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arXiv:2606.31005 · ACS Photonics

Quantum Imaging via Kurtosis-Difference Weighted Covariance on 2D Camera

Zhe He, Yanli Shi, Hui Wu, Qun Cao, Weidong Zheng, Zheng Cui

quant-phphysics.opticsSubmitted Jun 30, 2026• Announced Jul 1, 2026• 0 citations
v1 · Jun 30, 2026v2 · Oct 26, 2026
arXivHTMLPDF

Abstract

Camera-based quantum imaging detects spatially correlated photon pairs from spontaneous parametric down-conversion (SPDC). Conventional covariance methods typically require tens of thousands of frames to extract weak correlations from noise. While thick crystals can increase photon flux, they generate photon pairs from multiple emission positions within the crystal, producing multiple correlation centers with complex pairing geometries. In addition, conventional covariance methods assume a single pre-selected correlation center and cannot fully exploit these distributed correlations. We demonstrate that kurtosis difference, a fourth-order statistic measuring tail similarity, effectively discriminates correlated pixel pairs even when correlation coefficients remain low. Weighting covariance by an exponential function of absolute kurtosis difference can select symmetric pixels while preserving true coincidences. This kurtosis weighting automatically identifies correlated pairs within a broad search region and accommodates multiple pairing geometries without requiring precise correlation center calibration. At 5000 frames, our method yields a contrast-to-noise ratio (CNR) exceeding 7, whereas standard covariance remains below 2. Compared with standard covariance, the method reduces the acquisition time by 40-fold and could enable practical quantum imaging in sparse correlated-photon regimes.

DOI
10.1021/acsphotonics.6c01982
Comments
27 pages, 12 figures

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Camera-based quantum imaging detects spatially correlated photon pairs from spontaneous parametric down-conversion (SPDC). Conventional covariance methods typically require tens of thousands of frames to extract weak correlations from noise. While thick crystals can increase photon flux, they generate photon pairs from multiple emission positions within the crystal, producing multiple correlation centers with complex pairing geometries. In addition, conventional covariance methods assume a single pre-selected correlation center and cannot fully exploit these distributed correlations. We demonstrate that kurtosis difference, a fourth-order statistic measuring tail similarity, effectively discriminates correlated pixel pairs even when correlation coefficients remain low. Weighting covariance by an exponential function of absolute kurtosis difference can select symmetric pixels while preserving true coincidences. This kurtosis weighting automatically identifies correlated pairs within a broad search region and accommodates multiple pairing geometries without requiring precise correlation center calibration. At 5000 frames, our method yields a contrast-to-noise ratio (CNR) exceeding 7, whereas standard covariance remains below 2. Compared with standard covariance, the method reduces the acquisition time by 40-fold and could enable practical quantum imaging in sparse correlated-photon regimes.
Classical light sources emit a randomly-timed stream of individual photons, the spatial distribution of which can be detected with a camera to form an image. Quantum light sources, based on parametric down conversion, emit photons as correlated photon-pairs. The spatial correlations between the photons enables imaging systems where the preferential selection of photon-pairs allows for enhancements in the noise performance over what is possible using classical light sources. However, until now the technical challenge of measuring, and correlating both photons has led to system complexity. Here we show that a camera capable of resolving the number of individual photons in each pixel of the detector array can be used to record an image formed from these photon-pair events and hence achieve a greater contrast than possible using a classical light source. We achieve an enhancement in the ratio of two-photon events compared to one-photon events using spatially correlated SPDC light compared to uncorrelated illumination by a LED. These results indicate the potential advantages of using photon counting cameras in quantum imaging schemes and these advantages will further increase as the technology is developed. Operating in photon sparse regimes such systems have potential applications in low-light microscopy and covert imaging.
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The spatial correlations between the photon pairs produced by spontaneous parametric down conversion (SPDC) have been investigated in a number of different configurations over the last two decades (1). The high dimensionality of the transverse spatial degrees of freedom (DOF) of the photon pairs can be explored either by projections onto a discrete (infinite) basis, such as the LG modes, or by using a continuous basis defined by the transverse position or momentum of the photons. For instance, it has been shown that their transverse position and momentum display EPR-type correlations (2). Despite the continuous and unbounded nature of both these bases, the most common measurements to date have relied upon the scanning of a single avalanche photodiode or a very small number of individual detectors. This sequential scanning or small number of detectors negates any information capacity advantage in the use of spatial states. Recent years have seen a rapid advance in imaging technologies, particularly for low light levels. Of these technologies the highest quantum efficiency is achieved using electron multiplying CCDs (EMCCD). Developments in low noise EMCCD cameras suggest they are capable of greater than 80% quantum efficiencies and if operated in an ultra-low light environment whilst being maintained at low temperatures, can provide single photon sensitivity (3). EMCCDs have been used in measurements of sub-shot-noise correlations of intensity fluctuations (4, 5) as well as in intensity correlations measurements (6) in the far field of the photon pairs from SPDC. Here we report the observation of spatial correlations from SPDC using an EMCCD camera in both the image and far-field planes of the down conversion crystal. We pump a BBO crystal at 355nm with a few milli-Watts of optical power and use a simple lens system to relay the down-converted light to an EMCCD array which can be positioned in either the image plane or the far-field of the crystal. Our photon flux is around 1/100 per pixel, which approximately doubles the signal obtained when the light is blocked. We typically record 100,000 individual frames and then sum the auto-correlation of the individual frames. We observed intensity correlation and anti-correlation in the image and far-field planes, respectively. In both cases we make the correlations more visible by subtracting a background which is obtained as the average correlation obtained between successive frames. Using this approach we are able to visualize the strength of the correlations in both position and momentum, showing a variance product nearly one order of magnitude below the classical limit in both x and y directions.
Spatially entangled photon pairs (biphotons) generated by spontaneous parametric down-conversion offer unique opportunities for quantum imaging, but image-plane biphoton correlations are difficult to observe with camera-based detectors. Previous camera-based biphoton imaging experiments have relied on photon-counting detection, which necessitates operation deep in the photon-sparse regime and requires extremely low dark rates. Here, we demonstrate the detection of spatial biphoton joint probability distributions in both the image plane and the pupil plane (also termed "near-field plane" and "far-field plane" respectively) using a conventional scientific CMOS camera operated in linear mode. We work at mesoscopic intensity levels, corresponding to a photon flux approximately four orders of magnitude higher than typical photon-counting approaches. From the measured image- and pupil plane correlations, we observe position and momentum correlations consistent with an EPR-type entanglement witness. A tailored correlation analysis suited for image plane imaging suppresses detector artifacts and intensity fluctuations, enabling acquisition with significantly fewer frames. Our results demonstrate that spatially entangled-light imaging can be performed efficiently with standard imaging hardware, extending quantum imaging techniques beyond the photon-counting regime.
Quantum imaging leverages correlations between pairs of photons and has the potential to obtain image information beyond what classical sources provide. Extending this approach to the X-ray regime has been limited by low photon-pair generation rates and the lack of suitable detectors. Here, we demonstrate X-ray coincidence imaging using spontaneous parametric down-conversion (SPDC) and a pixelated area detector with time- and energy-resolved capabilities. This configuration enables simultaneous detection of correlated X-ray photon pairs and coincidence-based imaging of test objects, including a biological specimen. The increased coincidence rate and spatially resolved detection establish a basis for future quantum-enhanced and low-dose X-ray imaging.
Quantum imaging based on the entanglement from spontaneous parametric down-conversion (SPDC) can surpass the classical resolution limit. However, the application is often restricted by slow data acquisition, which requires a large number of frames. Here, we introduce a rapid quantum super-resolution method that integrates biphotons centered symmetrically about multiple spatially shifted positions. While traditional methods relying on biphotons symmetrically distributed around a single center require approximately 200,000 frames to achieve super-resolution imaging with a comparable signal-to-noise ratio (SNR), our approach accomplishes the same with only 10,000 frames. This method enhances the SNR and reduces the data acquisition time by a factor of 20, significantly improving the practicality and efficiency of quantum super-resolution imaging.