  It is shown that the condition for achieving the quantum Cramer-Rao bound of
phase estimation in conventional two-path interferometers is that the state is
symmetric with regard to an (unphysical) exchange of the two paths. Since path
symmetry is conserved under phase shifts, the maximal phase sensitivity can be
achieved at arbitrary bias phases, indicating that path symmetric states can
achieve their quantum Cramer-Rao bound in Bayesian estimates of a completely
unknown phase.
