A Note on Different Definitions of Momentum Disturbance

TL;DR

This paper compares different definitions of quantum momentum disturbance, highlighting that Ozawa's definition aligns better with Heisenberg's original concept and discussing the implications for error-disturbance relations.

Contribution

It clarifies the physical significance of two different disturbance definitions and advocates for Ozawa's definition as more consistent with Heisenberg's original ideas.

Findings

Ozawa's definition better matches Heisenberg's original disturbance concept

A new error-disturbance relation can be derived using Ozawa's definitions

Experimental confirmation supports Ozawa's approach

Abstract

In [1], Busch et al. showed that it is possible to construct an error-disturbance relation having the same form as Heisenberg's original heuristic definition[2], in contrast to the theory proposed by Ozawa[3] which we and others recently confirmed experimentally[4,5]. With Ozawa's definitions of measurement error and disturbance, a relation of Heisenberg's form is not in general valid, and a new error-disturbance relationship can be derived. Here we explain the different physical significance of the two definitions, and suggest that Ozawa's definition better corresponds to the usual understanding of the disturbance that Heisenberg discussed.