Ultimate sensitivity of multiparameter estimation in quantum sensing with undetected photons

TL;DR

This paper analyzes the fundamental limits and optimal strategies for multiparameter quantum sensing with undetected photons, providing theoretical insights and practical guidance for high-sensitivity experiments.

Contribution

It applies quantum estimation theory to determine the optimal measurement scheme and the use of multipass interactions in undetected photon sensing.

Findings

Optimal measurement requires only a single controllable phase shift.

Maximum information gain scales inversely with the log of the sample's transmission.

The work clarifies the metrological potential and design principles for quantum sensing with undetected photons.

Abstract

Quantum sensing with undetected photons is a technique where photons of one wavelength probe a sample, but information is extracted by measuring photons of another wavelength that never interacts with the sample. This has seen significant experimental advances in applications such as spectroscopy, microscopy, and bio-sensing. However, a detailed theoretical analysis using the tools of quantum metrology is currently lacking. Thus it is unclear how far away current schemes are from fundamental limits, and what the optimal measurement strategies are. We apply a multiparameter quantum estimation framework to quantify the error when estimating the unknown transmission and phase shift of a sample. The optimal measurement scheme is shown to require only a single controllable phase shift, easily implementable in existing setups. We also study how to use multipass interactions to maximise information gain. In general the optimum number of passes scales inversely with the log of the transmission of the sample. This work clarifies the metrological power of quantum sensing with undetected photons, and provides guidance for the design of experiments requiring high sensitivity.