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The optimal discrimination of coherent states of light with currenttechnology is a key problem in classical and quantum communication, whosesolution would enable the realization of efficient receivers for long-distancecommunications in free-space and optical fiber channels. In this article, weshow that reinforcement learning (RL) protocols allow an agent to learnnear-optimal coherent-state receivers made of passive linear optics,photodetectors and classical adaptive control. Each agent is trained and testedin real time over several runs of independent discrimination experiments andhas no knowledge about the energy of the states nor the receiver setup nor thequantum-mechanical laws governing the experiments. Based exclusively on theobserved photodetector outcomes, the agent adaptively chooses among a set of ~310^3 possible receiver setups, and obtains a reward at the end of eachexperiment if its guess is correct. At variance with previous applications ofRL in quantum physics, the information gathered in each run is intrinsicallystochastic and thus insufficient to evaluate exactly the performance of thechosen receiver. Nevertheless, we present families of agents that: (i) discovera receiver beating the best Gaussian receiver after ~3 10^2 experiments; (ii)surpass the cumulative reward of the best Gaussian receiver after ~10^3experiments; (iii) simultaneously discover a near-optimal receiver and attainits cumulative reward after ~10^5 experiments. Our results show that RLtechniques are suitable for on-line control of quantum receivers and can beemployed for long-distance communications over potentially unknown channels.

Real-time calibration of coherent-state receivers: learning by trial and error