Joint measurements of spin, operational locality, and uncertainty

Abstract

Joint, or simultaneous, measurements of noncommuting observables are possible within quantum mechanics, if one accepts an increase in the variances of the jointly measured observables. In this paper, we discuss joint measurements of a spin-$1∕2$ particle along any two directions. Starting from an operational locality principle, it is shown how to obtain a bound on how sharp the joint measurement can be. We give a direct interpretation of this bound in terms of an uncertainty relation.