Quantum-Channel Matrix Optimization for Holevo Bound Enhancement

2026-02-18

AI Summary

This work addresses the challenge of reliably transmitting classical information over quantum channels, which is fundamentally limited by the intractability of efficiently computing and optimizing the Holevo bound. While prior approaches typically optimize only the input ensemble for a fixed channel, this paper pioneers a paradigm shift by treating the quantum channel itself as the optimization variable. The authors propose a unified algorithm based on projected gradient ascent that directly optimizes the channel matrix to maximize the Holevo bound for a given input ensemble. Both theoretical analysis and numerical simulations demonstrate that this approach significantly outperforms conventional strategies that restrict optimization to the input ensemble alone, offering a more effective and practical means of enhancing the Holevo bound and thereby improving classical communication capacity over quantum channels.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Non-convex Optimization
• Constraint Satisfaction and Optimization: Constraint Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Quantum communication holds the potential to revolutionize information transmission by enabling secure data exchange that exceeds the limits of classical systems. One of the key performance metrics in quantum information theory, namely the Holevo bound, quantifies the amount of classical information that can be transmitted reliably over a quantum channel. However, computing and optimizing the Holevo bound remains a challenging task due to its dependence on both the quantum input ensemble and the quantum channel. In order to maximize the Holevo bound, we propose a unified projected gradient ascent algorithm to optimize the quantum channel given a fixed input ensemble. We provide a detailed complexity analysis for the proposed algorithm. Simulation results demonstrate that the proposed quantum channel optimization yields higher Holevo bounds than input ensemble optimization.

Problem

• Quantum Channel
• Holevo Bound
• Information Transmission
• Quantum Communication
• Channel Optimization

Innovation

• Quantum channel optimization
• Holevo bound
• Projected gradient ascent
• Quantum information theory
• Quantum communication