Factor Graphs for Quantum Information Processing

TL;DR

This paper extends classical factor graphs to quantum systems using double-edge and quantum factor graphs, proposing belief-propagation algorithms and applying them to analyze quantum channel capacities.

Contribution

It introduces two novel generalizations of factor graphs for quantum systems and develops belief-propagation algorithms tailored for these models.

Findings

Generalized factor graphs for quantum systems (DeFGs and QFGs)

Algorithms for belief propagation in quantum graphical models

Bounds and optimization methods for quantum channel information rates

Abstract

[...] In this thesis, we are interested in generalizing factor graphs and the relevant methods toward describing quantum systems. Two generalizations of classical graphical models are investigated, namely double-edge factor graphs (DeFGs) and quantum factor graphs (QFGs). Conventionally, a factor in a factor graph represents a nonnegative real-valued local functions. Two different approaches to generalize factors in classical factor graphs yield DeFGs and QFGs, respectively. We proposed/re-proposed and analyzed generalized versions of belief-propagation algorithms for DeFGs/QFGs. As a particular application of the DeFGs, we investigate the information rate and their upper/lower bounds of classical communications over quantum channels with memory. In this study, we also propose a data-driven method for optimizing the upper/lower bounds on information rate.