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arXiv:2511.12546 · Newton

Sparsity-Driven Entanglement Detection in High-Dimensional Quantum States

Stav Lotan, Hugo Defienne, Ronen Talmon, Guy Bartal

quant-phphysics.opticsSubmitted Nov 16, 2025• Announced Nov 18, 2025• 0 citations
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Abstract

The characterization of high-dimensional quantum entanglement is crucial for advanced quantum computing and quantum information algorithms. Traditional methods require extensive data acquisition and suffer from limited visibility due to experimental noise. Here, we introduce a sparsity-driven framework to enhance the detection and certification of high-dimensional entanglement in spatially entangled photon pairs. By applying $\ell_1$-regularized reconstruction to sample covariance matrices obtained from measurements on photons produced via spontaneous parametric down-conversion (SPDC) measurements, we enhance the visibility of the correlation signal while suppressing noise. We demonstrate, using a position-momentum Einstein-Podolsky-Rosen (EPR) entanglement criterion, that this approach enables certification of an entanglement dimensionality that cannot be achieved without regularization. Our method is scalable, simple to use and compatible with existing quantum-optics platforms, thus paves the way for efficient, real-time analysis of high-dimensional quantum states.

Comments
8 pages, 10 figures

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The characterization of high-dimensional quantum entanglement is crucial for advanced quantum computing and quantum information algorithms. Traditional methods require extensive data acquisition and suffer from limited visibility due to experimental noise. Here, we introduce a sparsity-driven framework to enhance the detection and certification of high-dimensional entanglement in spatially entangled photon pairs. By applying ℓ1\ell_1ℓ1​-regularized reconstruction to sample covariance matrices obtained from measurements on photons produced via spontaneous parametric down-conversion (SPDC) measurements, we enhance the visibility of the correlation signal while suppressing noise. We demonstrate, using a position-momentum Einstein-Podolsky-Rosen (EPR) entanglement criterion, that this approach enables certification of an entanglement dimensionality that cannot be achieved without regularization. Our method is scalable, simple to use and compatible with existing quantum-optics platforms, thus paves the way for efficient, real-time analysis of high-dimensional quantum states.
Abstract The successful employment of high-dimensional quantum correlations and its integration in telecommunication infrastructures is vital in cutting-edge quantum technologies for increasing robustness and key generation rate. Position-momentum Einstein-Podolsky-Rosen (EPR) entanglement of photon pairs are a promising resource of such high-dimensional quantum correlations. Here, we experimentally certify EPR correlations of photon pairs generated by spontaneous parametric down-conversion (SPDC) in a nonlinear crystal with type-0 phase-matching at telecommunication wavelength for the first time. To experimentally observe EPR entanglement, we perform scanning measurements in the near- and far-field planes of the signal and idler modes. We certify EPR correlations with high statistical significance of up to 45 standard deviations. Furthermore, we determine the entanglement of formation of our source to be greater than one, indicating a dimensionality of greater than 2. Operating at telecommunication wavelengths around 1550 nm, our source is compatible with today’s deployed telecommunication infrastructure, thus paving the way for integrating sources of high-dimensional entanglement into quantum-communication infrastructures.
The successful employment of high-dimensional quantum correlations and its integration in telecommunication infrastructures is vital in cutting-edge quantum technologies for increasing robustness and key generation rate. Position-momentum Einstein-Podolsky-Rosen (EPR) entanglement of photon pairs are a promising resource of such high-dimensional quantum correlations. Here, we experimentally certify EPR correlations of photon pairs generated by spontaneous parametric down-conversion (SPDC) in a nonlinear crystal with type-0 phase-matching at telecom wavelength for the first time. To experimentally observe EPR entanglement, we perform scanning measurements in the near- and far-field planes of the signal and idler modes. We certify EPR correlations with high statistical significance of up to 45 standard deviations. Furthermore, we determine the entanglement of formation of our source to be greater than one, which gives evidence for the the high-dimensional entanglement between the photons. Operating at telecom wavelengths around 1550 nm, our source is compatible with today's deployed telecommunication infrastructure, thus paving the way for integrating sources of high-dimensional entanglement into quantum-communication infrastructures.
High-dimensional entanglement is a promising resource for quantum technologies. Being able to certify it for any quantum state is essential. However, to date, experimental entanglement certification methods are imperfect and leave some loopholes open. Using a single-photon-sensitive time-stamping camera, we quantify high-dimensional spatial entanglement by collecting all output modes and without background subtraction, two critical steps on the route toward assumptions-free entanglement certification. We show position-momentum Einstein-Podolsky-Rosen (EPR) correlations and quantify the entanglement of formation of our source to be larger than 2.8 along both transverse spatial axes, indicating a dimension higher than 14. Our work overcomes important challenges in photonic entanglement quantification and paves the way toward the development of practical quantum information processing protocols based on high-dimensional entanglement.
High-dimensional entanglement is a promising resource for quantum technologies [1], [2]. Being able to certify it for any quantum state is essential. However, to date, experimental entanglement certification methods are imperfect and leave some loopholes open, due to the presence of accidental coincidences and the hypotheses necessary for their subtraction in post-processing [3], [4]. We present here an experimental study of the role of these accidentals depending on the temporal resolution of the coincidence detection apparatus. Our results show that high-dimensional entanglement certification can be achieved without accidental subtraction using current single-photon camera technologies. Using the recently developed time-stamping Tpx3Cam camera [5], we certify high-dimensional entanglement without accidental subtraction in under 16 seconds. In our experiment, we measure position-momentum Einstein-Podolsky-Rosen (EPR) [6] correlations in pairs of photons generated by Spontaneous Parametric Down Conversion (SPDC) by collecting all spatial output modes simultaneously on the camera. We achieved an EPR factor of0.13<1/20.13 < 1/20.13<1/2, which allows us to certify entanglement.
We implement a double-pixel compressive-sensing camera to efficiently characterize, at high resolution, the spatially entangled fields that are produced by spontaneous parametric down-conversion.This technique leverages sparsity in spatial correlations between entangled photons to improve acquisition times over raster scanning by a scaling factor up to n 2 = logðnÞ for n-dimensional images.We image at resolutions up to 1024 dimensions per detector and demonstrate a channel capacity of 8.4 bits per photon.By comparing the entangled photons' classical mutual information in conjugate bases, we violate an entropic Einstein-Podolsky-Rosen separability criterion for all measured resolutions.More broadly, our result indicates that compressive sensing can be especially effective for higher-order measurements on correlated systems.
High-dimensional entangled states, such as spatially-entangled photon pairs produced by Spontaneous Parametric Down-Conversion (SPDC), are a key resource for quantum technologies. In recent years, camera-based coincidence counting approaches have considerably improved the ability to characterize them in terms of speed and dimensionality. However, these methods have limitations, including in most of them the necessity to subtract accidental coincidences. Here, we study the role of these accidentals in entanglement certification for a single-photon avalanche diode (SPAD) array and an intensified time-stamping (Tpx3Cam) camera. Using both Einstein-Podolsky-Rosen (EPR) and entropy-based criteria, we show that the level of accidental coincidences - determined by the temporal characteristics of the camera - and whether they are subtracted critically impact entanglement certification. In particular, we demonstrate that current single-photon camera technologies enable entanglement certification without accidental subtraction only if a Gaussian approximation is applied to the measured two-photon state. Our work is important for developing quantum-optics application in adversarial scenarios, such as high-dimensional quantum key distribution (HD-QKD), and also for loophole-free experimental testing of quantum foundations.