Quantum metrology holds the promise of an early practical application of quantum technologies, in which measurements of physical quantities can be made with much greater precision than what is achievable with classical technologies. In this Review, the authors collect some of the key theoretical results in quantum parameter estimation by presenting the theory for the quantum estimation of a single parameter, multiple parameters, and optical estimation using Gaussian states. The authors give an overview of results in areas of current research interest, such as Bayesian quantum estimation, noisy quantum metrology, and distributed quantum sensing. The authors address the question of how minimum measurement errors can be achieved using entanglement as well as more general quantum states. This review is presented from a geometric perspective. This has the advantage that it unifies a wide variety of estimation procedures and strategies, thus providing a more intuitive big picture of quantum parameter estimation.
Quantum metrology holds the promise of an early practical application of quantum technologies, in which measurements of physical quantities can be made with much greater precision than what is achievable with classical technologies. In this Review, the authors collect some of the key theoretical results in quantum parameter estimation by presenting the theory for the quantum estimation of a single parameter, multiple parameters, and optical estimation using Gaussian states. The authors give an overview of results in areas of current research interest, such as Bayesian quantum estimation, noisy quantum metrology, and distributed quantum sensing. The authors address the question of how minimum measurement errors can be achieved using entanglement as well as more general quantum states. This review is presented from a geometric perspective. This has the advantage that it unifies a wide variety of estimation procedures and strategies, thus providing a more intuitive big picture of quantum parameter estimation.
Quantum metrology holds the promise of an early practical application of quantum technologies, in which measurements of physical quantities can be made with much greater precision than what is achievable with classical technologies. In this Review, the authors collect some of the key theoretical results in quantum parameter estimation by presenting the theory for the quantum estimation of a single parameter, multiple parameters, and optical estimation using Gaussian states. The authors give an overview of results in areas of current research interest, such as Bayesian quantum estimation, noisy quantum metrology, and distributed quantum sensing. The authors address the question of how minimum measurement errors can be achieved using entanglement as well as more general quantum states. This review is presented from a geometric perspective. This has the advantage that it unifies a wide variety of estimation procedures and strategies, thus providing a more intuitive big picture of quantum parameter estimation.
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.
We present a review on quantum metrology and sensing, from its foundations to current applications. Highlights of the review include consideration of both frequentist and Bayesian approaches to parameter estimation; single as well as multiparameter estimation; estimation for different encoding processes comprising unitary as well as noisy channels, quantum thermometry, and channels involving indefinite causal order; different estimation strategies incorporating also recent advances like quantum error correction-aided methods and reservoir engineering; usefulness of quantum Fisher information to detect resources; applications of quantum metrology in diverse arenas covering quantum many-body sensors, sensing protocols in atomic ensembles, atom-photon systems, and continuous-variable systems, quantum imaging, quantum illumination, atomic clocks and atom interferometry, etc; and experimental realizations of quantum sensors in different physical platforms.
Quantum metrology is one of the most promising applications of quantum technologies. The aim of this research field is the estimation of unknown parameters exploiting quantum resources, whose application can lead to enhanced performances with respect to classical strategies. Several physical quantum systems can be employed to develop quantum sensors, and photonic systems represent ideal probes for a large number of metrological tasks. Here, the authors review the basic concepts behind quantum metrology and then focus on the application of photonic technology for this task, with particular attention to phase estimation. The authors describe the current state of the art in the field in terms of platforms and quantum resources. Furthermore, the authors present the research area of multiparameter quantum metrology, where multiple parameters have to be estimated at the same time. The authors conclude by discussing the current experimental and theoretical challenges and the open questions toward implementation of photonic quantum sensors with quantum-enhanced performances in the presence of noise.
The statistical error is ineluctable in any measurement. Quantum techniques, especially with the development of quantum information, can help us squeeze the statistical error and enhance the precision of measurement. In a quantum system, there are some quantum parameters, such as the quantum state, quantum operator, and quantum dimension, which have no classical counterparts. So quantum metrology deals with not only the traditional parameters, but also the quantum parameters. Quantum metrology includes two important parts: measuring the physical parameters with a precision beating the classical physics limit and measuring the quantum parameters precisely. In this review, we will introduce how quantum characters (e.g., squeezed state and quantum entanglement) yield a higher precision, what the research areas are scientists most interesting in, and what the development status of quantum metrology and its perspectives are.
Precise measurement of physical quantities plays a crucial role in the development of science and technology.The main purpose of the dissertation is two-fold: to investigate the ultimate precision for estimation of physical quantities using Gaussian states and to propose an efficient method for certification of Bayesian error region in general quantum parameter estimation.In the first part, we begin with analyzing sensitivity for estimating a phase difference in an optical interferometer.Optical interferometry is widely used in science and industry for measuring small displacements.Recently, a large-scale optical interferometer socalled the Laser interferometer Gravitational-Wave Observatory (LIGO) has succeeded in detecting a gravitational wave, the signal of which is extremely small.On the other hand, it has been shown that a non-classical feature of quantum states can improve the sensitivity of estimation, such as in optical interferometer, including the LIGO.From a practical point of view, we inspect the practically achievable precision using non-classical Gaussian states in Mach-Zehnder interferometer with feasible measurements and realistic photon loss.We then investigate the precision of single-mode phase estimation using Gaussian measurement, which can be realized by using homodyne detection, and i show that non-Gaussian measurement is necessary to utilize the power of Gaussian input probes optimally.Finally, we find the optimal measurement for general Gaussian quantum metrology and identify three distinct optimal measurements corresponding to different circumstances.In the second part, we study the Bayesian error region, which is a crucial concept for a general estimation process.When estimating a physical quantity, one has to supply the error interval (single-parameter) or error region (multi-parameter) as well as the estimate.However, it has been shown that as the dimension of quantum systems of interest grows, it becomes intractable to calculate the size and credibility of Bayesian error regions.As an alternative, we derive an analytical expression for the properties, the size and credibility, of Bayesian error regions, in an asymptotic regime.We then propose an efficient numerical method to calculate them for high-dimensional quantum systems even in a non-asymptotic regime.