Fully-Optimized Quantum Metrology: Framework, Tools, and Applications

IF 4.4 Q1 OPTICS
Qiushi Liu, Zihao Hu, Haidong Yuan, Yuxiang Yang
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Abstract

This tutorial introduces a systematic approach for addressing the key question of quantum metrology: For a generic task of sensing an unknown parameter, what is the ultimate precision given a constrained set of admissible strategies. The approach outputs the maximal attainable precision (in terms of the maximum of quantum Fisher information) as a semidefinite program and optimal strategies as feasible solutions thereof. Remarkably, the approach can identify the optimal precision for different sets of strategies, including parallel, sequential, quantum SWITCH-enhanced, causally superposed, and generic indefinite-causal-order strategies. The tutorial consists of a pedagogic introduction to the background and mathematical tools of optimal quantum metrology, a detailed derivation of the main approach, and various concrete examples. As shown in the tutorial, applications of the approach include, but are not limited to, strict hierarchy of strategies in noisy quantum metrology, memory effect in non-Markovian metrology, and designing optimal strategies. Compared with traditional approaches, the approach here yields the exact value of the optimal precision, offering more accurate criteria for experiments and practical applications. It also allows for the comparison between conventional strategies and the recently discovered causally-indefinite strategies, serving as a powerful tool for exploring this new area of quantum metrology.

Abstract Image

全优化量子计量学:框架、工具和应用
本教程介绍了一种解决量子计量学关键问题的系统方法:对于感知未知参数的一般任务,在一组受限的可接受策略下,最终精度是多少。该方法将最大可实现精度(量子费雪信息的最大值)输出为一个半定式程序,并将最优策略输出为其可行解。值得注意的是,该方法可以确定不同策略集的最佳精度,包括并行、顺序、量子 SWITCH 增强、因果叠加和通用不定因果阶策略。教程包括最优量子计量学背景和数学工具的教学介绍、主要方法的详细推导以及各种具体示例。如教程所示,该方法的应用包括但不限于噪声量子计量学中的严格策略层次、非马尔可夫计量学中的记忆效应以及设计最优策略。与传统方法相比,该方法能得出最佳精度的精确值,为实验和实际应用提供更准确的标准。它还可以将传统策略与最近发现的因果无限策略进行比较,是探索量子计量学这一新领域的有力工具。
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CiteScore
7.90
自引率
0.00%
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