  Considering the simultaneous measurement of non-commuting observables, we
define a geometric measure for the degree of non-commuting behavior of quantum
measurements coming from the initial and final states of the measurements. The
rationality of our geometric measure is demonstrated and the application of it
is presented. The connection between our measure and Heisenberg's uncertainty
principle is discussed as well. Our work deepens the understanding of quantum
non-commuting measurement.
