Pauli Channel Online Estimation Protocol for Quantum Turbo Codes

In this paper, we tackle the channel estimation problem for Pauli channels. Online estimation methods for the depolarizing channel have been proposed in previous literature. However, realistic quantum devices often exhibit an asymmetric behaviour not captured by the symmetric depolarizing model, implying that the estimation method used by Quantum Turbo Codes (QTC) should exploit such asymmetry for the error correcting operations to be successful. Consequently, we propose an online iterative method that aids in successfully estimating each of the individual error probabilities associated with the Pauli channel, ultimately increasing the probability of correct decoding. The benefits this method provides come at the expense of an increase in the decoding complexity.