Transmission Estimation at the Fundamental Quantum Cram\'er-Rao Bound with Macroscopic Quantum Light

TL;DR

This paper demonstrates experimentally that quantum states of light can achieve the fundamental limit of transmission estimation precision, surpassing classical methods, with potential broad applications in sensing and measurement fields.

Contribution

The authors experimentally saturate the quantum Cramér-Rao bound for transmission estimation using a bright two-mode squeezed state, extending theory to account for real-world imperfections.

Findings

Achieved saturation of the quantum Cramér-Rao bound over a wide transmission range.

Demonstrated a 62% reduction in variance compared to classical protocols at 84% transmission.

Validated the practical feasibility of quantum-enhanced transmission sensing.

Abstract

The field of quantum metrology seeks to apply quantum techniques and/or resources to classical sensing approaches with the goal of enhancing the precision in the estimation of a parameter beyond what can be achieved with classical resources. Theoretically, the fundamental minimum uncertainty in the estimation of a parameter for a given probing state is bounded by the quantum Cram\'er-Rao bound. From a practical perspective, it is necessary to find physical measurements that can saturate this fundamental limit and to show experimentally that it is possible to perform measurements with the required precision to do so. Here we perform experiments that saturate the quantum Cram\'er-Rao bound for transmission estimation over a wide range of transmissions when probing the system under study with a bright two-mode squeezed state. To properly take into account the imperfections in the generation of the quantum state, we extend our previous theoretical results to incorporate the measured properties of the generated quantum state. For our largest transmission level of 84%, we show a 62% reduction over the optimal classical protocol in the variance in transmission estimation when probing with a bright two-mode squeezed state with 8 dB of intensity-difference squeezing. Given that transmission estimation is an integral part of many sensing protocols, such as plasmonic sensing, spectroscopy, calibration of the quantum efficiency of detectors, etc., the results presented promise to have a significant impact on a number of applications in various fields of research.