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We generalize the quantum Arimoto-Blahut algorithm by Ramakrishnan et al.(IEEE Trans. IT, 67, 946 (2021)) to a function defined over a set of densitymatrices with linear constraints so that our algorithm can be applied tooptimizations of quantum operations. This algorithm has wider applicability.Hence, we apply our algorithm to the quantum information bottleneck with threequantum systems, which can be used for quantum learning. We numerically compareour obtained algorithm with the existing algorithm by Grimsmo and Still (Phys.Rev. A, 94, 012338 (2016)). Our numerical analysis shows that our algorithm isbetter than their algorithm.

Generalized quantum Arimoto-Blahut algorithm and its application to quantum information bottleneck