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arXiv:2504.16294 · The European Physical Journal Plus

Ultimate quantum sensitivity in the 3D relative localisation of two single-photon emitters via two-photon interference

Luca Maggio, Vincenzo Tamma

Published Jan 23, 2026• 1 citation
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Abstract

Abstract We present a quantum sensing protocol for the simultaneous estimation of the difference in the localization parameters of two single-photon sources, paving the way to single-photon 3D imaging and 3D nanoscopy beyond the diffraction limit. This is achieved by exploiting two-photon interference of the two emitted photons at a beam splitter via sampling measurements in the frequency and transverse momenta at the output. We prove theoretically that this technique reaches the ultimate sensitivity in the 3D relative localization of two emitters, already with a number of sampling measurements of $$\sim 2000$$ ∼ 2000 and a bias in the three localization parameters below $$1\%$$ 1 % . These results are independent of the values of the localization parameters to estimate.

DOI
10.1140/epjp/s13360-025-07257-1

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Abstract We present a quantum sensing protocol for the simultaneous estimation of the difference in the localization parameters of two single-photon sources, paving the way to single-photon 3D imaging and 3D nanoscopy beyond the diffraction limit. This is achieved by exploiting two-photon interference of the two emitted photons at a beam splitter via sampling measurements in the frequency and transverse momenta at the output. We prove theoretically that this technique reaches the ultimate sensitivity in the 3D relative localization of two emitters, already with a number of sampling measurements of ∼2000\sim 2000∼2000 ∼ 2000 and a bias in the three localization parameters below 1%1\%1% 1 % . These results are independent of the values of the localization parameters to estimate.
We present a quantum sensing scheme achieving the ultimate quantum sensitivity in the estimation of the transverse displacement between two photons interfering at a balanced beam splitter, based on transverse-momentum sampling measurements at the output. This scheme can possibly lead to enhanced high-precision nanoscopic techniques, such as superresolved single-molecule localization microscopy with quantum dots, by circumventing the requirements in standard direct imaging of camera resolution at the diffraction limit, and of highly magnifying objectives. Interestingly, we show that our interferometric technique achieves the ultimate spatial precision in nature irrespectively of the overlap of the two displaced photonic wave packets, while its precision is only reduced of a constant factor for photons differing in any nonspatial degrees of freedom. This opens a new research paradigm based on the interface between spatially resolved quantum interference and quantum-enhanced spatial sensitivity.
We present a quantum sensing protocol for three-dimensional estimation of the difference between the momenta of two photons based on spatially resolved interferometric sampling measurements. The protocol attains ultimate quantum precision in the simultaneous estimation of the components of the relative momentum for any values of the parameters already with ∼2000\sim 2000∼2000 sampling measurements and a bias below 1%1\%1%. These results identify 3D spatially resolved two-photon interference as an efficient tool for multi-parameter quantum sensing, with potential applications in high-precision 3D localization, refractometry, and near-field calibration in free-space quantum technologies.
Abstract 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 ∼1000\sim 1000∼1000 ∼ 1000 sampling measurements, the Cramér–Rao bound for the specific input state chosen is saturated independently of the value of the difference in frequency.
Hong-Ou-Mandel (HOM) interference is an intrinsic quantum phenomena that goes beyond the possibilities of classical physics, and enables various applications in quantum metrology. While the timing resolution of HOM-based sensor is generally investigated, the ultimate quantum sensitivity in the estimation of transverse deflection or displacement between paired photons interfering at a balanced beam splitter has been explored relatively little. Here, we present an experimental demonstration of a spatial HOM interferometry for measuring the transverse deflection of an optical beam by using transverse momentum sampling measurements. This feasible scheme suffices to achieve great precision with comparatively little technological effort, which circumvents the stringent requirement in direct imaging resolution at the diffraction limit. We can adaptively determine optimum working points using a Fisher information analysis, and demonstrate an optimized spatial HOM interferometry according to practical applications. These results may significantly facilitate the use of quantum interference for high precision spatial sensing, and pave the way to more complex quantum imaging techniques like nanoscopic microscopy.
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