Algorithm 1 Blahut–Arimoto algorithm for discrete memoryless classical-quantum channel.

set $p_x^0=\frac{1}{\left|\mathcal{X}\right|}$, $x\in \mathcal{X}$; repeat     $p_x^{{}^{\prime }t}=p_x^t;$     $p_x^{t+1}=\frac{r_x^t}{{\sum }_x{r}_x^t}$, where $r_x^t=exp(\mathrm{Tr}\left\{{\rho }_x[log\left(p_x^t{\rho }_x\right)-log{\rho }^t]\right\}-s_x\lambda )$;    until convergence.