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arXiv:2603.08602

Quantum-limited estimation of the difference between photonic momenta via spatially resolved two-photon interference

Luca Maggio, Vincenzo Tamma

quant-phSubmitted Mar 9, 2026• Announced Mar 10, 2026• 0 citations
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Abstract

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 $\sim 2000$ sampling measurements and a bias below $1\%$. 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.

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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 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.
Abstract A two-photon interfering technique based on polarization-resolved measurements is presented for the simultaneous estimation with maximum quantum sensitivity of multiple parameters associated with the polarization state of two interfering photonic qubits. This estimation is achieved by exploiting a novel interferometric technique based on polarization-resolved two-photon interference. The experimental feasibility and accuracy of this technique is shown, even when a limited number of sampling measurements is employed. This work is relevant for the development of quantum technologies with photonic qubits and sheds light on the physics at the interface between multiphoton interference, boson sampling, multi-parameter quantum sensing, and quantum information processing.
Abstract We demonstrate an experimental scheme for high-precision position measurements based on transverse-momentum-resolved two-photon interferometry with independent photons and single photon avalanche diode (SPAD) arrays. Our scheme extends the operative range of Hong–Ou–Mandel interferometry beyond its intrinsic constraints due to photons indistinguishability, paving the way to applications in high-resolution imaging. We assess the experimental results against the ultimate precision bounds as determined by quantum estimation theory. Our experiment ultimately proves that transverse-momentum resolved measurements of fourth-order correlations in the fields can be employed to overcome spatial distinguishability between independent photons. The relevance of our results extends beyond sensing and imaging towards quantum information processing, as we show that partial photon distinguishability and entanglement impurity are not necessarily a nuisance in a technique that relies on two-photon interference.
Photonic quantum metrology has demonstrated advantages in precision and resource efficiency for a wide range of applications, with several schemes approaching the fundamental quantum Cramér-Rao precision bound (QCRB). However, the intrinsic incompatibility of quantum measurements represents a hurdle in extending these advantages to the simultaneous estimation of multiple parameters. In this paper, we present an experimental protocol approaching the QCRB simultaneously in two polarisation parameters, across a wide range of the parameter space, with as few as ∼200\sim 200∼200 photon pairs, offering advantages for polarimetric sensing for dim sources such as in X-ray astronomy or photosensitive samples.
We propose a quantum interferometric protocol that leverages spin-dependent spatial displacements to enable high-precision parameter estimation beyond classical limits. By inducing a unitary coupling between a particle's spin degree of freedom and its momentum, the protocol generates entanglement between spin states and spatial positions, resulting in coherent spatial superpositions. Interferometric reconstruction of the resulting phase differences enables Heisenberg-limited sensitivity for parameters encoded in the spin Hamiltonian. As a concrete application, we demonstrate the protocol's effectiveness in magnetic field sensing, where the field is transduced into spatial interference fringes. Quantum Fisher information analysis confirms sub-shot-noise scaling, and the protocol's feasibility is discussed for physical platforms including ultracold atoms and nitrogen-vacancy centers. Our framework provides a versatile approach to quantum metrology with potential extensions to multiparameter sensing and gravitational wave detection.