[论文解读] Noise as a resource

Stefano Gherardini|arXiv (Cornell University)|May 4, 2018

Advanced Thermodynamics and Statistical Mechanics参考文献 202被引用 3

一句话总结

本博士论文提出了一种噪声的资源理论，证明了通过环境的随机相互作用可被利用以增强状态估计、量子输运效率及量子测量协议。通过利用大偏离理论与随机估计将噪声建模为可控参数，该研究表明噪声可优化系统响应，实现抗噪声传感，并揭示非平衡热力学特征，如熵产生与量子Zeno动力学。

ABSTRACT

In this thesis we aim to analyze and quantify the energetic and information contents that can be extracted from a dynamical system subject to the external environment. The latter is usually assumed to be deleterious for the feasibility of specific control tasks, since it can be responsible for uncontrolled time-dependent changes of the system. However, if the effects of the random interaction with a noisy environment are properly modeled by the introduction of a given stochasticity within the dynamics of the system, then even noise contributions might be seen as control knobs. As a matter of fact, even a partial knowledge of the environment can allow to set the system in a dynamical condition in which the response is optimized by the presence of noise sources. In particular, we have investigated what kind of measurement devices can work better in noisy dynamical regimes and studied how to maximize the resultant information via the adoption of estimation algorithms. Moreover, we have shown the optimal interplay between quantum dynamics, environmental noise and complex network topology in maximizing the energy transport efficiency. Then, foundational scientific aspects, such as the occurrence of an ergodic property for the system-environment interaction modes of a randomly perturbed quantum system or the characterization of the stochastic quantum Zeno phenomena, have been analyzed by using the predictions of the large deviation theory. Finally, the energy cost in maintaining the system in the non-equilibrium regime due to the presence of the environment is evaluated by reconstructing the corresponding thermodynamics entropy production. In conclusion, the present thesis can constitute the basis for an effective resource theory of noise, which is given by properly engineering the interaction between a dynamical system and its external environment.

研究动机与目标

• 将环境噪声从有害因素重新定义为动力系统中可控制的资源。
• 开发利用噪声以提升状态重构精度的估计框架，适用于二元传感器与随机测量。
• 通过调控噪声与网络拓扑结构，优化量子网络中的能量输运效率。
• 利用大偏离理论分析基础量子现象（如随机量子Zeno效应与遍历性）。
• 通过随机投影测量与熵产生量化非平衡动力学的热力学代价。

提出的方法

• 构建统一框架，整合开放量子系统、统计估计与统计力学。
• 应用大偏离理论分析重复测量中的存活概率与随机量子Zeno效应。
• 为具有约束条件的二元传感器数据开发移动时域估计（MHE）与最大后验概率（MAP）滤波。
• 提出一种快速MH-MAP滤波器，通过顺序采样与近似技术实现对大规模系统的高效状态估计。
• 采用随机投影测量协议推导量子热量统计与涨落定理。
• 利用特征函数与谱分解计算随机量子过程中费舍尔信息与熵产生。

实验结果

研究问题

• RQ1 能否系统性地设计噪声以提升噪声动力系统中状态估计的精度？
• RQ2 测量序列中的随机性如何影响量子Zeno动力学的出现？
• RQ3 环境噪声在复杂量子网络中提升能量输运效率方面起到何种作用？
• RQ4 能否利用大偏离理论观测并表征随机量子Zeno效应？
• RQ5 非平衡量子系统中，热力学不可逆性如何通过随机熵产生进行量化？

主要发现

• 噪声可被用作控制旋钮：最优噪声水平可提升状态估计精度与能量输运效率。
• 通过大偏离理论对随机量子Zeno效应进行了解析表征，表明频繁的随机测量可抑制系统演化。
• 快速MH-MAP滤波器在大规模系统中实现高效状态估计，具备稳定性与收敛性。
• 利用费舍尔信息可检测测量序列中的噪声相关性，从而实现抗噪声量子传感。
• 量子热量传输由投影测量中的随机等待时间引发，模型中已验证涨落定理。
• 在随机扰动的量子系统中，系统-环境相互作用模式的遍历性得以证明，支持统计可预测性。