On von Neumann and Bell theorems applied to quantumness tests

TL;DR

This paper critically examines the applicability of von Neumann and Bell theorems to quantumness tests, analyzing their relevance and limitations in single-system and macroscopic quantum system contexts.

Contribution

It provides a detailed discussion on the relevance of von Neumann and Bell theorems for quantumness tests and clarifies the proper quantum mechanical description of photon polarization experiments.

Findings

Von Neumann theorem's limited relevance for single-system quantumness tests

Bell's inequality's limited usefulness for macroscopic quantum systems

Proper quantum mechanical description of polarized photon experiments

Abstract

The issues, raised in arXiv:0809.011, concerning the relevance of the von Neumann theorem for the single-system's quantumness test proposed in arXiv:0704.1962 and performed for the case of single photon polarization in arXiv:0804.1646, and the usefulness of Bell's inequality for testing the idea of macroscopic quantum systems are discussed in some details. Finally, the proper quantum mechanical description of the experiment with polarized photon beams is presented.