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

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.

15 pages, 3 figures

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Cited by in corpus (12)

• Frequency estimation by frequency jumps
• Hybrid III-V/Silicon Quantum Photonic Device Generating Broadband Entangled Photon Pairs
• Approaching maximal precision of Hong-Ou-Mandel interferometry with non-perfect visibility
• Time-frequency metrology with two single-photon states: phase space picture and the Hong-Ou-Mandel interferometer
• Single-shot Quantum Signal Processing Interferometry
• Gottesman-Kitaev-Preskill encoding in continuous modal variables of single photons
• Superselection rules and bosonic quantum computational resources
• Monitoring the energy of a cavity by observing the emission of a repeatedly excited qubit
• Quantum-limited estimation of the frequency shift between two interfering photons by time sampling of their quantum beats
• The Role of Symmetry in Generalized Hong-Ou-Mandel Interference and Quantum Metrology
• Quantum-to-Classical Transition via Single-Shot Generalized Measurements
• Measuring entanglement along collective operators