  Phase measurement using a lossless Mach-Zehnder interferometer with certain
entangled $N$-photon states can lead to a phase sensitivity of the order of
1/N, the Heisenberg limit. However, previously considered output measurement
schemes are different for different input states to achieve this limit. We show
that it is possible to achieve this limit just by the parity measurement for
all the commonly proposed entangled states. Based on the parity measurement
scheme, the reductions of the phase sensitivity in the presence of photon loss
are examined for the various input states.
