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Noise affects the performance of quantum technologies, hence the importance of elaborating operative figures of merit that can capture its impact in exact terms. In quantum metrology, the introduction of the Fisher information measurement…
Measuring a weak force is an important task for micro-mechanical systems, both when using devices as sensitive detectors and, particularly, in experiments of quantum mechanics. The optimal strategy for resolving a weak stochastic signal…
Many imaging systems are used to estimate a vector of parameters associated with the object being imaged. In many cases there are other parameters in the model for the imaging data that are not of interest for the task at hand. We refer to…
Weak value amplification (WVA) is a concept that has been extensively used in a myriad of applications with the aim of rendering measurable tiny changes of a variable of interest. In spite of this, there is still an on-going debate about…
A weak measurement performed on a pre- and post-selected quantum system can result in an average value that lies outside of the observable's spectrum. This effect, usually referred to as an "anomalous weak value", is generally believed to…
The task of wavefront sensing is to measure the phase of the optical field. Here, we demonstrate that the widely used Shack-Hartmann wavefront sensor detects the weak value of transverse momentum, usually achieved by the method of quantum…
We consider weakly coupled LQ optimal control problems and derive estimates on the sensitivity of the optimal value function in dependence of the coupling strength. In order to improve these sensitivity estimates a "coupling adapted" norm…
We examine weak anticipations in discrete-time and continuous-time financial markets consisting of one risk-free asset and multiple risky assets, defining a minimal probability measure associated with the anticipation that does not depend…
A precise definition of "weak [quantum] measurements" and "weak value" (of a quantum observable) is offered, and simple finite dimensional examples are given showing that weak values are not unique and therefore probably do not correspond…
Three recent results on weak measurements are presented. They are: i) repeated measurements on a single copy can not provide any information on it and further, that in the limit of very large such measurements, weak measurements have…
In the weak measurement formalism of Y. Aharonov et al. the so-called weak value A_w of any observable A is generally a complex number. We derive a physical interpretation of its value in terms of the shift in the measurement pointer's mean…
Weak form Scientific Machine Learning (WSciML) is a recently developed framework for data-driven modeling and scientific discovery. It leverages the weak form of equation error residuals to provide enhanced noise robustness in system…
Quantum metrology that employs weak-values can potentially effectuate parameter estimation with an ultra-high sensitivity and has been typically explored across quantum optics setups. Recognizing the importance of sensitive parameter…
We explore several strategies of eliminating (or nulling) the small-scale information in weak lensing convergence power spectrum measurements in order to protect against undesirable effects, for example the effects of baryonic cooling and…
A preselection-free fiber-optic weak measurement sensing framework is proposed and experimentally verified in this paper. In view of the limitation that fiber-optic weak measurement require specific preselection, this scheme innovates…
Sample selection is a necessary preparation for weak lensing measurement. It is well-known that selection itself may introduce bias in the measured shear signal. Using image simulation and the Fourier_Quad shear measurement pipeline, we…
Conventional quantum mechanics describes a pre- and post-selected system in terms of virtual (Feynman) paths via which the final state can be reached. In the absence of probabilities, a weak measurement (WM) determines the probability…
It is known that weak measurement can significantly amplify the mean of measurement results, sometimes out of the range limited in usual quantum measurement. This fact, as actively demonstrated recently in both theory and experiment,…
Fisher forecasts are a common tool in cosmology with applications ranging from survey planning to the development of new cosmological probes. While frequently adopted, they are subject to numerical instabilities that need to be carefully…
Quantum metrology is being gradually studied for weak measurement systems. For weak measurement systems with thermal state pointer, we find that in the displacement space corresponding to imaginary weak values, the maximal QFI after…