Quantum Metrology Using Time-Frequency as Quantum Continuous Variables: Resources, Sub-Shot-Noise Precision and Phase Space Representation

We study the role of the electromagnetic field's frequency on the precision limits of time measurements from a quantum perspective, using single photons as a paradigmatic system. We demonstrate that a quantum enhancement of precision is possible only when combining both intensity and spectral resources and, in particular, that spectral correlations enable a quadratic scaling of precision with the number of probes. We identify the general mathematical structure of nonphysical states that achieve the Heisenberg limit and show how a finite spectral variance may cause a quantum-to-classical-like transition in precision scaling for pure states similar to the one observed for noisy systems. Finally, we provide a clear and consistent geometrical time-frequency phase space interpretation of our results, identifying what should be considered as spectral classical resources.

Automated summary

We investigate the impact of the electromagnetic field's frequency on the precision limits of time measurements from a quantum perspective, utilizing single photons as a representative system. Our results show that quantum precision enhancement is only achievable by combining both intensity and spectral resources, with spectral correlations allowing for quadratic scaling of precision with the number of probes. We reveal the mathematical structure of nonphysical states that attain the Heisenberg limit and demonstrate how finite spectral variance can induce a quantum-to-classical-like transition in precision scaling similar to noisy systems. In addition, we offer a comprehensive interpretation of our findings in the time-frequency phase space, identifying the spectral classical resources.