Factor Graphs for Quantum Probabilities

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 marg...

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Bibliographic Details
Published in:IEEE transactions on information theory 2017-09, Vol.63 (9), p.5642-5665
Main Authors: Loeliger, Hans-Andrea, Vontobel, Pascal O.
Format: Article
Language:English
Subjects:
closing-the-box operation
factor graphs
Graph representations
graphical models
Graphical representations
Hidden Markov models
marginalization
Probability distribution
quantum coding
Quantum mechanics
Random variables
State variable
Statistical analysis
Statistical models
Tensile stress
tensor networks
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Summary: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.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2017.2716422