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arXiv:2111.12279 · Advanced Quantum Technologies

Optimal Scheme for Quantum Metrology

Jing Liu, Zhang Mao, Hongzhen Chen, Lingna Wang, Haidong Yuan

Published Nov 23, 2021• 80 citations
arXivHTMLPDF

Abstract

Abstract Quantum metrology can achieve far better precision than classical metrology, and is one of the most important applications of quantum technologies in the real world. To attain the highest precision promised by quantum metrology, all steps of the schemes need to be optimized, which include the state preparation, parametrization, and measurement. Here the recent progresses on the optimization of these steps, which are essential for the identification and achievement of the ultimate precision limit in quantum metrology, are reviewed. It is hoped this provides a useful reference for the researchers in quantum metrology and related fields.

DOI
10.1002/qute.202100080

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Abstract Quantum metrology can achieve far better precision than classical metrology, and is one of the most important applications of quantum technologies in the real world. To attain the highest precision promised by quantum metrology, all steps of the schemes need to be optimized, which include the state preparation, parametrization, and measurement. Here the recent progresses on the optimization of these steps, which are essential for the identification and achievement of the ultimate precision limit in quantum metrology, are reviewed. It is hoped this provides a useful reference for the researchers in quantum metrology and related fields.
Quantum metrology holds the promise of improving the measurement precision beyond the limit of classical approaches. To achieve such enhancement in performance requires the development of quantum estimation theories as well as novel experimental techniques. In this article, we provide a brief review of some recent results in the field of quantum metrology. We emphasize that the unambiguous demonstration of the quantum-enhanced precision needs a careful analysis of the resources involved. In particular, the implementation of quantum metrology in practice requires us to take into account the experimental imperfections included, for example, particle loss and dephasing noise. For a detailed introduction to the experimental demonstrations of quantum metrology, we refer the reader to another article ‘Quantum metrology’ in the same issue.
Recent years have witnessed a growing interest in understating the limitations imposed by quantum noise in precision measurements and devising techniques to reduce it. The attention is currently turning to the simultaneously estimation of several parameters of interest, driven by its promising potential across a wide range of sensing applications as well as fueled by experimental progress in various optical and atomic platforms. Here, we provide a comprehensive overview of key research directions in multiparameter quantum sensing and metrology, highlighting both opportunities and challenges. We introduce the basic framework, discuss ultimate sensitivity bounds, optimal measurement strategies, and the role of quantum incompatibility, showing important differences with respect to single-parameter estimation. Additionally, we discuss emerging experimental implementations in distributed quantum sensing, including cutting-edge optimization techniques. This review aims to bridge the gap between theory and experiments, paving the way for the next-generation of quantum sensors and their integration with other quantum technologies.
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It can be said that all of humanity's efforts can be understood as a problem of optimization. We each have a natural sense of what is ``good'' or ``bad'' and thus our actions tend towards maximizing -- or optimizing -- some notion of good and minimizing those things we perceive as bad or undesirable. Within the sciences, the greatest form of good is knowledge. It is this pursuit of knowledge that leads to not only life-saving innovations and technology, but also to furthering our understanding of our natural world and driving our philosophical pursuits. The principle method of obtaining knowledge in the sciences is by performing measurements; the simple act of comparing one attribute of a system to a known standard and recording the observed value is how all scientific progress is made. The act of performing measurements is in fact so important that there is an entire field of study surrounding it: metrology. One critical component of metrology is the development of new techniques to perform measurements, or alternative measurement schemes that are more optimal in some way. This is where there is room to exploit quantum physics to improve our techniques \--- we can perform quantum metrology. In quantum mechanics we routinely deal with the smallest, weakest, most delicate of systems. Quantum properties are inherently very sensitive to their environment; this of course makes them highly intolerant of noise but also makes them great resources to perform sensitive measurements. Quantum metrology concerns itself with utilizing quantum phenomena to extract more information from the natural world than is possible by conventional, or classical, means. To perform optimal measurements, these quantum systems must of course be optimal by some metric. Performing the ``optimal'' measurement requires several ingredients. First, we need the optimal tools or instrumentation. In quantum mechanical language, this means we need the optimal probe state. Then, we need to optimize the interaction of our instrumentation with the system we which to interrogate so that we can extract the desired information. This translates to needing the best possible interaction between the probe state and the system in question -- in other words, we need to optimize the evolution of the probe. Finally, we must take care to extract the most information as possible at the output; we must not neglect any information present in the evolved probe state. The entire quantum metrology process can be summarized as thus: probe
A pivotal task in quantum metrology, and quantum parameter estimation in general, is to design schemes that achieve the highest precision with the given resources. Standard models of quantum metrology usually assume that the dynamics is fixed and that the highest precision is achieved by preparing the optimal probe states and performing optimal measurements. However, in many practical experimental settings, additional controls are usually available to alter the dynamics. Here we propose to use optimal control methods for further improvement of the precision limit of quantum parameter estimation. We show that, by exploring the additional degree of freedom offered by the controls, a higher-precision limit can be achieved. In particular, we show that the precision limit under the controlled schemes can go beyond the constraints put by the coherent time, which is in contrast with the standard scheme where the precision limit is always bounded by the coherent time.