Compressing the hidden variable space of a qubit

TL;DR

This paper introduces a simplified hidden variable model for a qubit with a one-dimensional hidden variable space, challenging previous models that required higher-dimensional spaces, and discusses potential generalizations.

Contribution

It presents a novel one-dimensional hidden variable model for qubits, reducing the complexity of hidden variable representations compared to prior models.

Findings

Hidden variable space for a qubit can be one-dimensional.

The model's probability distributions meet regularity criteria.

Potential for extending the model to higher-dimensional Hilbert spaces.

Abstract

In previously exhibited hidden variable models of quantum state preparation and measurement, the number of continuous hidden variables describing the actual state of a single realization is never smaller than the quantum state manifold dimension. We introduce a simple model for a qubit whose hidden variable space is one-dimensional, i.e., smaller than the two-dimensional Bloch sphere. The hidden variable probability distributions associated with the quantum states satisfy reasonable criteria of regularity. Possible generalizations of this shrinking to a N-dimensional Hilbert space are discussed.