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arXiv:2607.24718

Coincidence free certification and quantification of spatial entanglement with stimulated parametric down conversion

M. G. Damaceno, G. H. dos Santos, N. Rubiano da Silva, S. P. Walborn, P. H. Souto Ribeiro

quant-phphysics.opticsSubmitted Jul 27, 2026• Announced Jul 28, 2026• 0 citations
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Abstract

Using stimulated emission, a photon pair source can be characterized by seeding the signal mode with a bright classical beam and measuring the stimulated idler field, thus replacing two-photon coincidence counting with classical intensity detection. We apply this approach to the continuous transverse spatial degrees of freedom of a down conversion source and show that it is possible to certify spatial entanglement with only intensity measurements. We demonstrate this capability through variance-based entanglement and steering witnesses, as well as the Fedorov ratio. This method is useful for studying entanglement properties of photon pair sources in conditions where alignment and photon counting measurements are difficult and time-consuming.

Comments
8 pages, 8 figures

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Using stimulated emission, a photon pair source can be characterized by seeding the signal mode with a bright classical beam and measuring the stimulated idler field, thus replacing two-photon coincidence counting with classical intensity detection. We apply this approach to the continuous transverse spatial degrees of freedom of a down conversion source and show that it is possible to certify spatial entanglement with only intensity measurements. We demonstrate this capability through variance-based entanglement and steering witnesses, as well as the Fedorov ratio. This method is useful for studying entanglement properties of photon pair sources in conditions where alignment and photon counting measurements are difficult and time-consuming.
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We verify transverse spatial entanglement of photon-pairs generated in spontaneous parametric down conversion using a nonlinear interferometric technique without relying on any coincidence detection. We experimentally demonstrate the violation of the Einstein-Podolsky-Rosen criterion and of the Mancini-Giovannetti-Vitali-Tombesi criterion using single photon interference of one of the photons of the pairs. We also provide a comprehensive theoretical analysis. The experimental results that we have obtained show good agreement with the theoretical values. Our method performs well under experimental losses and can be applied to highly non-degenerate sources, where there are no suitable detectors for one of the photons in the quantum state and our method could also be extended to the discrete degrees of freedom to certify high-dimensional (OAM) entanglement.
We verify transverse spatial entanglement of photon pairs generated in spontaneous parametric down conversion using a nonlinear interferometric technique without relying on any coincidence detection. We experimentally demonstrate the violation of the Einstein-Podolsky-Rosen criterion and of the Mancini-Giovannetti-Vitali-Tombesi criterion using single photon interference of one of the photons of the pairs. We also provide a comprehensive theoretical analysis. Our method performs well under experimental losses and can be applied to highly non-degenerate sources, where there are no suitable detectors for one of the photons in the quantum state, and our method could also be extended to the discrete degrees of freedom to certify high-dimensional entanglement.
We measure the transverse entanglement of photon pairs on their propagation from the near to the far field of spontaneous parametric down-conversion (SPDC). The Fedorov ratio, depending on the widths of conditional and unconditional intensity measurements, is shown to be only able to characterize entanglement in the near and far field zones of the source. Therefore we also follow a different approach. By evaluating the first-order coherence of a subsystem of the state we can quantify its entanglement. Unlike previous measurements, which determine the Fedorov ratio via intensity correlations, our setup is sensitive to both phase and modulus of the biphoton state and thus always grants experimental access to the full transverse entanglement of the SPDC state. It is shown theoretically that this scheme represents a direct measurement of the Schmidt number.
We characterize the entanglement in position and momentum of photon pairs generated in type-II parametric down-conversion. Coincidence maps of the photon positions in the near-field and far-field planes are observed in two transverse dimensions using scanning fiber probes. We estimate the covariance matrix of an effective two-mode system and apply criteria for entanglement based on covariance matrices to certify space–momentum entanglement. The role of higher-order spatial modes for observing spatial entanglement between the two photons is discussed.