipation

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.

Source: arXiv:2609.38160v1 - http://arxiv.org/abs/2609.38160v1 PDF: https://arxiv.org/pdf/2609.38160v1 Original Link: http://arxiv.org/abs/2609.38160v1