Optimal Binary Codes and Measurements for Classical Communication over Qubit Channels

TL;DR

This paper develops constructive methods to optimize binary classical communication over noisy qubit channels, focusing on error probability and capacity, using orthogonal measurements and coherence vector parametrization for efficient numerical solutions.

Contribution

It introduces a novel parametrization of transition probabilities and demonstrates that optimal measurements are orthogonal, enabling practical numerical optimization for qubit channels.

Findings

Optimal measurements are orthogonal projections.

A coherence vector parametrization simplifies the optimization.

The approach provides insights into the structure of optimal solutions.

Abstract

We propose constructive approaches for the optimization of binary classical communication over a general noisy qubit quantum channel, for both the error probability and the classical capacity functionals. After showing that the optimal measurements are always associated to orthogonal projections, we construct a parametrization of the achievable transition probabilities via the coherence vector representation. We are then able to rewrite the problem in a form that can be solved by standard, efficient numerical algorithms and provides insights on the form of the solutions.