Quantum phase estimation and realistic detection schemes in Mach-Zehnder interferometer using SU(2) coherent states

TL;DR

This paper investigates quantum phase estimation in a Mach-Zehnder interferometer using SU(2) coherent states, comparing detection schemes and demonstrating that all can reach the quantum Cramér-Rao bound under optimal conditions.

Contribution

It provides a comparative analysis of different detection schemes in MZI with SU(2) coherent states, showing all can achieve optimal precision without external phase references.

Findings

All three detection schemes can reach the QCRB with SU(2) coherent states.

Optimal pressure is achieved at high total angular momentum quantum number j.

SU(2) coherent states are effective input states for quantum phase estimation.

Abstract

In quantum parameter estimation, the quantum Cram\'er-Rao bound (QCRB) sets a fundamental limit on the precision achievable with unbiased estimators. It relates the uncertainty in estimating a parameter to the inverse of the quantum Fisher information (QFI). Both QCRB and QFI are valuable tools for analyzing interferometric phase sensitivity. This paper compares the single-parameter and two-parameter QFI for a Mach-Zehnder interferometer (MZI) with three detection schemes: single-mode and difference intensity detection, neither has access to an external phase reference and balanced homodyne detection with access to an external phase reference. We use a spin-coherent state associated with the su(2) algebra as the input state in all scenarios and show that all three schemes can achieve the QCRB for the spin-coherent input state. Furthermore, we explore the utilization of SU(2) coherent states in diverse scenarios. Significantly, we find that the best pressure is obtained when the total angular momentum quantum number $j$ is high, and we demonstrate that given optimal conditions, all detection schemes can achieve the QCRB by utilizing SU(2) coherent states as input states.