Related papers: Minimum uncertainty measurements of angle and angu…

The Mori-Zwanzig formalism of statistical mechanics is used to estimate the uncertainty caused by underresolution in the solution of a nonlinear dynamical system. A general approach is outlined and applied to a simple example. The noise…

The `missing baryons' of the near universe are believed to be principally in a partially ionized state. Although passing electromagnetic waves are dispersed by the plasma, the effect has hitherto not been utilized as a means of detection…

So-called quantum limits and their achievement are important themes in physics. Heisenberg's uncertainty relations are the most famous of them but are not universally valid and violated in general. In recent years, the reformulation of…

We illustrate the use of the statistical method of moments for determining the position and momentum distributions of a quantum object from the statistics of a single measurement. The method is used for three different, though related,…

Modifications of Heisenberg's uncertainty relations have been proposed in the literature which imply a minimum position uncertainty. We study the low energy effects of the new physics responsible for this by examining the consequent change…

State estimation allows to monitor power networks, exploiting field measurements to derive the most likely grid state. In the literature, measurement errors are usually assumed to follow zero-mean Gaussian distributions; however, it has…

In standard formulations of the uncertainty principle, two fundamental features are typically cast as impossibility statements: two noncommuting observables cannot in general both be sharply defined (for the same state), nor can they be…

Unconstrained partial-wave amplitudes obtained at discrete energies from fits to complete sets of experimental data may not vary smoothly with energy, and are in principle non-unique. We demonstrate how this behavior can be ascribed to the…

The result of a physical measurement depends on the timescale of the experimental probe. In solid-state systems, this simple quantum mechanical principle has far-reaching consequences: the interplay of several degrees of freedom close to…

Uncertainty relations are usually formulated as trade-off relations between two or more observables. Here we show that the uncertainty of a single observable already has a nontrivial lower bound originating from the noncommutativity between…

The optimal and minimal measuring strategy is obtained for a two-state system prepared in a mixed state with a probability given by any isotropic a priori distribution. We explicitly construct the specific optimal and minimal generalized…

Quantum mechanics predicts that measurements of incompatible observables carry a minimum uncertainty which is independent of technical deficiencies of the measurement apparatus or incomplete knowledge of the state of the system. Nothing yet…

Starting from considerations about meaning and subsequent use of asymmetric uncertainty intervals of experimental results, we review the issue of uncertainty propagation. We show that, using a probabilistic approach (the so-called Bayesian…

The Schrodinger equation is incomplete, inherently unable to explain the collapse of the wavefunction caused by measurement; a fundamental issue known as the quantum measurement problem. Quantum mechanics is generally constrained by the…

The von Neumann interaction between a particle and an apparatus has been considered in the measurement of the position of a particle when the interaction lasts for a finite amount of time. When the measurement has finite duration, both the…

Exploring high sensitivity on the measurement of angular rotations is an outstanding challenge in optics and metrology. In this work, we employ the mn-order Hermite-Gaussian beam in the weak measurement scheme with an angular rotation…

The uncertainty relations for the position and momentum of a quantum particle on a circle are identified minimized by the corresponding coherent states. The sqeezed states in the case of the circular motion are introduced and discussed in…

We provide a decision-theoretic framework for dealing with uncertainty in quantum mechanics. This uncertainty is two-fold: on the one hand there may be uncertainty about the state the quantum system is in, and on the other hand, as is…

Our goal is to obtain a complete set of angular observables arising in a generic multi-body process. We show how this can be achieved without the need to carry out a likelihood fit of the angular distribution to the measured events.…

We study the problem of joint estimation of real squeezing and amplitude of the radiation field, deriving the measurement that maximizes the probability density of detecting the true value of the unknown parameters. More generally, we…