  In this paper, we investigate the phase sensitivities in two-path optical
interferometry with asymmetric beam splitters. Here, we present the optimal
conditions for the transmission ratio and the phase of the beam splitter to
gain the highest sensitivities for a general class of non-classical states with
parity symmetry. Additionally, we address the controversial question of whether
the scheme with a combination of coherent state and photon-added or
photon-subtracted squeezed vacuum state is better or worse than the most
celebrated one using a combination of coherent state and squeezed vacuum state.
