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We study the weak-value amplification (WVA) in a phase measurement with an optical interferometer in which shot noise limits the sensitivity. We compute the signal and the shot noise including the full-order interaction terms of the WVA,…
Weak measurement [1,19] combined with quantum delayed-choice experiment that use quantum beam splitter instead of the beam splitter give rise to a surprising amplification effect, i.e., counterintuitive negative amplification effect. We…
To resolve the non-convex optimization problem in partial wave analysis, this paper introduces a novel approach that incorporates fraction constraints into the likelihood function. This method offers significant improvements in both the…
Power corrections to exclusive processes are usually calculated using models for twist-four distribution amplitudes (DA) which are based on the leading-order terms in the conformal expansion. In this work we develop a different approach…
In pump-probe spectroscopy, one often needs to analyse the transmission or reflection of electromagnetic waves through optically pumped media. Here, it is common practice to approximate the analysis in order to extract non-equilibrium…
A simple inverse problem for the wave equation requires determination of both the wave velocity in a homogenous acoustic material and the transient waveform of an isotropic point radiator, given the time history of the wavefield at a remote…
In this paper we explore the potential of the double phase functional in an image processing context. To this end, we study minimizers of the double phase energy for functions with bounded variation and show that this energy can be obtained…
We consider the problem of approximating the solution of variational problems subject to the constraint that the admissible functions must be convex. This problem is at the interface between convex analysis, convex optimization, variational…
In a quantum-noise limited system, weak-value amplification using post-selection normally does not produce more sensitive measurements than standard methods for ideal detectors: the increased weak value is compensated by the reduced power…
The maximum (or minimum) generalized eigenvalue of symmetric positive semidefinite matrices that depend on optimization variables often appears as objective or constraint functions in structural topology optimization when we consider…
In this paper, we pursue our series of papers aiming to show the applicability of the concept of very weak solutions. We consider a wave model with irregular position dependent mass and dissipation terms, in particular, allowing for…
This paper deals with the problem of estimating the delays and amplitudes of a weighted superposition of pulses, called stream of pulses. This problem is motivated by a variety of applications, such as ultrasound and radar. This paper shows…
Kedem's Comment [arXiv:1402.1352] on our Letter [PRL 112, 040406 (2014)] contains only the criticism that we did not consider complex weak values. We point out follow-up work which uses the same analysis as in our Letter, includes any type…
The group $G_2$ of invertible affine transformations of $\mathbb{R}^2$ has, up to equivalence, one square--integrable representation. Two new realizations of this representation are presented and novel continuous wavelet transforms, acting…
Some iterative techniques are defined to solve reversible inverse problems and a common formulation is explained. Numerical improvements are suggested and tests validate the methods.
This paper presents an analytical formulation for correcting the diffraction associated to the second harmonic of an acoustic wave, more compact than that usually used. This new formulation, resulting from an approximation of the correction…
This paper is intended to give a characterization of the optimality case in Nash's inequality, based on methods of nonlinear analysis for elliptic equations and techniques of the calculus of variations. By embedding the problem into a…
The assumptions of Ferrie and Combes are irrelevant for realistic experimental situations. This undermines their conclusions.
Optical phase measurement is a simple example of a quantum--limited measurement problem with important applications in metrology such as gravitational wave detection. The formulation of optimal strategies for such measurements is an…
This article handles in a short manner a few Laplace transform pairs and some extensions to the basic equations are developed. They can be applied to a wide variety of functions in order to find the Laplace transform or its inverse when…