Classical Extensions, Classical Representations and Bayesian Updating in Quantum Mechanics

TL;DR

This paper reviews classical extensions and representations of quantum mechanics, comparing their formalism and Bayesian updating, highlighting the strong analogy in the classical extension framework.

Contribution

It provides a comparative analysis of classical extensions and representations in quantum mechanics, focusing on Bayesian analogues of state transitions.

Findings

Classical extension formalism closely models quantum measurement updates.

Comparison reveals differences and similarities between classical extensions and representations.

Bayesian analogues are effectively constructed within the classical extension framework.

Abstract

I review the formalism of classical extensions of quantum mechanics introduced by Beltrametti and Bugajski, and compare it to the classical representations discussed e.g. by Busch, Hellwig and Stulpe and recently used by Fuchs in his discussion of quantum mechanics in terms of standard quantum measurements. I treat the problem of finding Bayesian analogues of the state transition associated with measurement in the canonical classical extension as well as in the related 'uniform' classical representation. In the classical extension, the analogy is extremely good.