A probabilistic-statistical model of quantum mechanics

B. Freedman. Physics Department

Jincheng Zhang

Quantum entanglement, a fundamental phenomenon in quantum mechanics, offers a unique approach to probability distribution modeling. This paper explores the potential of harnessing this principle to create novel statistical frameworks, specifically designed to capture probabilistic systems with strong correlations. We introduce a novel algorithm predicated on quantum entanglement, aiming to move beyond traditional deterministic models by enabling inherent, non-deterministic probabilistic behavior. The core claim is that this framework provides a pathway towards improved precision in modeling complex probabilistic systems. The paper details the algorithm's mechanism, highlighting its potential advantages over existing probabilistic models. This work contributes to a growing body of research exploring the application of quantum mechanics to statistical analysis and modeling.

Michael J. Creutz, Barry A. Freedman

Theory

Quantum mechanics is a statistical theory (see, e.g., Margenau [239, 240], Ballentine [25, 26], Klyshko [216], Holevo [115, 116], Khrennikov [192]). It cannot tell us anything about an individual quantum system, e.g., an electron or a photon. It predicts only probabilities for results of measurements for large ensembles of quantum systems. Classical statistical mechanics (CSM) does the same.Why are QM and CSM based on different probabilistic models?

Kazuyuki Tanaka

Abstract We review sublinear modeling in probabilistic graphical models by statistical mechanical informatics and statistical machine learning theory. Our statistical mechanical informatics schemes are based on advanced mean-field methods including loopy belief propagations. This chapter explores how phase transitions appear in loopy belief propagations for prior probabilistic graphical models. The frameworks are mainly explained for loopy belief propagations in the Ising model which is one of the elementary versions of probabilistic graphical models. We also expand the schemes to quantum statistical machine learning theory. Our framework can provide us with sublinear modeling based on the momentum space renormalization group methods.

James S. Albertson