Concept of Experimental Accuracy and Simultaneous Measurements of Position and Momentum

Abstract

The concept of experimental accuracy isinvestigated in the context of the unbiased jointmeasurement processes defined by Arthurs and Kelly. Adistinction is made between the errors of retrodictionand prediction. Four error-disturbancerelationships are derived, analogous to the singleerror-disturbance relationship derived by Braginsky andKhalili in the context of single measurements ofposition only. A retrodictive and a predictive error-errorrelationship are also derived. The connection betweenthese relationships and the extended uncertaintyprinciple of Arthurs and Kelly is discussed. Thesimilarities and differences between the quantum mechanicaland classical concepts of experimental accuracy areexplored. It is argued that these relationships providegrounds for questioning Uffink's conclusion that the concept of a simultaneous measurement ofnoncommuting observables is not fruitful.