  The fidelity (Shannon mutual information between measurements and physical
quantities) is proposed as a quantitative measure of the quality of physical
measurements. The fidelity does not depend on the true value of unknown
physical quantities (as does the Fisher information) and it allows for the role
of prior information in the measurement process. The fidelity is general enough
to allow a natural comparison of the quality of classical and quantum
measurements. As an example, the fidelity is used to compare the quality of
measurements made by a classical and a quantum Mach-Zehnder interferometer.
