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arXiv:2409.18803 · Physical Review Research

Verifying energy-time entanglement with irregularly sampled correlations

James Schneeloch, Christopher C. Tison, Richard J. Birrittella, Ian Brinkley, Michael L. Fanto, Paul M. Alsing

Published Jul 14, 2025• 0 citations

Abstract

Verifying entanglement with experimental measurements requires that we take the limitations of experimental techniques into account, while still proving that the data obtained could not have been generated from a classical source. In the energy-time degree of freedom, this challenge is exacerbated because realistic high-resolution frequency measurements are obtained as a function of light passing through arbitrary filters positioned at uneven intervals. In this work, we show how the data gathered from these kinds of measurements can be used to fully certify the degree of energy and timing correlations needed to certify energy-time entanglement without having to make special assumptions about the state or the measurement device. We accomplish this by showing how to construct a continuous-variable probability density from the data that can closely estimate, but never overestimate the correlations (and entanglement) actually present in the system, and note that these methods are applicable to all continuous-variable degrees of freedom (e.g., spatial, field quadratures, etc.). We illustrate the feasibility of these methods using frequency and timing correlations obtainable from photon pairs in spontaneous parametric down-conversion.

DOI: 10.1103/6nws-mlgs

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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 lay down a general scheme to quantify the amount of genuine tripartite entanglement present in the spatial and energy-time degrees of freedom of entangled photon triplets using a resource-based measure known as the tripartite entanglement of formation. Quantifying genuine tripartite entanglement relative to a number of maximally entangled three-qubit Greenberger-Horne-Zeilinger (GHZ) states called gebits, the tripartite entanglement of formation serves as a basis of comparison between different tripartite entangled states of differing dimension. Demonstrating genuine tripartite entanglement is doubly challenging because it is not enough to show that each party is inseparable from the other two (which is sufficient only for pure states). Instead, one must rule out all mixtures of all combinations of biseparable states from describing the tripartite state. To meet this challenge, we use entropic measures of the statistics of tripartite systems to simultaneously bound the correlations each party has with the other two, and in so doing place a lower limit to the tripartite entanglement of formation. Even though our measure never over-estimates the entanglement present, we estimate the effectiveness of our technique by determining the exact tripartite entanglement of a triple-gaussian triphoton wavefunction with the same correlations as seen in photon triplets generated in third-order spontaneous parametric down-conversion (SPDC). Between these two efforts, we show that a substantial amount of tripartite entanglement exists in both the spatial and energy-time degrees of freedom of these systems, and propose an experiment that can measure them.

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