  In this paper, we revisit the quantum Fisher information (QFI) calculation in
SU(1,1) interferometer considering different phase configurations. When one of
the input modes is a vacuum state, we show by using phase averaging, different
phase configurations give same QFI. In addition, by casting the phase
estimation as a two-parameter estimation problem, we show that the calculation
of the quantum Fisher information matrix (QFIM) is necessary in general.
Particularly, within this setup, the phase averaging method is equivalent to a
two parameter estimation problem. We also calculate the phase sensitivity for
different input states using QFIM approach.
