Quantum Metrology under Coarse-Grained Measurement

TL;DR

This paper demonstrates that quantum-enhanced phase estimation remains effective even with highly coarse-grained measurements, combining theoretical analysis and experimental validation to show practical quantum metrology under imperfect detection.

Contribution

It introduces a method to achieve quantum-enhanced phase estimation using only two measurement bins, even with severe coarse-graining, and provides calibration procedures for practical implementation.

Findings

Coarse-grained homodyne detection can surpass the standard quantum limit.

Quantum enhancement of 1.2 dB observed with only two measurement bins.

Heisenberg scaling achieved despite severe measurement coarse-graining.

Abstract

While quantum metrology enables measurement precision beyond classical limits, its performance is often susceptible to experimental imperfections. Most prior studies have focused on imperfections in quantum states and operations. Here, we investigate the effect of coarse graining in quantum measurement through both theoretical analysis and experimental demonstration. Using an interferometer with a squeezed vacuum and a laser input, we analyze how coarse graining in homodyne detection affects the precision of phase estimation. We evaluate the Fisher information under various coarse-graining conditions and determine, in each case, an optimal estimation strategy that saturates the Cram\'{e}r-Rao bound. Remarkably, even extremely coarse-grained measurement -- with only two bins -- enables phase estimation beyond the standard quantum limit and even achieves a precision that follows the Heisenberg scaling. We experimentally demonstrate quantum-enhanced phase estimation under coarse-grained homodyne detection. To determine an optimal estimation strategy, we employ the method of moments and present calibration procedures that enable its application to general experimental settings. Using only two bins, we observe a quantum enhancement of 1.2 dB compared to the classical method using the ideal measurement, improving towards 3.8 dB as the bin number increases. These results highlight a practical pathway to achieving quantum enhancement under the presence of severe experimental imperfections.