Quantum metrology using time-frequency as quantum continuous variables: Resources, sub shot-noise precision and phase space representation

TL;DR

This paper explores how the frequency of single photons influences time measurement precision, demonstrating quantum advantages and a transition from quantum to classical scaling by analyzing spectral resources and phase space representations.

Contribution

It introduces a quantum continuous variable framework for time-frequency metrology, revealing how spectral and intensity resources affect precision scaling and providing a phase space interpretation.

Findings

Quadratic scaling of precision using quantum mode correlations

States that saturate the Heisenberg limit are explicitly characterized

A quantum-to-classical transition in scaling is observed by changing spectral variance

Abstract

We study the role of the electromagnetic field's frequency in time precision measurements using single photons as a paradigmatic system. For such, we independently identify the contributions of intensity and spectral resources and show that both can play a role on the scaling of the precision of parameter estimation with the number of probes. We show in particular that it is possible to observe a quadratic scaling using quantum mode correlations only and explicit the mathematical expression of states saturating the Heisenberg limit. We also provide a geometrical and phase space interpretation of our results, and observe a curious quantum-to-classical-like transition on scaling by modifying the spectral variance of states. Our results connect discrete and continuous aspects of single photons and quantum optics by considering from a quantum mechanical perspective the role of frequency.