The Concept of Experimental Accuracy and Simultaneous Measurements of Position and Momentum

Abstract

The concept of experimental accuracy is investigated in the context of the unbiased joint measurement processes defined by Arthurs and Kelly. A distinction is made between the errors of retrodiction and prediction. Four error-disturbance relationships are derived, analogous to the single error-disturbance relationship derived by Braginsky and Khalili in the context of single measurements of position only. A retrodictive and a predictive error-error relationship are also derived. The connection between these relationships and the extended Uncertainty Principle of Arthurs and Kelly is discussed. The similarities and differences between the quantum mechanical and classical concepts of experimental accuracy are explored. It is argued that these relationships provide grounds for questioning Uffink's conclusion, that the concept of a simultaneous measurement of non-commuting observables is not fruitful.