Optimizing Bounds on the Classical Information Rate of Quantum Channels with Memory

We are interested in classical communication over a quantum channel with memory, in particular, we are interested in quantum-auxiliary-channel-based upper and lower bounds on the information rate. Toward improving these bounds, we propose efficient algorithms for optimizing the auxiliary channel. From a practical perspective, the lower bounds are of significant interest because they represent mismatched information rates, i.e., information rates that are achievable by a communication system where the decoder is matched to the auxiliary channel, instead of the original channel. Moreover, the auxiliary channels are learned in a data-driven approach, i.e., only input/output sequences of the true channel are needed, but not the channel model of the true channel.