Unconditional no-hidden-variables theorem

TL;DR

This paper proves that quantum theory for a single spin-1/2 system cannot be explained by hidden variables within the two-dimensional Hilbert space formalism, emphasizing the incompatibility with classical probability models.

Contribution

It presents a definitive no-hidden-variables theorem for a single spin-1/2 system, extending previous results and clarifying the incompatibility with classical probability spaces.

Findings

Classical probability space cannot model measurement outcomes in quantum spin-1/2 systems.

Quantum theory rejects hidden-variable interpretations in two-dimensional Hilbert space.

The theorem strengthens the foundational understanding of quantum non-classicality.

Abstract

Recently, [{arXiv:0810.3134}] is accepted and published. We present ultimate version of no-hidden-variables theorem. We derive a proposition concerning the quantum theory under the existence of the Bloch sphere in a single spin-1/2 system. The existence of a single classical probability space for measurement outcome within the formalism of von Neumann's projective measurement does not coexist with the proposition concerning the quantum theory. We have to give up the existence of such a classical probability space for measurement outcome in the two-dimensional Hilbert space formalism of the quantum theory. The quantum theory does not accept a hidden-variable interpretation in the two-dimensional space.