Riemannian Optimization for Holevo Capacity

• URL: http://arxiv.org/abs/2501.11576v1
• Date: Mon, 20 Jan 2025 16:26:21 GMT
• Title: Riemannian Optimization for Holevo Capacity
• Authors: Chengkai Zhu, Renfeng Peng, Bin Gao, Xin Wang,
• Abstract summary: We formulate the computation of the Holevo capacity as an optimization problem on a product manifold constructed from probability distributions.<n>A gradient gradient descent algorithm is proposed to solve the problem, providing lower bounds on the classical capacity of general quantum channels.
• Score: 5.746235925946808
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Computing the classical capacity of a noisy quantum channel is crucial for understanding the limits of communication over quantum channels. However, its evaluation remains challenging due to the difficulty of computing the Holevo capacity and the even greater difficulty of regularization. In this work, we formulate the computation of the Holevo capacity as an optimization problem on a product manifold constructed from probability distributions and their corresponding pure input states for a quantum channel. A Riemannian gradient descent algorithm is proposed to solve the problem, providing lower bounds on the classical capacity of general quantum channels and outperforming existing methods in numerical experiments in both efficiency and scale.

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