Optimal Tolerant Testing of Lindbladian Dissipation
Abstract
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 ε1 from strength of at least ε2, for 0 ≤ ε1 < ε2, measured in the canonical dissipator's normalized Frobenius norm. We give an algorithm that solves this task in total evolution time O(ε2/(ε2−ε1)2) for all nontrivial thresholds, with constant success probability, and provide a matching lower bound Ω(ε2/(ε2−ε1)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.
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BibTeX
@misc{bao2026optimal,
title = {{Optimal Tolerant Testing of Lindbladian Dissipation}},
author = {Jinge Bao and Yiyi Cai and Zhong-Xia Shang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38160},
eprint = {2609.38160},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38160},
}
RIS
TY - UNPB
TI - Optimal Tolerant Testing of Lindbladian Dissipation
AU - Jinge Bao
AU - Yiyi Cai
AU - Zhong-Xia Shang
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.38160
UR - https://arxiv.org/abs/2609.38160
AB - 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 ε_1 from strength of at least ε_2, for 0 ≤ ε_1 < ε_2, measured in the canonical dissipator's normalized Frobenius norm. We give an algorithm that solves this task in total evolution time O(ε_2/(ε_2−ε_1)^2) for all nontrivial thresholds, with constant success probability, and provide a matching lower bound Ω(ε_2/(ε_2−ε_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.
ER -