Reinforcement-learning calibration of coherent-state receivers on variable-loss optical channels

We study the problem of calibrating a quantum receiver for optical coherent states when transmitted on a quantum optical channel with variable transmissivity, a common model for long-distance optical-fiber and free/deep-space optical communication [1]-[7]. We optimize the error probability of legacy adaptive receivers, such as Kennedy's and Dolinar's [8], [9], on average with respect to the channel transmissivity distribution. We then compare our results with the ultimate error probability attainable by a general quantum device, computing the Helstrom bound for mixtures of coherent-state hypotheses, for the first time to our knowledge, and with homodyne measurements. With these tools, we first analyze the simplest case of two different transmissivity values; we find that the strategies adopted by adaptive receivers exhibit strikingly new features as the difference between the two transmissivities increases. Finally, we employ a recently introduced library of shallow reinforcement learning methods [10], demonstrating that an intelligent agent can learn the optimal receiver setup from scratch by training on repeated communication episodes on the channel with variable transmissivity and receiving rewards if the coherent-state message is correctly identified.