Weak measurement refers to a type of quantum measurement that disturbs the system very little. In the framework of weak measurement, Aharonov, Albert, and Vaidman introduced the concept of postselection and thereby defined the weak value. In recent research, weak-value measurement (WVM) has offered a novel perspective for studying intricate problems in quantum mechanics, leading to many conceptual breakthroughs. More importantly in practice, WVM has shown an unprecedented impact on precision sensing. In this review, we begin by presenting the fundamental theory of WVM based on quantum parameter estimation, from which the effects of weak-value amplification and weak-coupling amplification can be derived. The two effects can significantly improve the precision in various sensing schemes based on WVM. We point out the technical advantages that enable the WVM schemes to outperform the conventional ones under the same measurement conditions. Notably, the capability of information compression is underscored, which is garnering increasing attention in the field of quantum metrology. This review aims to show the possibility for broadening the application of WVM to address more critical problems, and on the other hand, for leveraging its advantages to accomplish tasks that are currently unattainable, such that WVM could play a more important role in the future of precision sensing.
Weak measurement refers to a type of quantum measurement that disturbs the system very little. In the framework of weak measurement, Aharonov, Albert, and Vaidman introduced the concept of postselection and thereby defined the weak value. In recent research, weak-value measurement (WVM) has offered a novel perspective for studying intricate problems in quantum mechanics, leading to many conceptual breakthroughs. More importantly in practice, WVM has shown an unprecedented impact on precision sensing. In this review, we begin by presenting the fundamental theory of WVM based on quantum parameter estimation, from which the effects of weak-value amplification and weak-coupling amplification can be derived. The two effects can significantly improve the precision in various sensing schemes based on WVM. We point out the technical advantages that enable the WVM schemes to outperform the conventional ones under the same measurement conditions. Notably, the capability of information compression is underscored, which is garnering increasing attention in the field of quantum metrology. This review aims to show the possibility for broadening the application of WVM to address more critical problems, and on the other hand, for leveraging its advantages to accomplish tasks that are currently unattainable, such that WVM could play a more important role in the future of precision sensing.
ABSTRACT Weak measurement has emerged as a pivotal technique in precision metrology, utilizing unique amplification effects to enhance the capabilities of quantum sensing and quantum imaging. Quantum sensing can provide systems with unprecedented accuracy and sensitivity by utilizing its quantum properties. Quantum imaging uses entangled photon states to capture information, enabling signal‐to‐noise ratio and resolution that surpass the limits of classical imaging. The synergistic integration of weak measurement with quantum sensing and imaging paves the way for next‐generation technologies with practical value, significantly advancing frontiers of precision metrology and imaging science. This review elucidates the fundamental theory of weak value amplification and comprehensively discusses the performance of weak measurement strategies in quantum sensing and imaging frameworks, highlighting both classical techniques and emerging quantum applications. It covers four main directions: nanostructure, 2D atomic crystal, biochemistry, and optical imaging, including from structural parameters characterization to chemical reaction sensing to nonlocal weak measurement microscopy. This work aims to discuss recent advances in weak measurement applications for quantum sensing and imaging platforms, while outlining future development opportunities arising from the convergence of these three fields.
Recently, the weak-value amplification (WVA) has been extensively investigated as a promising quantum technique for improving an accuracy of a precision measurement.The basic idea of WVA comes from the weak measurement introduced by Aharonov, Albert, and Vaidman in 1988.The weak measurement is the indirect quantum measurement with the weak interaction and postselection of the final state of the measured system.The attention point is that we can measure the quantity called the weak value, which appears in the shift of the measuring probe given by the weak measurement.Because the weak value can be outside the range of the eigenvalues, the shift of the measuring probe obtained by the weak measurement becomes larger than the one given by the conventional measurement.This shift amplification effect by the weak value is the WVA, which has been studied for precisely measuring the small coupling constant.In this thesis, we propose the two possible applications of the WVA.First, we analytically obtain the optimal probe wave function for a given weak value by the variational method.It is shown that the amplification factor obtained by the optimal probe has noupper bound while the one in the Gaussian probe already reported by some researchers has the upper bound.Furthermore, the variance of the optimal probe after the measurement can be zero.We can derive the optimal probe by the Lagrange multiplier method for maximizing the shift of the probe position or minimizing the variance of the final distribution.Second we have developed the way which has a technical advantage of the WVA from the viewpoint of statistics.It is often argued that the WVA is not helpfull for the parameter estimation.Therefore we consider the statistical inferences that the WVA will be advantageous.We propose a method to determine whether the interaction is present or not and evaluate the capability of the WVA for this interaction detection problem by using the hypothesis testing in statistics.As the main result, it is shown that the merit of the WVA is the reduction of the possibility to miss the presence of the interaction more than the conventional measurement while keeping the probability of a misdetection, when the absolute value of the weak value is outside the range of the eigenvalues.In this discussion, we assume that the number of the obtained data is infinitely large and we neglect the data loss by the failure of the postseleciton.iii the deepest appreciation to my ex-supervisor
Weak Value Measurements (WVMs) with pre- and post-selected quantum mechanical ensembles were proposed by Aharonov, Albert, and Vaidman in 1988 and have found numerous applications in both theoretical and applied physics. In the field of precision metrology, WVM techniques have been demonstrated and proven valuable as a means to shift, amplify, and detect signals and to make precise measurements of small effects in both quantum and classical systems, including: particle spin, the Spin-Hall effect of light, optical beam deflections, frequency shifts, field gradients, and many others. In principal, WVM amplification techniques are also possible in radar and could be a valuable tool for precision measurements. However, relatively limited research has been done in this area. This article presents a quantum-inspired model of radar range and range-rate measurements of arbitrary strength, including standard and pre- and post-selected measurements. The model is used to extend WVM amplification theory to radar, with the receive filter performing the post-selection role. It is shown that the description of range and range-rate measurements based on the quantum-mechanical measurement model and formalism produces the same results as the conventional approach used in radar based on signal processing and filtering of the reflected signal at the radar receiver. Numerical simulation results using simple point scatterrer configurations are presented, applying the quantum-inspired model of radar range and range-rate measurements that occur in the weak measurement regime. Potential applications and benefits of the quantum inspired approach to radar measurements are presented, including improved range and Doppler measurement resolution.
The ability to manipulate light has allowed scientists to verify fundamental theories of physics and to develop a new generation of technologies that use photons as a primary resource. Recent developments in quantum measurement theory have offered new alternatives to approach some of the most remarkable problems in quantum physics. Consequently, the principles of quantum mechanics have been exploited in the development of quantum technologies such as optical metrology, quantum communication, and quantum information. In recent years, weak measurements and two of its most remarkable variants: weak value amplification and direct measurement, have been developed and are considered important resources for quantum applications. In this paper, we discuss weak measurements and some significant applications of weak values. We elaborate on how distinct forms of weak values are used to observe and amplify small effects or to directly measure the quantum wave function of photons, a crucial task for schemes for quantum communication and quantum information. We also review some of the most recent methods for weak value amplification and direct measurement that our group has developed.
Abstract Even though weak measurements and weak value amplification (WVA) are founded on the principles of quantum mechanics and quantum measurements, these have found widespread applications in optics due to their inherent origin in wave interference. Besides their use in addressing foundational questions of quantum mechanics or for resolving quantum paradoxes, weak measurements and WVA have thus been used for numerous metrological applications, e.g., quantification of small optical beam displacement, tiny angular rotation, determination of extremely small phase shifts, spectral shifts, unraveling weak fundamental optical effects, improved optical imaging, amplifying weak signal and extracting small physical parameters and so forth. In this review, after providing the mathematical foundation of weak measurement and WVA, some of the metrological applications of weak measurements in the classical optics domain are briefly summarized, and the controversies and debates on the potential advantages of WVA in the estimation and detection of weak signal are discussed, and the interferometric philosophy of WVA is elucidated. The experimental weak measurement and WVA schemes in the domain of quantum optics are also discussed and highlighted the new perspectives and emerging trends of weak measurements in both the classical and quantum optics domain and their prospects in the development of next‐generation ultra‐sensitive optical devices.
The weak-value (WV) measurement proposed by Aharonov, Albert, and Vaidman (AAV) has attracted a great deal of interest in connection with quantum metrology. In this paper, we extend the analysis beyond the AAV limit and obtain a few main results. (i) We obtain a nonperturbative result for the signal-to-noise ratio (SNR). In contrast to the AAV prediction, we find that the SNR asymptotically gets worse when the AAV WV Aw becomes large, i.e., in the case $g|{A}_{w}{|}^{2}\ensuremath{\gg}1$, where g is the measurement strength. (ii) With the increase of g (but also small), we find that the SNR is comparable to the result under the AAV limit, while both can reach---actually the former can slightly exceed---the SNR of the standard measurement. However, with a further increase of g, the WV technique will become less efficient than the standard measurement, despite the fact that the postselection probability is increased. (iii) We find that the Fisher information can characterize the estimate precision qualitatively well as the SNR, yet the difference will become more prominent with the increase of g. (iv) We carry out analytic expressions of the SNR in the presence of technical noises and illustrate the particular advantage of the imaginary WV measurement. The nonperturbative result of the SNR manifests a favorable range of the noise strength and allows an optimal determination.