Abstract Weak value amplification is crucial in quantum metrology because it enhances the detection of subtle interactions between quantum entities. However, current weak value quantum metrology techniques are only effective for extremely weak interactions, significantly narrowing its range of potential applications. In this work, we present the ‘metrological weak value (MWV)’, designed for use with quantum interactions of any strengths, making it unnecessary to have prior knowledge of how strong or weak a quantum interaction might be. Additionally, we demonstrate an adaptive estimation scheme for weak value quantum metrology tailored for gauging an undetermined interaction strength. This scheme, rooted in MWV measurements, aligns perfectly with the quantum Cramér–Rao lowest bound. The versatility and effectiveness of the MWV enables weak value quantum metrology beyond weak interactions, paving the way for precision in quantum measurement and broadening its utility across various quantum systems.
Abstract Weak value amplification is crucial in quantum metrology because it enhances the detection of subtle interactions between quantum entities. However, current weak value quantum metrology techniques are only effective for extremely weak interactions, significantly narrowing its range of potential applications. In this work, we present the ‘metrological weak value (MWV)’, designed for use with quantum interactions of any strengths, making it unnecessary to have prior knowledge of how strong or weak a quantum interaction might be. Additionally, we demonstrate an adaptive estimation scheme for weak value quantum metrology tailored for gauging an undetermined interaction strength. This scheme, rooted in MWV measurements, aligns perfectly with the quantum Cramér–Rao lowest bound. The versatility and effectiveness of the MWV enables weak value quantum metrology beyond weak interactions, paving the way for precision in quantum measurement and broadening its utility across various quantum systems.
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 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.
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.
Measurements are crucial in quantum mechanics, for fundamental research as well as for applicative fields like quantum metrology, quantum-enhanced measurements and other quantum technologies. In the recent years, weak-interaction-based protocols like Weak Measurements and Protective Measurements have been experimentally realized, showing peculiar features leading to surprising advantages in several different applications. In this work we analyze the validity range for such measurement protocols, that is, how the interaction strength affects the weak value extraction, by measuring different polarization weak values on heralded single photons. We show that, even in the weak interaction regime, the coupling intensity limits the range of weak values achievable, setting a threshold on the signal amplification effect exploited in many weak measurement based experiments.
Weak values and measurements have been proposed as a means to achieve dramatic enhancements in metrology based on the greatly increased range of possible measurement outcomes. Unfortunately, the very large values of measurement outcomes occur with highly suppressed probabilities. This raises three vital questions in weak-measurement-based metrology. Namely, (Q1) Does postselection enhance the measurement precision? (Q2) Does weak measurement offer better precision than strong measurement? (Q3) Is it possible to beat the standard quantum limit or to achieve the Heisenberg limit with weak measurement using only classical resources? We analyze these questions for two prototypical, and generic, measurement protocols and show that while the answers to the first two questions are negative for both protocols, the answer to the last is affirmative for measurements with phase-space interactions, and negative for configuration space interactions. Our results, particularly the ability of weak measurements to perform at par with strong measurements in some cases, are instructive for the design of weak-measurement-based protocols for quantum metrology.
Abstract Hamiltonian estimation is a cardinal task in applications of quantum metrology, quantum computation, quantum simulation, etc. When the evolution time is short in order to suppress noise and enhance sensitivity, the measurement and postprocessing may incur high cost. In this paper, we propose an adaptive weak measurement scheme for Hamiltonian estimation, which adjusts the pre- and post-selection according to the difference of the mean shift between two orthogonal post-selected states. According to the angle of the post-selected state, the proposed scheme can change from weak value amplification (WVA) to joint weak measurement (JWM). A study of the quantum Fisher information shows that the JWM situation is always optimal. Meanwhile, the WVA approach loses a little information but it can inherit the WVA’s technical advantages, which are suitable for short evolution times. The widely applicable scope of the proposed scheme makes us believe that it offers a new path for the understanding of unknown Hamiltonians.