Conditional measurement in noncontextual hidden variables models

TL;DR

This paper addresses the challenge of modeling conditional measurements in noncontextual hidden variables models for two-dimensional systems, proposing a branching approach to improve their descriptive power.

Contribution

It introduces a branching mechanism in hidden variables space to effectively handle conditional measurements and state preparation in noncontextual models.

Findings

Branching approach enables modeling of conditional measurements.

Improves the explanatory capacity of noncontextual hidden variables models.

Addresses limitations of previous models in $d=2$ systems.

Abstract

The noncontextual hidden variables models in $d=2$, such as the ones constructed by Bell and by Kochen and Specker, have difficulties in accounting for the conditional measurement of two non-orthogonal projectors. An idea of branching in the hidden variables space, which provides a means to realize the notion of reduction effectively and describe the state preparation, is suggested as a way to resolve the difficulties associated with the conditional measurement.