Quantum-enhanced SU(1,1) interferometry via a Fock state

TL;DR

This paper derives a general formula for quantum Fisher information in SU(1,1) interferometers with arbitrary and Fock state inputs, demonstrating enhanced phase sensitivity and optimal measurement strategies.

Contribution

It provides a universal expression for quantum Fisher information and proves parity measurement saturation, advancing quantum metrology with Fock states.

Findings

Quantum Fisher information is independent of the arbitrary state form.

Parity measurement saturates the quantum Cramer-Rao bound at optimal phase.

Fock states enhance phase sensitivity under photon number constraints.

Abstract

In this paper, we derive a general expression of the quantum Fisher information of an SU(1,1) interferometer with an arbitrary state and a Fock state as inputs by the phase-averaging method. Our results show that the same quantum Fisher information can be obtained regardless of the specific form of the arbitrary state. Then, we analytically prove that the parity measurement can saturate the quantum Cramer-Rao bound when the estimated phase sits at the optimal working point. For practical reasons, we investigate the phase sensitivity when the arbitrary state is a coherent or thermal state. We further show that a Fock state can indeed enhance the phase sensitivity within a constraint on the total mean photon number inside the interferometer.