Related papers: Information amplification via postselection: A par…
Weak measurements with imaginary weak values are reexamined in light of recent experimental results. The shift of the meter, due to the imaginary part of the weak value, is derived via the probability of postselection, which allows…
Weak measurement is unique in enabling measurements of non-commuting operators as well as otherwise-undetectable peculiar phenomena predicted by the Two-State-Vector-Formalism (TSVF). This article, the first in two parts, explores novel…
Quantum estimation theory provides optimal observations for various estimation problems for unknown parameters in the state of the system under investigation. However, the theory has been developed under the assumption that every observable…
First, a misconception about the spectrum of a confined particle is evidentiated. Then, the results are shown to be incorrect by means of a counter-example, an explicit preparation for the probe is given that yields an arbitrary…
The information-theoretic definition of quantum correlation, e.g., quantum discord, is measurement dependent. By considering the more general quantum measurements, weak measurements, which include the projective measurement as a limiting…
The quantum Cram\'er-Rao bound sets a fundamental limit on the accuracy of unbiased parameter estimation in quantum systems, relating the uncertainty in determining a parameter to the inverse of the quantum Fisher information. We…
We prove lower bounds on the error of any estimator for the mean of a real probability distribution under the knowledge that the distribution belongs to a given set. We apply these lower bounds both to parametric and nonparametric…
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…
Weak measurements have thus far been considered instrumental in the so-called direct measurement of the quantum wavefunction [Nature (London) 474, 188 (2011)]. Here we show that direct measurement of the wavefunction can be obtained by…
A recent analysis [quant-ph/0104062] suggests that weak measurements can be used to give observational meaning to counterfactual reasoning in quantum physics. A weak measurement is predicted to assign a negative unit population to a…
Weak lensing of galaxies by large scale structure can potentially measure cosmological quantities as accurately as the cosmic microwave background (CMB). However, the relation between observables and fundamental parameters is more complex…
The Fisher information matrix is a quantity of fundamental importance for information geometry and asymptotic statistics. In practice, it is widely used to quickly estimate the expected information available in a data set and guide…
A problem of improving the accuracy of nonparametric entropy estimation for a stationary ergodic process is considered. New weak metrics are introduced and relations between metrics, measures, and entropy are discussed. Based on weak…
In this paper, we consider signals with a low-rank covariance matrix which reside in a low-dimensional subspace and can be written in terms of a finite (small) number of parameters. Although such signals do not necessarily have a sparse…
Measurements are crucial in quantum mechanics, in fundamental research as well as in applicative fields like quantum metrology, quantum-enhanced measurements and other quantum technologies. In the recent years, weak-interaction-based…
Traditional uncertainty relations dictate a minimal amount of noise in incompatible projective quantum measurements. However, not all measurements are projective. Weak measurements are minimally invasive methods for obtaining partial state…
We study quantum measurement with preselection and postselection, and derive the precise expressions of the measurement results without any restriction on the coupling strength between the system and the measuring device. For a qubit…
Recent controversy regarding the meaning and usefulness of weak values is reviewed. It is argued that in spite of recent statistical arguments by Ferrie and Combes, experiments with anomalous weak values provide a useful amplification…
The article recapitulates the concept of weak measurement in its broader sense encapsulating the trade between asymptotically weak measurement precision and asymptotically large measurement statistics. Essential applications in…
We describe a compact and reliable method to calculate the Fisher information for the estimation of a dynamical parameter in a continuously measured linear Gaussian quantum system. Unlike previous methods in the literature, which involve…