  For a generic interferometer, the conditional probability density
distribution, $p(\phi|m)$, for the phase $\phi$ given measurement outcome $m$,
will generally have multiple peaks. Therefore, the phase sensitivity of an
interferometer cannot be adequately characterized by the standard deviation,
such as $\Delta\phi\sim 1/\sqrt{N}$ (the standard limit), or $\Delta\phi\sim
1/N$ (the Heisenberg limit). We propose an alternative measure of phase
sensitivity--the fidelity of an interferometer--defined as the Shannon mutual
information between the phase shift $\phi$\ and the measurement outcomes $m$.
As an example application of interferometer fidelity, we consider a generic
optical Mach-Zehnder interferometer, used as a sensor of a classical field. We
find the surprising result that an entangled {\it N00N} state input leads to a
lower fidelity than a Fock state input, for the same photon number.
