  We find a phase matching condition for enhancement of sensitivity in a
Mach-Zehnder interferometer illuminated by an arbitrary state in one input port
and an odd(even) state in the other port. Under this condition, the Fisher
information becomes maximal with respect to the relative phase of two modes and
the phase sensitivity is enhanced. For the case with photon losses, we further
find that the phase matching condition keeps unchanged with a coherent state
and a coherent superposition state as the input states.

Quantum Physics