Quantum-enhanced stochastic phase estimation with SU(1,1) interferometer

TL;DR

This paper introduces a quantum-enhanced method using SU(1,1) interferometers with coherent states to improve stochastic phase estimation, surpassing classical limits and achieving quantum scaling in precision.

Contribution

It proposes a practical SU(1,1) interferometer-based approach for stochastic phase estimation, demonstrating quantum advantage over traditional methods.

Findings

Significant reduction in mean square error compared to Mach-Zehnder interferometer.

Achieves stochastic Heisenberg scaling in phase estimation.

Surpasses the precision of canonical measurement methods.

Abstract

The quantum stochastic phase estimation has many applications in the precise measurement of various physical parameters. Similar to the estimation of a constant phase, there is a standard quantum limit for stochastic phase estimation, which can be obtained with the Mach-Zehnder interferometer and coherent input state. Recently, it has been shown that the stochastic standard quantum limit can be surpassed with non-classical resources such as the squeezed light. However, practical methods to achieve the quantum enhancement in the stochastic phase estimation remains largely unexplored. Here we propose a method utilizing the SU(1,1) interferometer and coherent input states to estimate a stochastic optical phase. As an example, we investigate the Ornstein-Uhlenback stochastic phase. We analyze the performance of this method for three key estimation problems: prediction, tracking and smoothing. The results show significant reduction of the mean square error compared with the Mach-Zehnder interferometer under the same photon number flux inside the interferometers. In particular, we show that the method with the SU(1,1) interferometer can achieve the fundamental quantum scaling, the stochastic Heisenberg scaling, and surpass the precision of the canonical measurement.