The Blahut-Arimoto Algorithm for Classical-quantum Channel

A Blahut-Arimoto Type Algorithm for Computing Classical-Quantum Channel Capacity

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 accuracy, the iteration complexity of the algorithm is up bounded by where is the size of the input alphabet.in particular, when the output state is linearlyindependent in complex matrix space, the algorithm has a geometric convergence.We also show that the algorithm reaches an accurate solution with a complexity of and in the special case, where is the output dimension and is the relative entropy of two distributions and is a positive number.