Quantum Absorbance Estimation and the Beer-Lambert Law

TL;DR

This paper explores quantum-enhanced transmission measurements, demonstrating that classical strategies can nearly reach the quantum limit in absorbance estimation by optimizing conditions based on the Beer-Lambert law, including experimental factors.

Contribution

It provides a comprehensive analysis of classical and quantum strategies for absorbance estimation, deriving optimal conditions and validating them experimentally with Fock and thermal states.

Findings

Classical strategies can reach 83% of the quantum limit with optimization.

Experimental results agree with theoretical predictions.

Optimal conditions are derived for both classical and quantum light sources.

Abstract

The utility of transmission measurement has made it a target for quantum enhanced measurement strategies. Here we find if the length of an absorbing object is a controllable variable, then via the Beer-Lambert law, classical strategies can be optimised to reach within 83% of the absolute quantum limit. Our analysis includes experimental losses, detector noise, and input states with arbitrary photon statistics. We derive optimal operating conditions for both classical and quantum sources, and observe experimental agreement with theory using Fock and thermal states.