  It has been proposed and demonstrated that path-entangled Fock states (PEFSs)
are robust against photon loss over NOON states [S. D. Huver \emph{et al.},
Phys. Rev. A \textbf{78}, 063828 (2008)]. However, the demonstration was based
on a measurement scheme which was yet to be implemented in experiments. In this
work, we quantitatively illustrate the advantage of PEFSs over NOON states in
the presence of photon losses by analytically calculating the quantum Fisher
information. To realize such an advantage in practice, we then investigate the
achievable sensitivities by employing three types of feasible measurements:
parity, photon-number-resolving, and homodyne measurements. We here apply a
double-port measurement strategy where the photons at each output port of the
interferometer are simultaneously detected with the aforementioned types of
measurements.
