Quantum theory within the probability calculus: a there-you-go theorem and partially exchangeable models

TL;DR

This paper argues that quantum mechanics does not violate classical probability laws and demonstrates that quantum inferences can be modeled as partially exchangeable statistical models with specific prior constraints.

Contribution

It shows that quantum theory aligns with classical probability through partially exchangeable models and advocates for dialogue between quantum physics and exchangeable statistical models.

Findings

Quantum inferences are cases of partially exchangeable models.

Classical probability laws remain valid in quantum contexts.

Encourages integration of quantum theory with exchangeable model frameworks.

Abstract

"Ever since the advent of modern quantum mechanics in the late 1920's, the idea has been prevalent that the classical laws of probability cease, in some sense, to be valid in the new theory. [...] The primary object of this presentation is to show that the thesis in question is entirely without validity and is the product of a confused view of the laws of probability" (Koopman, 1957). The secondary objects are: to show that quantum inferences are cases of partially exchangeable statistical models with particular prior constraints; to wonder about such constraints; and to plead for a dialogue between quantum theory and the theory of exchangeable models.