Optimal Mach-Zehnder phase sensitivity with Gaussian states

TL;DR

This paper analyzes the phase sensitivity of a Mach-Zehnder interferometer using Gaussian states, identifying optimal conditions and realistic detection schemes to maximize quantum Fisher information and improve measurement precision.

Contribution

It provides a comprehensive analysis of the most general Gaussian input states for phase sensitivity, including optimal phase-matching and detection strategies, with comparisons to prior specific cases.

Findings

Optimal phase-matching conditions identified for Gaussian states.

Realistic detection schemes approach the quantum Cramér-Rao bound.

Advantages of general Gaussian states over specific input states are demonstrated.

Abstract

We address in this work the phase sensitivity of a Mach-Zehnder interferometer with Gaussian input states. A squeezed-coherent plus squeezed vacuum input state allows us to unambiguously determine the optimal phase-matching conditions in order to maximize the quantum Fisher information. Realistic detection schemes are described and their performance compared in respect with the quantum Cram\'er-Rao bound. The core of this paper discusses in detail the most general Gaussian input state, without any apriori parameter restrictions. Prioritizing the maximization of various terms in the quantum Fisher information has the consequence of imposing the input phase-matching conditions. We discuss in detail when each scenario yields an optimal performance. Realistic detection scenarios are also considered and their performance compared to the theoretical optimum. The impact of the beam splitter types employed on the optimum phase-matching conditions is also discussed. We find a number of potentially interesting advantages of these states over the coherent plus squeezed vacuum input case.