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arXiv:2111.03285 · Physical Review Research

Using quantum states of light to probe the retinal network

A. Pedram, Özgür Esat Müstecaplıoğlu, Iannis K. Kominis

Published Jul 19, 2022• 8 citations
arXivHTMLPDF

Abstract

The minimum number of photons necessary for activating the sense of vision has been a topic of research for over a century. The ability of rod cells to sense a few photons has implications for understanding the fundamental capabilities of the human visual and nervous system and creating new vision technologies based on photonics. We investigate the fundamental metrological capabilities of different quantum states of light to probe the retina, which is modeled using a simple neural network. Stimulating the rod cells by Fock, coherent, and thermal states of light, and calculating the Cramer-Rao lower bound and Fisher information matrix for the signal produced by the ganglion cells in various conditions, we determine the volume of minimum error ellipsoid. Comparing the resulting ellipsoid volumes, we determine the metrological performance of different states of light for probing the retinal network. The results indicate that the thermal state yields the largest error ellipsoid volume and hence the worst metrological performance, and the Fock state yields the best performance for all parameters. This advantage persists even if another layer is added to the network or optical losses are considered in the calculations.

DOI
10.1103/physrevresearch.4.033060

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The minimum number of photons necessary for activating the sense of vision has been a topic of research for over a century. The ability of rod cells to sense a few photons has implications for understanding the fundamental capabilities of the human visual and nervous system and creating new vision technologies based on photonics. We investigate the fundamental metrological capabilities of different quantum states of light to probe the retina, which is modeled using a simple neural network. Stimulating the rod cells by Fock, coherent, and thermal states of light, and calculating the Cramer-Rao lower bound and Fisher information matrix for the signal produced by the ganglion cells in various conditions, we determine the volume of minimum error ellipsoid. Comparing the resulting ellipsoid volumes, we determine the metrological performance of different states of light for probing the retinal network. The results indicate that the thermal state yields the largest error ellipsoid volume and hence the worst metrological performance, and the Fock state yields the best performance for all parameters. This advantage persists even if another layer is added to the network or optical losses are considered in the calculations.
The human eye contains millions of rod photoreceptor cells, and each one is a single-photon detector. Whether people can actually see a single photon|which requires the rod signal to propagate through the rest of the noisy visual system and be perceived in the brain|has been the subject of research for nearly 100 years. Early experiments hinted that people could see just a few photons, but classical light sources are poor tools for answering these questions. Single-photon sources have opened up a new area of vision research, providing the best evidence yet that humans can indeed see single photons, and could even be used to test quantum effects through the visual system. We discuss our program to study the lower limits of human vision with a heralded single-photon source based on spontaneous parametric downconversion, and present two proposed experiments to explore quantum effects through the visual system: testing the perception of superposition states, and using a human observer as a detector in a Bell test.
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It was recently proposed to use the human visual system’s ability to perform efficient photon counting in order to devise a new biometric authentication methodology. The relevant “fingerprint” is represented by the optical losses light suffers along different paths from the cornea to the retina. The “fingerprint” is accessed by interrogating a subject on perceiving or not weak light flashes, containing few tens of photons, thus probing the subject’s visual system at the threshold of perception, at which regime optical losses play a significant role. The name “quantum biometrics” derives from the fact that the photon statistics of the illuminating light, as well as the quantum efficiency at the light detection level of rod cells, are central to the method. Here we elaborate further on this methodology, addressing several aspects like aging effects of the method’s “fingerprint,” as well as its inter-subject variability. We then review recent progress towards the experimental realization of the method. Finally, we summarize a recent proposal to use quantum light sources, in particular a single photon source, in order to enhance the performance of the authentication process. This further corroborates the “quantum” character of the methodology and alludes to the emerging field of quantum vision.
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Deep neural networks have been shown to achieve exceptional performance for computer vision tasks like image recognition, segmentation, and reconstruction or denoising. Here, we evaluate the ultimate performance limits of deep convolutional neural network models for image reconstruction, by comparing them against the standard quantum limit set by shot-noise and the Heisenberg limit on precision. We train U-Net models on images of natural objects illuminated with coherent states of light, and find that the average mean-squared error of the reconstructions can surpass the standard quantum limit, and in some cases reaches the Heisenberg limit. Further, we train models on well-parameterized images for which we can calculate the quantum Cramér-Rao bound to determine the minimum possible measurable variance of an estimated parameter for a given probe state. We find the mean-squared error of the model predictions reaches these bounds calculated for the parameters, across a variety of parameterized images. These results suggest that deep convolutional neural networks can learn to become the optimal estimators allowed by the laws of physics, performing parameter estimation and image reconstruction at the ultimate possible limits of precision for the case of classical illumination of the object.