  We investigate an optimal distance of two components in an entangled coherent
state for quantum phase estimation in lossy interferometry. The optimal
distance is obtained by an economical point, representing the quantum Fisher
information that we can extract per input energy. Maximizing the formula of the
quantum Fisher information over an input mean photon number, we show that, as
the losses of the interferometer increase, it can be more beneficial to prepare
an initially entangled coherent state that is less entangled. This represents
that the optimal distance of the two-mode components decreases with more loss
in the interferometry. Under the constraint of the input mean photon number, we
obtain that the optimal entangled coherent state is more robust than a
separable coherent state, even in a high photon loss rate. The optimal
entangled coherent state preserves quantum advantage over the standard
interferometric limit of the separable coherent state. We also show that the
corresponding optimal measurement requires correlation measurement bases.
