Quantum Blahut-Arimoto Algorithms

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Quantum Blahut-Arimoto Algorithms

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Creation Date: Jun 21, 2020

Published In: Jun 2020

Paper Type: Conference Paper

Book Title: Proceedings of the 2020 IEEE International Symposium on Information Theory

Address: Los Angeles, CA, USA

Abstract:

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.

Link: https://2020.ieee-isit-virtual.org/presentation/lecture/quantum-blahut-arimoto-algorithms

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