Simultaneous Communication and Parameter Estimation of Pauli Channels

We propose a scheme for simultaneous classical communication and parameter estimation of generalized Pauli channels. This framework relies on the facts that i) under certain conditions, Pauli channels act as classical symmetric channel, and ii) a recently proposed parameter estimation method of Pauli channels can be executed while satisfying the conditions of i). The performance of the parameter estimation part in this simultaneous scheme relies on the symbol error rate of the communication module. This reliance gives rise to a natural tradeoff between the communication rate and the performance of parameter estimation in this simultaneous scheme. We exemplify our protocol by utilizing repetition codes for communication and the aforementioned parameter estimation scheme for the characterization of the channel at hand. We explore the tradeoff behavior between the communication rate and the performance of parameter estimation in the numerical examples. Our proposal paves the way for practical methods in simultaneous communication and channel estimation over unknown quantum channels.