Quantum Fisher information analysis for absorption measurements with undetected photons

TL;DR

This paper compares the quantum Fisher information of three absorption spectroscopy configurations with undetected photons, identifying which setup offers the highest information gain under various loss and gain conditions.

Contribution

It provides a theoretical comparison of three different quantum spectroscopy schemes, revealing their optimal regimes based on loss and gain parameters.

Findings

SU(1,1) setup is optimal at low to moderate gain with less than 99% loss.

Induced-coherence scheme outperforms others at high gain and intermediate loss.

Distributed-loss scheme is best under extreme attenuation (less than 1% transmission).

Abstract

We theoretically compare the quantum Fisher information (QFI) for three configurations of absorption spectroscopy with undetected idler photons: an SU(1,1) interferometer with inter-source idler loss, an induced-coherence (IC) setup in which the idler partially seeds a second squeezer together with a vacuum ancilla, and a distributed-loss (DL) scheme with in-medium attenuation. We calculate the QFI as a function of parametric gain for both full and signal-only detection access. For losses below 99% and low to moderate gain, the SU(1,1) configuration provides the largest QFI. At high gain and intermediate loss, the IC scheme performs best, while under extreme attenuation (transmission $<$ 1%) the DL model becomes optimal. These results delineate the measurement regimes in which each architecture is optimal in terms of information theory.