Hidden variable problem for a family of continuously many spin 1 measurements

TL;DR

This paper investigates a continuous family of spin 1 measurements and demonstrates that the existence of a hidden-variable explanation is a discontinuous property within this set.

Contribution

It reveals that for a specific family of measurements, the hidden-variable describability changes discontinuously with the parameter, highlighting a novel aspect of quantum measurement theory.

Findings

Hidden-variable models are discontinuous across the measurement family.

Certain measurement parameters admit hidden-variable explanations, others do not.

Discontinuity in hidden-variable describability challenges assumptions of smooth transition.

Abstract

We study a continuous set of spin 1 measurements and show that for a special family of measurements parametrized by a single variable $\theta$ the possibility of hidden-variable description is a discontinuous property.