  We present a new operator method in the Heisenberg representation to obtain
the signal of parity measurement within a lossless SU(1,1) interferometer.
Based on this method, it is convenient to derive the parity signal directly in
terms of input states, including general Gaussian or non-Gaussian state. As
applications, we revisit the signal of parity measurement within an SU(1,1)
interferometer when a coherent or thermal state and a squeezed vacuum state are
considered as input states. In addition, we also obtain the parity signal of a
Fock state when it passes through an SU(1,1) interferometer, which is also a
new result. Therefore, the operator method proposed in this work may bring
convenience to the study of quantum metrology, particularly the phase
estimation based on an SU(1,1) interferometer.
