Experimental implementations of Hamiltonian dynamics are often affected by dissipative noise arising from interactions with the environment. This raises the question of whether one can detect the presence or absence of such dissipation using only access to the observed time evolution of the system. We consider the following decision problem: given black-box access to the time-evolution channels $e^{t\mathcal{L}}$ generated by an unknown time-independent Lindbladian $\mathcal{L}$, determine whether the dynamics are purely Hamiltonian or contain dissipation of magnitude at least $ε$ in normalized Frobenius norm. We give a randomized procedure that solves this task using total evolution time $\mathcal{O}(ε^{-1})$, which is information-theoretically optimal. This guarantee holds under the assumptions that the Lindblad generator has bounded strength and its dissipative part is of constant locality with bounded degree. Our work provides a practical method for detecting dissipative noise in experimentally implemented quantum dynamics.

翻译：哈密顿动力学的实验实现常常受到环境相互作用产生的耗散噪声的影响。这提出了一个问题：是否仅通过观测系统的时间演化就能检测这种耗散的存在与否。我们考虑以下判定问题：给定未知时不变林德布拉德算子 $ \mathcal{L} $ 生成的时间演化通道 $ e^{t\mathcal{L}} $ 的黑盒访问，确定动力学是纯哈密顿型的，还是包含归一化Frobenius范数下至少 $ \varepsilon $ 量级的耗散。我们给出一个随机化程序，利用总演化时间 $ \mathcal{O}(\varepsilon^{-1}) $ 解决此任务，这在信息论意义上是最优的。该保证在以下假设下成立：林德布拉德生成元具有有界强度，且其耗散部分具有常数局域性和有界度。我们的工作为实验实现的量子动力学中检测耗散噪声提供了一种实用方法。