2026-10-22 · arXiv Quantum Physics
arXiv:2610.29373v1 Announce Type: new
Abstract: In this work, we investigate the convergence rate of the quantum Blahut-Arimoto (BA) algorithm proposed for computing the coherent information of less noisy quantum channels. Previous work established exponential convergence under certain restrictive assumptions on the channel. Using a Taylor expansion around a positive definite optimizer, we show that, for an injective degradable channel whose degrading channel has a relative-entropy contraction coefficient strictly less than one, the algorithm converges at an exponential rate after sufficiently many iterations. We further verify this condition for qubit amplitude-damping (AD) channels in the relevant parameter regime.
In addition, by analyzing the Bogoliubov-Kubo-Mori (BKM) metric on the Bloch ball, we derive an explicit characterization of the relative-entropy contraction coefficient of qubit AD channels. The proposed approach is further extended to calculate the relative contraction coefficient and the relative expansion coefficient of two qubit AD channels.
原文链接：https://arxiv.org/abs/2610.29373
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