We generalize alternating optimization algorithms of Blahut-Arimoto type to the quantum setting. In particular, we give iterative algorithms to compute the mutual information of quantum channels, the thermodynamic capacity of quantum channels, the coherent information of less noisy quantum channels, and the Holevo quantity of classical-quantum channels. Our convergence analysis is based on quantum entropy inequalities and leads to a priori additive eps-approximations after O(eps^(-1)*log N) iterations, where N denotes the input dimension of the channel. We complement our analysis with an a posteriori stopping criterion which allows us to terminate the algorithm after significantly fewer iterations compared to the a priori criterion in numerical examples. Finally, we discuss heuristics to accelerate the convergence.


Navneeth Ramakrishnan

Imperial College London

Raban Iten

ETH Zurich

Volkher Scholz

Ghent University

Mario Berta

Imperial College London

Session Chair

Marco Tomamichel

National University of Singapore