SU(1,1) interferometry with parity measurement

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 and non-Gaussian states. 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 obtain the parity signal of an arbitrary single-mode state when it passes through an SU(1,1) interferometer, which is also a new result. Then, we analytically prove that parity measurement can saturate the quantum Cramer–Rao bound when the estimated phase approaches zero. 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.