Monitoring dispersive samples with single photons: the role of frequency correlations

TL;DR

This paper investigates how frequency correlations in photon pairs affect the quantum limits and practical measurement strategies for simultaneously estimating phase and dephasing in dispersive media.

Contribution

It derives the quantum Cramér-Rao bounds for joint phase and dephasing estimation considering frequency correlations, and analyzes the impact of these correlations on measurement performance.

Findings

Frequency correlations influence the quantum limits of estimation.

Measurement schemes based on Stokes operators can approach these limits.

Correlations play a crucial role in the simultaneous estimation of multiple parameters.

Abstract

The physics that governs quantum monitoring may involve other degrees of freedom than the ones initialised and controlled for probing. In this context we address the simultaneous estimation of phase and dephasing characterizing a dispersive medium, and we explore the role of frequency correlations within a photon pair generated via parametric down-conversion, when used as a probe for the medium. We derive the ultimate quantum limits on the estimation of the two parameters, by calculating the corresponding quantum Cram\'er-Rao bound; we then consider a feasible estimation scheme, based on the measurement of Stokes operators, and address its absolute performances in terms of the correlation parameters, and, more fundamentally, of the role played by correlations in the simultaneous achievability of the quantum Cram\'er-Rao bounds for each of the two parameters.