Einstein-Podolsky-Rosen paradox in single pairs of images

Abstract

Spatially entangled twin photons provide a test of the Einstein-Podolsky-Rosen (EPR) paradox in its original form of position (image plane) versus impulsion (Fourier plane). We show that recording a single pair of images in each plane is sufficient to safely demonstrate an EPR paradox. On each pair of images, we have retrieved the fluctuations by subtracting the fitted deterministic intensity shape and then have obtained an intercorrelation peak with a sufficient signal to noise ratio to safely distinguish this peak from random fluctuations. A 95% confidence interval has been determined, confirming a high degree of paradox whatever the considered single pairs. Last, we have verified that the value of the variance of the difference between twin images is always below the quantum (poissonian) limit, in order to ensure the particle character of the demonstration. Our demonstration shows that a single image pattern can reveal the quantum and non-local behavior of light, without any need of averaging after repeating the experiment.Statistical properties of fluctuations in quantum mechanics are described by ensemble averages, which are often estimated by time averages if the signal is stationary in time, but which can also be estimated by spatial averages if the signal is stationary in space on a sufficiently large area. Most of the experiments in quantum imaging record averages of temporal coincidences, i.e. characterize the spatial repartition of temporal averages, rather than spatial averages, with accent on the high dimensionality of the underlying entanglement, in order to demonstrate that an image conveys a great number of spatially correlated quantum (temporal) channels in parallel [1][2][3]. However, patterns in an image are pure spatial information, without any time aspect, that is ultimately degraded by spatial fluctuations of quantum origin in very weak images. Studying these fluctuations involve the use of cameras and needed so far the use of several images to exhibit quantum features. The sub shot-noise nature of the correlation between twin images issued from spontaneous down-conversion has been demonstrated either for a mean of several photons per pixel with low noise charge coupled devices [4,5] or in the photon-counting regime with electron-multiplying charge coupled devices (EM-CCD) [6]. These correlations were subsequently used to improve imaging [7]. In that work, the fluctuations of the idler image were subtracted from the signal image, resulting in an improvement of the image only for a degree of correlation higher than 0.5., attained for slightly more than half of the images. Hence, though the improvement was purely spatial, the use of a set of numerous images was necessary in this experiment, leaving open the question of demonstrating pure spatial quantum effects in single images, without the need of either temporal averages or averages of set of images.The same remark can be applied to our recent demonstration of spatial Einstein-Podolsky-Rosen (EPR) paradox [8]. EPR showed [9] that quantum me...

A Semi-Harmonic Frequency Pattern Organizes Local and Non-Local States by Quantum Entanglement in both EPR-Studies and Life Systems

“…Schrödinger pointed out that the EPR two-particle wave function does not represent the separable form but rather of the entangled form [37]. Experiments carried out to test Bell's inequality during eight decades, therefore, have led to a re-examination of the concepts of quantum mechanics, and revealed the importance of the notion of entanglement and non-locality Many experiments have measured violation of the inferred Heisenberg uncertainty principle, and confirmed EPR-entanglement (see Appendix 1, and Appendix 2).…”

Quality of spatial entanglement propagation

“…(11) of (1.89/1.0) 2 = 3.57. To confirm this behavior, we performed experiments using an electron multiplying CCD (EMCCD) camera, which has both single-photon sensitivity and massively parallel measurement capabilities, making it convenient for biphoton measurements [14,[37][38][39]. A spatially filtered 405 nm CW laser beam pumps a type I SPDC crystal (BBO, L = 3 mm), generating near-collinear entangled photons, and nearly degenerate pairs are selected via spectral filter.…”

Imaging with quantum states of light

“…Cameras allow the characterisation of very high dimensional quantum correlation features [62,63] through the great number of pixels they posses (typically ∼ 300k − 1M pixels) but also they allow the opportunity to perform highly parallel detections of such quantum correlations. Using a similar scheme, the EPR paradox was shown with only a single pair of frames in each of the two configurations (position or momentum detection) [64]. This signifies that no temporal averaging had to be performed in order to detect these features.…”