  In the general theory of quantum measurement, one associates a positive
semidefinite operator on a $d$-dimensional Hilbert space to each of the $n$
possible outcomes of an arbitrary measurement. In the special case of a
projective measurement, these operators are pairwise Hilbert--Schmidt
orthogonal, but when $n>d$, orthogonality is restricted by positivity. This
restriction allows us to more precisely state the quantum adage: information
gain of a system is always accompanied by unavoidable disturbance.
Specifically, we investigate three properties of a measurement with L\"uders
rule updating: its disturbance, a measure of how the expected post-measurement
state deviates from the input; its measurement strength, a measure of the
intrinsic information producing capacity of the measurement; and its
orthogonality, a measure of the degree to which the measurement operators
differ from an orthonormal set. These quantities satisfy an
information-disturbance trade-off relation that highlights the additional role
played by orthogonality. Finally, we assess several classes of measurements on
these grounds and identify symmetric informationally complete quantum
measurements as the unique quantum analogs of a perfectly informative and
nondisturbing classical ideal measurement.
