在李普布朗动力学中最优检测耗散
Optimal detection of dissipation in Lindbladian dynamics
AI总结：
研究通过随机算法检测量子系统中耗散噪声的存在，利用总演化时间O(ε⁻¹)实现信息论最优的耗散检测。
AI中文摘要：
实验实现哈密顿动力学时，往往受到环境相互作用引起的耗散噪声影响。本文考虑以下决策问题：给定对未知时间不变李普布朗生成元生成的时间演化通道$e^{t\mathcal{L}}$的黑盒访问，确定动力学是否纯哈密顿或包含至少幅度为ε的耗散（以归一化弗罗贝尼乌斯范数衡量）。我们给出一种随机程序，使用总演化时间$\mathcal{O}(ε^{-1})$解决此任务，该保证在李普布朗生成元强度有界且其耗散部分具有常数局部性且度数有界的情况下成立。本文提供了一种实用方法，用于检测实验实现的量子动力学中的耗散噪声。
英文摘要：
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.
