  Uncertainty relations are often considered to be a measure of incompatibility
of noncommuting observables. However, such a consideration is not valid in
general, motivating the need for an alternate measure that applies to any set
of noncommuting observables. We present an operational approach to quantifying
incompatibility without invoking uncertainty relations. Our measure aims to
capture the incompatibility of noncommuting observables as manifest in the
non-orthogonality of their eigenstates. We prove that this measure has all the
desired properties: it is zero when the observables commute, strictly greater
than zero when they do not, and is maximum when they are mutually unbiased. We
also obtain tight upper bounds on this measure for any N noncommuting
observables and compute it exactly when the observables are mutually unbiased.
