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

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