https://doi.org/10.1140/epjp/s13360-025-06903-y
Regular Article
Quantum-limited estimation of the frequency shift between two interfering photons by time sampling of their quantum beats
1
School of Mathematics and Physics, University of Portsmouth, PO1 3HF, Portsmouth, UK
2
Dipartimento Interateneo di Fisica, Politecnico di Bari, 70126, Bari, Italy
3
Dipartimento di Fisica, Università di Bari, 70126, Bari, Italy
4
INFN, Sezione di Bari, 70126, Bari, Italy
5
Institute of Cosmology and Gravitation, University of Portsmouth, PO1 3FX, Portsmouth, UK
Received:
29
May
2025
Accepted:
25
September
2025
Published online:
7
October
2025
We present a sensing scheme for estimating the frequency difference of two non-entangled photons. The technique consists of time-resolving sampling measurements at the output of a beam splitter. With this protocol, we can achieve the ultimate precision for the estimation of the frequency shift between two non-entangled photons, overcoming the limits in precision and the range of detection of frequency-resolving detectors employed in standard direct measurements of the frequencies. The sensitivity can be increased by increasing the coherence time of the photons. We show that, already with 
sampling measurements, the Cramér–Rao bound for the specific input state chosen is saturated independently of the value of the difference in frequency.
© The Author(s) 2025
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