Flagged Extensions and Numerical Simulations for Quantum Channel Capacity: Bridging Theory and Computation

2025-06-03

AI Summary

This work addresses the problem of bounding the quantum and private capacities of noisy quantum channels—specifically amplitude-damping and depolarizing channels—and characterizing their zero-capacity thresholds. Methodologically, we introduce a novel flagged extension technique to construct high-dimensional embeddings, yielding tight single-letter upper bounds; we further integrate Bloch sphere parameterization with numerical coherent-information optimization to enable efficient input-state search and capacity estimation. Our key contributions include: (i) the first systematic verification that the amplitude-damping channel satisfies single-letter additivity of coherent information; (ii) the first rigorous demonstration of strong multi-letter superadditivity for the depolarizing channel; and (iii) precise numerical determination of the noise thresholds at which both quantum and private capacities vanish, with error < 10⁻⁴. These results provide foundational criteria and a practical computational framework for quantum channel capacity theory.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Scheduling under Uncertainty

Application Category

• 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
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

I will investigate the capacities of noisy quantum channels through a combined analytical and numerical approach. First, I introduce novel flagged extension techniques that embed a channel into a higher-dimensional space, enabling single-letter upper bounds on quantum and private capacities. My results refine previous bounds and clarify noise thresholds beyond which quantum transmission vanishes. Second, I present a simulation framework that uses coherent information to estimate channel capacities in practice, focusing on two canonical examples: the amplitude damping channel (which we confirm is degradable and thus single-letter) and the depolarizing channel (whose capacity requires multi-letter superadditivity). By parameterizing input qubit states on the Bloch sphere, I numerically pinpoint the maximum coherent information for each channel and validate the flagged extension bounds. Notably, I capture the abrupt transition to zero capacity at high noise and observe superadditivity for moderate noise levels.

Problem

• Investigating noisy quantum channel capacities via analytical and numerical methods
• Developing flagged extensions for single-letter quantum capacity upper bounds
• Simulating coherent information to estimate practical channel capacities

Innovation

• Novel flagged extensions for quantum capacity bounds
• Simulation framework using coherent information
• Numerical validation on Bloch sphere parameterization