SU(1,1) interferometry with parity measurement

TL;DR

This paper introduces a new operator method in the Heisenberg picture to efficiently derive the parity measurement signal in lossless SU(1,1) interferometers, applicable to various input quantum states.

Contribution

A novel operator approach in the Heisenberg representation simplifies calculating parity signals for diverse input states in SU(1,1) interferometers.

Findings

Derived parity signals for coherent, thermal, and squeezed vacuum states.

Obtained the first known parity signal for a Fock state in an SU(1,1) interferometer.

Demonstrated the method's utility in quantum phase estimation.

Abstract

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.