The Standard Statistical Model of Quantum Mechanics

Claudio Garola, Sandro Sozzo, Claudio Calosi

The belief that quantum mechanics (QM) does not admit a realistic interpretation is widespread. According to some scholars concerned with the foundations of QM all existing interpretations of this theory (except for the statistical interpretation) presuppose instead a form of realism which consists in assuming that QM deals with individual objects and their properties. We uphold in the present paper that the arguments supporting the contextuality and the nonlocality of QM are a significant clue to the implicit adoption of stronger forms of realism (realism of theoretical entities and realism of theories). If these kinds of realism are substituted by a simpler and more intuitive semantic realism one can contrive a noncontextual and local interpretation of the formalism of QM (SR interpretation). Moreover one can provide a model for such an interpretation (ESR model) in which local realism and QM do not conflict and some fundamental problems of the standard interpretation of QM are avoided.

Ola Bratteli, Derek W. Robinson

Hans‐Andrea Loeliger, Pascal O. Vontobel

A factor-graph representation of quantum-mechanical probabilities is proposed. Unlike standard statistical models, the proposed representation uses auxiliary variables (state variables) that are not random variables.

Carl S. Helrich

Evgenii Igorevich Zelenov

A p -adic realization of the standard statistical model of quantum mechanics is constructed. Within this realization, a p -adic linear bosonic channel is defined, and its properties are analyzed. In particular, a criterion for the existence of a linear Gaussian bosonic channel is obtained, and its explicit construction is described. It is shown that the p -adic Gaussian bosonic channels possess an additivity property.

Ivo Sachs, Siddhartha Sen, James Sexton