A Pauli channel is defined as a convex combination of Pauli operators, i.e. $\epsilon_{Pauli} (\rho)=\sum_{j} q_j\sigma_j\rho \sigma_j$, where $0 \leq q_j \leq 1$ and $\sum_j q_j=1$. Now, I have to transmit firstly pure state Qubit through it and then Bell state. Please hint me towards the mathematics I should start working on. Thanks.