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

TL;DR

This paper introduces new flagged extension techniques and a simulation framework to better estimate quantum channel capacities, providing refined bounds and insights into noise thresholds and superadditivity effects.

Contribution

It develops novel flagged extension methods for upper bounds and a numerical simulation approach to evaluate capacities, bridging theoretical bounds with practical estimation.

Findings

Refined upper bounds on quantum capacities using flagged extensions.

Confirmed amplitude damping channel is degradable with single-letter capacity.

Observed superadditivity and zero-capacity thresholds in numerical simulations.

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.