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arXiv:2209.06693 · Journal of the Optical Society of America A

Quantum detector tomography applied to the human visual system: a feasibility study

Thomas H. A. van der Reep, Dylan Molenaar, W. Löffler, Yaïr Pinto

Published Dec 16, 2022• 2 citations
arXivHTMLPDF

Abstract

We show that quantum detector tomography can be applied to the human visual system to explore human perception of photon number states. In detector tomography, instead of using very hard-to-produce photon number states, the response of a detector to light pulses with known photon statistics of varying intensity is recorded, and a model is fitted to the experimental outcomes, thereby inferring the detector's photon number state response. Generally, light pulses containing a Poisson-distributed number of photons are utilized, which are very easy to produce in the lab. This technique has not been explored to study the human visual system before because it usually requires a very large number of repetitions not suitable for experiments on humans. Yet, in the present study we show that detector tomography is feasible for human experiments. Assuming a simple model for this accuracy, the results of our simulations show that detector tomography is able to reconstruct the model using Bayesian inference with as few as 5000 trials. We then optimize the experimental parameters in order to maximize the probability of showing that the single-photon accuracy is above chance. As such, our study opens the road to study human perception on the quantum level.

DOI
10.1364/josaa.477639

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We show that quantum detector tomography can be applied to the human visual system to explore human perception of photon number states. In detector tomography, instead of using very hard-to-produce photon number states, the response of a detector to light pulses with known photon statistics of varying intensity is recorded, and a model is fitted to the experimental outcomes, thereby inferring the detector's photon number state response. Generally, light pulses containing a Poisson-distributed number of photons are utilized, which are very easy to produce in the lab. This technique has not been explored to study the human visual system before because it usually requires a very large number of repetitions not suitable for experiments on humans. Yet, in the present study we show that detector tomography is feasible for human experiments. Assuming a simple model for this accuracy, the results of our simulations show that detector tomography is able to reconstruct the model using Bayesian inference with as few as 5000 trials. We then optimize the experimental parameters in order to maximize the probability of showing that the single-photon accuracy is above chance. As such, our study opens the road to study human perception on the quantum level.
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.
Photon-number-resolving detectors with hundreds of pixels are now readily available, while the characterization of these detectors using detector tomography is computationally intensive. Here, we present a modified detector tomography model that reduces the number of variables that need optimization. To evaluate the effectiveness and accuracy of our model, we reconstruct the photon number distribution of optical coherent and thermal states using the expectation-maximization-entropy algorithm. Our results indicate that the fidelity of the reconstructed states remains above 99%, and the second- and third-order correlations agree well with the theoretical values for a mean number of photons up to 100. We also investigate the computational resources required for detector tomography and find out that our approach reduces the solving time by around half compared to the standard detector tomography approach, and the required memory resources are the main obstacle for detector tomography of a large number of pixels. Our results suggest that detector tomography is viable on a supercomputer with 1 TB RAM for detectors with up to 340 pixels.
We discuss our progress towards testing whether humans can see single photons, using a single-photon source based on spontaneous parametric downconversion and techniques from quantum optics. We review the existing evidence on single-photon vision, and show why no previous experiments with classical light sources (or otherwise) have truly been able to test it. We describe the heralded single-photon source we have built, which can be used for a definitive single-photon vision test, and discuss the statistical requirements and challenges of such a test. In pilot studies, we demonstrate that a two-alternative forced-choice design and our observer viewing station can measure the perception of very weak visual stimuli (including the weakest flashes of light ever directly tested, with just ~3 photons absorbed). We present two proposed experiments to test quantum effects through the visual system, which could contribute to our understanding of wavefunction collapse and the quantum-classical transition. We also discuss our work on other questions related to visual perception near threshold, including the length and completeness of temporal summation, which we have investigated in detail with a new experimental paradigm. We found that temporal summation continues for at least 650 ms when photons are delivered at a rate of about 30 in 100 ms, and that the completeness of summation may remain efficient over this window. Finally, we present some preliminary results on how 8- to 13-Hz alpha oscillations in the brain (which have complex effects on neural excitability and visual perception) might impact the detection of few-photon stimuli.
Measurement is the only part of a general quantum system that has yet to be characterised experimentally in a complete manner. Detector tomography provides a procedure for doing just this; an arbitrary measurement device can be fully characterised, and thus calibrated, in a systematic way without access to its components or its design. The result is a reconstructed POVM containing the measurement operators associated with each measurement outcome. We consider two detectors, a single-photon detector and a photon-number counter, and propose an easily realised experimental apparatus to perform detector tomography on them. We also present a method of visualising the resulting measurement operators.
The rod photoreceptors in the retina are known to be sensitive to single photons, but it has long been debated whether these single-photon signals propagate through the rest of the visual system and lead to perception. Recently, single-photon sources developed in the field of quantum optics have enabled direct tests of single-photon vision that were not possible with classical light sources. Using a heralded source based on spontaneous parametric downconversion to generate single photons which were sent to an observer at either an early or late time, Tinsley and Molodtsov et al. (2016) had observers judge when the photon was seen. Based on the above-chance accuracy in both a subset of high-confidence trials and in all post-selected trials, they claimed to show that humans can see single photons. However, we argue that this work suffers from three major issues: self-contradicting results, inappropriate statistical analyses, and a critical lack of statistical power. As a result, we cannot conclude that humans can see single photons based on the data of this study. We present a careful examination of the statistical analyses and the internal consistency of the data, which indicated that none of the key evidence holds.
Abstract We address state reconstruction by photon-number-resolving detectors, and demonstrate that they may be effectively exploited to perform quantum tomography of states of light. In particular, we find that the pattern function technique, originally developed for optical homodyne tomography, may be also applied to discrete data. Our results open new perspectives for quantum-state reconstruction in the mesoscopic regime, and pave the way to the use of photon-number-resolving-based detection schemes in Quantum Information science.