Classical-Information Theoretical View of Physical Measurements and Generalized Uncertainty Relations

TL;DR

This paper explores the fundamental limits of physical measurements using classical information theory, deriving generalized uncertainty relations and analyzing how boundary conditions can reduce uncertainties.

Contribution

It introduces a classical information theoretical framework for physical measurements and generalizes uncertainty relations for dynamic systems under various equations of motion.

Findings

Uncertainty relations are formulated within an information theory framework.

Boundary conditions can quantitatively reduce measurement uncertainties.

Mean-square errors of Gaussian-like distributions are analyzed in this context.

Abstract

General characterization of physical measurements is discussed within the framework of a classical information theory. Uncertainty relation for simultaneous measurements of two physical observables is defined in this framework for generalized dynamic systems controlled under general kinds of equations of motion. We have treated only a mean-square error of the Gauss(-like) distributions in this report. Lessening of the Kennard-Robertson type uncertainties due to boundary conditions are quantitatively discussed using the information entropy.