Related papers: Statistical hypothesis testing by weak-value ampli…
While the novel applications of weak values have recently attracted wide attention, weak measurement, the usual way to extract weak values, suffers from risky approximations and severe quantum noises. In this paper, we show that the…
In this work, we consider the systematic error of quantum metrology by weak measurements under decoherence. We derive the systematic error of maximum likelihood estimation in general to the first-order approximation of a small deviation in…
We consider the problem of estimating the number of false null hypotheses among a very large number of independently tested hypotheses, focusing on the situation in which the proportion of false null hypotheses is very small. We propose a…
Post-selection strategies have been proposed with the aim of amplifying weak signals, which may help to overcome detection thresholds associated with technical noise in high-precision measurements. Here we use an optical setup to…
We investigate the power of weak measurements in the framework of quantum state discrimination. First, we define and analyze the notion of weak consecutive measurements. Our main result is a convergence theorem whereby we demonstrate when…
We propose a scheme for enhanced probing of an interaction between two single fermions based on weak-value amplification. The scheme is applied to measuring the anisotropic electron-hole exchange interaction strength in semiconductor…
An important issue for many economic experiments is how the experimenter can ensure sufficient power for rejecting one or more hypotheses. Here, we apply methods developed mainly within the area of clinical trials for testing multiple…
We discuss a general approach to handling "multiple hypotheses" testing in the case when a particular hypothesis states that the vector of parameters identifying the distribution of observations belongs to a convex compact set associated…
A model is proposed for the statistical analysis of arbitrary-strength quantum measurements, based on a picture of "sampling weak values" from different configurations of the system. The model is comprised of two elements: a "local weak…
We present a parameter estimation technique based on performing joint measurements of a weak interaction away from the weak-value-amplification approximation. Two detectors are used to collect full statistics of the correlations between two…
Weak measurement is a new technique which allows one to describe the evolution of postselected quantum systems. It appears to be useful for resolving a variety of thorny quantum paradoxes, particularly when used to study properties of pairs…
Hypothesis testing in high dimensional data is a notoriously difficult problem without direct access to competing models' likelihood functions. This paper argues that statistical divergences can be used to quantify the difference between…
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,…
Weak values are traditionally obtained using a weak interaction between the measured system and a pointer state. It has, however, been pointed out that weak coupling can be replaced by a carefully tailored strong interaction. This paper…
Sensors that harness exclusively quantum phenomena (such as entanglement) can achieve superior performance compared to those employing only classical principles. Recently, a technique based on postselected, weakly-performed measurements has…
Motivated by the desire to generate labels for real-time data we develop a method to estimate the dependency structure and accuracy of weak supervision sources incrementally. Our method first estimates the dependency structure associated…
We study the phenomenon of bias amplification in classifiers, wherein a machine learning model learns to predict classes with a greater disparity than the underlying ground truth. We demonstrate that bias amplification can arise via an…
We analytically and numerically investigate the performance of weak-value amplification (WVA) and related parameter estimation methods in the presence of temporally correlated noise. WVA is a special instance of a general measurement…
We study the statistical decision process of detecting the signal from a `signal+noise' type matrix model with an additive Wigner noise. We propose a hypothesis test based on the linear spectral statistics of the data matrix, which does not…
Most studies for postselected weak measurement in optomechanical system focus on using a single photon as a measured system. However, we find that using weak coherent light instead of a single photon can also amplify the mirror's position…