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

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 utilised, 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 little as $5000$ trials. We then optimize the experimental parameters in order to maximise the probability of showing that the single-photon accuracy is above chance. As such, our study opens the road to study human perception on quantum level.