The inaccuracy principle

The problem of joint measurement of incompatible observables is investigated. Measurements are represented by positive operator-valued measures. A quantitative notion of inaccuracy is defined. It is shown that within this framework joint inaccurate measurements are possible for arbitrary maximal projection-valued measures on finite-dimensional spaces. The accuracy of such measurements is limited, as is shown by an inaccuracy inequality we derive. This new type of uncertainty relation can be unambiguously interpreted as referring to measurement precision rather than preparative quality. Several recent experiments are seen to be realizations of such joint measurements.