All joint von Neumann measurements on a quantum state admit a quasi-classical probability model

TL;DR

This paper demonstrates that all joint von Neumann measurements on a quantum state can be represented within a single quasi-classical probability model, providing new insights into quantum randomness and measurement theory.

Contribution

It introduces a quasi-classical probability model that reproduces the Hilbert space description of all joint von Neumann measurements on a quantum state.

Findings

All joint von Neumann measurements can be modeled with a single measure space.

A random variable can represent each quantum observable across all measurements.

The model offers new perspectives on quantum randomness and measurement interpretation.

Abstract

We prove that the Hilbert space description of all joint von Neumann measurements on a quantum state can be reproduced in terms of a single measure space ({\Omega}, F, {\mu}) with a normalized real-valued measure {\mu}, that is, in terms of a new general probability model, the quasi-classical probability model, developed in [Loubenets: J. Math. Phys. 53 (2012), 022201; J. Phys. A: Math. Theor. 45 (2012), 185306]. In a quasi-classical probability model for all von Neumann measurements, a random variable models the corresponding quantum observable in all joint measurements and depends only on this quantum observable. This mathematical result sheds a new light on some important issues of quantum randomness discussed in the literature since the seminal article (1935) of Einstein, Podolsky and Rosen.