A Blahut-Arimoto Type Algorithm for Computing Classical-Quantum Channel Capacity
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Based on Arimoto's work in 1978, we propose an iterative algorithm for computing the capacity of a discrete memoryless classical-quantum channel with a finite input alphabet and a finite dimensional output, which we call the Blahut-Arimoto algorithm for classical-quantum channel, and an input cost constraint is considered. We show that to reach ε accuracy, the iteration complexity of the algorithm is up bounded by nε/ε where n is the size of the input alphabet. In particular, when the output state {ρ_x}_x∈X is linearly independent in complex matrix space, the algorithm has a geometric convergence. We also show that the algorithm reaches an ε accurate solution with a complexity of O(m^3 nε/ε), and O(m^3ε_(1-δ)ε/D(p^*||p^N_0)) in the special case, where m is the output dimension and D(p^*||p^N_0) is the relative entropy of two distributions and δ is a positive number.
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