Spatial correlations between two photons are the key resource in realising many quantum imaging schemes. Measurement of the bi-photon correlation map is typically performed using single-point scanning detectors or single-photon cameras based on charged coupled device (CCD) technology. However, both approaches are limited in speed due to the slow scanning and the low frame rate of CCD-based cameras, resulting in data acquisition times on the order of many hours. Here, we employ a high frame rate, single-photon avalanche diode (SPAD) camera, to measure the spatial joint probability distribution of a bi-photon state produced by spontaneous parametric down-conversion, with statistics taken over 107 frames. Through violation of an Einstein–Podolsky–Rosen criterion by 227 sigmas, we confirm the presence of spatial entanglement between our photon pairs. Furthermore, we certify, in just 140 s, an entanglement dimensionality of 48. Our work demonstrates the potential of SPAD cameras in the rapid characterisation of photonic entanglement, leading the way towards real-time quantum imaging and quantum information processing.

Traditional paradigms for imaging rely on the use of a spatial structure, either in the detector (pixels arrays) or in the illumination (patterned light). Removal of the spatial structure in the detector or illumination, i.e., imaging with just a single-point sensor, would require solving a very strongly ill-posed inverse retrieval problem that to date has not been solved. Here, we demonstrate a data-driven approach in which full 3D information is obtained with just a single-point, single-photon avalanche diode that records the arrival time of photons reflected from a scene that is illuminated with short pulses of light. Imaging with single-point time-of-flight (temporal) data opens new routes in terms of speed, size, and functionality. As an example, we show how the training based on an optical time-of-flight camera enables a compact radio-frequency impulse radio detection and ranging transceiver to provide 3D images. Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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The propagation of monochromatic light through a scattering medium produces speckle patterns in reflection and transmission, and the apparent randomness of these patterns prevents direct imaging through thick turbid media. Yet, since elastic multiple scattering is fundamentally a linear and deterministic process, information is not lost but distributed among many degrees of freedom that can be resolved and manipulated.Here we demonstrate experimentally that the reflected and transmitted speckle patterns are correlated, even for opaque media with thickness much larger than the transport mean free path, proving that information survives the multiple scattering process and can be recovered. The existence of mutual information between the two sides of a scattering medium opens up new possibilities for the control of transmitted light without any feedback from the target side, but using only information gathered from the reflected speckle.In multiply scattering materials, the random inhomogeneities in the refractive index scramble the incident wavefront, mixing colors and spatial degrees of freedom, resulting in a white and opaque appearance [1]. Under illumination with coherent light and for elastic scattering, interference produces large intensity fluctuations that is not averaged out by a single realization of the disorder, resulting in a seemingly random speckle pattern [2]. In principle the speckle pattern encodes all the information on the sample and the incident light [3]. A complete knowledge of the scattering matrix allows one to reverse the multiple scattering process and to recover the initial wavefront, thus permitting imaging through turbid materials [4,5]. Conversely, if the scattering matrix is not known, a multiply scattering material effectively behaves as an opaque screen.Speckle patterns are not as random as they appear at first sight. Interference between the possible scattering paths in the medium are known to produce spatial correlations between the intensity measured at different positions [6][7][8], and correlations of different ranges have been identified [9]. Short-range correlations determine the size of a speckle spot. Long-range correlations emerge as a consequence of constraints such as energy conservation or reciprocity [10][11][12]. Spatial correlations have not been used for imaging, a notable exception being the optical memory effect [13], a correlation of purely geometrical origin that has been exploited for non-invasive imaging through an opaque scattering layer [14,15].At first glance, as transmitted and reflected waves are expected to undergo very different multiple scattering sequences, correlations between transmitted and reflected wavefronts are expected to quickly average to zero. Very little attention has been given to cross-correlations between transmitted and reflected speckles, their existence being only mentionned in passing [16,17]. However, a recent theoretical study suggested that a long-range correlation should survive even for thick (opaque) scattering media [18]. Th...

Ghost imaging is an unconventional optical imaging technique that reconstructs the shape of an object combining the measurement of two signals: one that interacted with the object, but without any spatial information, the other containing spatial information, but that never interacted with the object [1,2]. Ghost imaging is a very flexible technique, that has been generalized to the singlephoton regime [3], to the time domain [4], to infrared and terahertz frequencies [5], and many more conditions [6]. Here we demonstrate that ghost imaging can be performed without ever knowing the patterns illuminating the object, but using patterns correlated with them, doesn't matter how weakly. As an experimental proof we exploit the recently discovered correlation between the reflected and transmitted light from a scattering layer [7,8], and reconstruct the image of an object hidden behind a scattering layer using only the reflected light, which never interacts with the object. This method opens new perspectives for non-invasive imaging behind or within turbid media.