Factor Graphs for Quantum Probabilities

TL;DR

This paper introduces a novel factor-graph framework for representing quantum probabilities, utilizing auxiliary variables and complex functions to connect quantum mechanics concepts with graphical models.

Contribution

It proposes a new factor-graph representation for quantum probabilities that incorporates non-random auxiliary variables and complex-valued functions, differing from traditional statistical models.

Findings

Joint quantum probabilities are marginals of a complex function q.

The framework relates quantum concepts to factorizations and marginals of q.

The representation accommodates any number of measurements.

Abstract

A factor-graph representation of quantum-mechanical probabilities (involving any number of measurements) is proposed. Unlike standard statistical models, the proposed representation uses auxiliary variables (state variables) that are not random variables. All joint probability distributions are marginals of some complex-valued function $q$, and it is demonstrated how the basic concepts of quantum mechanics relate to factorizations and marginals of $q$.