Simultaneous estimation of multiple phases in generalised Mach-Zehnder interferometer

TL;DR

This paper explores the simultaneous estimation of multiple phases in a generalized multi-mode Mach-Zehnder interferometer, demonstrating Heisenberg-like precision scaling for subsets of phases within a fixed experimental setup.

Contribution

It introduces a method for joint phase estimation in multi-mode interferometers that maintains high precision despite correlations between estimators.

Findings

Heisenberg-like scaling achieved for estimating subsets of phases

Method applicable to quantum-enhanced 3D interferometric sensing

Fixed setup with the same initial state and measurements for all estimations

Abstract

In this work we investigate the problem of simultaneous estimation of phases using generalised three- and four-mode Mach-Zehnder interferometer. In our setup, we assume that the phases are placed in each of the modes in the interferometer, which introduces correlations between estimators of the phases. These correlations prevent simultaneous estimation of all these phases, however we show that we can still obtain the Heisenberg-like scaling of precision of joint estimation of any subset of $d-1$ phases, $d$ being the number of modes, within completely fixed experimental setup, namely with the same initial state and set of measurements. Our estimation scheme can be applied to the task of quantum-enhanced sensing in three-dimensional interferometric configurations.