Factor Graphs for Quantum Probabilities
This provides a novel mathematical framework for quantum probabilities, potentially aiding researchers in quantum information and foundations, but it appears incremental as it builds on existing factor-graph concepts.
The paper tackles the representation of quantum-mechanical probabilities by proposing a factor-graph model using auxiliary state variables, demonstrating that all joint distributions are marginals of a complex-valued function and relating quantum concepts to factorizations and marginals.
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 $q$.