发表机构
National University of Singapore; Nanyang Technological University; University of Maryland; Joint Quantum Institute, NIST/University of Maryland; Joint Center for Quantum Information and Computer Science, NIST/University of Maryland（新加坡国立大学; 南洋理工大学; 马里兰大学; 美国国家标准与技术研究院/马里兰大学联合量子研究所; 美国国家标准与技术研究院/马里兰大学联合量子信息与计算科学中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对序贯量子传感提出MSE下界，以SDP形式推广Nagaoka-Hayashi界，并给出紧性证明及局部最优策略构造，应用于纠错传感、多参数估计等场景。
AI 中文摘要
估计量子信道参数的最一般策略是借助相干辅助系统多次序贯地探测该信道。然而，找到使均方误差（MSE）最小化的策略是一个公认的难题，需要对初始探测态、中间演化、最终测量以及经典后处理进行优化。在本工作中，我们研究了在此设定下最小可达MSE如何从下方进行界定。我们提出了一个适用于任何物理可实现序贯传感策略的MSE下界，该下界适用于估计任何物理量子演化的参数，包括在时间相关噪声下跨多个时间步探测的量子信道以及一般的时间相关量子过程。我们证明该下界可以表述为半定规划（SDP）。我们的界将Nagaoka-Hayashi下界（适用于具有可分离测量的参数估计任务）推广到量子信道可被多次序贯访问的情形。对于存在最优策略的正则有限维单参数序贯估计任务，我们证明我们的SDP界是紧的，并提供了一种从SDP优化器获得局部最优策略的程序。利用我们的优化界，我们计算了MSE下界，并为其他几个物理动机问题推导了新协议，包括在未知相关噪声模型下的纠错量子传感、多参数估计以及使用qudit系统的估计。
英文摘要
The most general strategy for estimating parameters of a quantum channel is to probe the channel many times sequentially with the help of coherent ancillary systems. However, finding the strategy that minimizes the mean-squared error (MSE) is a notoriously hard problem, requiring optimization over the initial probe state, intermediate evolutions, final measurement, and classical postprocessing. In this work, we study how the minimum attainable MSE can be bounded from below in this setting. We propose a lower bound for the MSE of any physically implementable sequential sensing strategy that applies to estimating parameters of any physical quantum evolution, including quantum channels probed over multiple time steps under temporally correlated noise and general temporally correlated quantum processes. We show that this lower bound can be formulated as a semidefinite program (SDP). Our bound generalizes the Nagaoka-Hayashi lower bound (that applies to parameter estimation tasks with separable measurements) to the regime where the quantum channel can be accessed sequentially multiple times. For regular finite-dimensional single-parameter sequential estimation tasks admitting an optimal strategy, we show that our SDP bound is tight and provide a procedure to obtain a locally optimal strategy from the SDP optimizer. Using our optimization bound, we compute the MSE lower bound and derive new protocols for several other physically motivated problems including error-corrected quantum sensing under an unknown correlated noise model, multiparameter estimation, and estimation with qudit systems.
Comments62 pages, 10 figures
