Related papers: The Error Principle
Here, we investigate the uncertainty of dynamical observables in classical systems manipulated by repeated measurements and feedback control; the precision should be enhanced in the presence of an external controller but limited by the…
Often, one would like to determine some observable A, but can only measure some (hopefully related) observable M. This can arise, for example, in quantum eavesdropping, or when the research lab budget isn't large enough for that 100%…
Recently, Kosugi [arXiv:1504.03779v2 [quant-ph]] argued that Heisenberg's error-disturbance relation (EDR) must be interpreted as being between the resolution, the preparational error for the post-measurement observable, and the…
Entropic uncertainty relations for the position and momentum within the generalized uncertainty principle are examined. Studies of this principle are motivated by the existence of a minimal observable length. Then the position and momentum…
We prove an uncertainty relation, which imposes a bound on any joint measurement of position and momentum. It is of the form $(\Delta P)(\Delta Q)\geq C\hbar$, where the `uncertainties' quantify the difference between the marginals of the…
The challenge of understanding quantum measurement persists as a fundamental issue in modern physics. Particularly, the abrupt and energy-non-conserving collapse of the wave function appears to contradict classical thermodynamic laws. The…
We examine error-disturbance relations in the quantum measurement of spin systems using an atom-light interface scheme. We model a single spin-1/2 system that interacts with a polarized light meter via a Faraday interaction. We formulate…
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…
We study uncertainty relations for pairs of conjugate variables like number and angle, of which one takes integer values and the other takes values on the unit circle. The translation symmetry of the problem in either variable implies that…
In its original formulation, Heisenberg's uncertainty principle dealt with the relationship between the error of a quantum measurement and the thereby induced disturbance on the measured object. Meanwhile, Heisenberg's heuristic arguments…
In a statistical analysis in Particle Physics, nuisance parameters can be introduced to take into account various types of systematic uncertainties. The best estimate of such a parameter is often modeled as a Gaussian distributed variable…
Recent years have witnessed a controversy over Heisenberg's famous error-disturbance relation. Here we resolve the conflict by way of an analysis of the possible conceptualizations of measurement error and disturbance in quantum mechanics.…
The error on a real quantity Y due to the graduation of the measuring instrument may be represented, when the graduation is regular and fines down, by a Dirichlet form on R whose square field operator do not depend on the probability law of…
How well can multiple incompatible observables be implemented by a single measurement? This is a fundamental problem in quantum mechanics with wide implications for the performance optimization of numerous tasks in quantum information…
The application of machine learning to physics problems is widely found in the scientific literature. Both regression and classification problems are addressed by a large array of techniques that involve learning algorithms. Unfortunately,…
A prominent formulation of the uncertainty principle identifies the fundamental quantum feature that no particle may be prepared with certain outcomes for both position and momentum measurements. Often the statistical uncertainties are…
Quantum uncertainty is the cornerstone of quantum mechanics which underlies many counterintuitive nonclassical phenomena. Recent studies remarkably showed that it also fundamentally limits nonclassical correlation, and crucially, a…
In this comment on the paper by F. Kaneda, S.-Y. Baek, M. Ozawa and K. Edamatsu [Phys. Rev. Lett. 112, 020402, 2014, arXiv:1308.5868], we point out that the claim of having refuted Heisenberg's error-disturbance relation is unfounded since…
We propose a class of incompatibility measures for quantum observables based on quantifying the effect of a measurement of one observable on the statistics of the outcomes of another. Specifically, for a pair of observables $A$ and $B$ with…
We employ quantum relative entropy to establish the relation between the measurement uncertainty and its disturbance on a state in the presence (and absence) of quantum memory. For two incompatible observables, we present the…