Multiple-parameter estimation in a sagnac interferometer

TL;DR

This paper investigates the limits of multi-parameter estimation in a Sagnac interferometer, revealing fundamental constraints on achieving Heisenberg limits simultaneously and identifying conditions for optimal measurement precision.

Contribution

It provides a detailed analysis of the quantum limits in two-parameter estimation within Sagnac interferometers and identifies conditions for saturating the quantum Cramer-Rao bound.

Findings

One cannot reach the Heisenberg limit for both parameters simultaneously with maximally entangled input.

Optimal measurement conditions depend on evolution time and input state.

Two-parameter estimation can outperform single-parameter measurement under certain constraints.

Abstract

We explored the general characteristics of a Sagnac interferometer in a multiparameter estimation process. We find that in the two-parameter estimation scenario, one cannot make both parameter measurement results reach the Heisenberg limit (HL) simultaneously when the input resources are maximally entangled. Only one of the parameters' uncertainty can approach the HL while the other is only scaled by the standard quantum limit (SQL). We also discussed the constraint conditions that make the quantum Cramer-Rao bound saturable. These constraint conditions would prompt one to choose proper evolution time and optimal input state. Under the constraint conditions, we find that the HL result obtained in the two parameter scenario would catch up with or even be more precise than that acquired by the single parameter measurement process in some special cases. Such general features about the Sagnac system revealed in our work may have a reference value in actual experiments.