A Monty-Hall test of non-contextual determinism with a single qutrit
Abstract
We present a simple equality that distinguishes non-contextual deterministic hidden-variable theories (NCHV) from standard quantum mechanics using a single three-level system. The protocol is inspired by the Monty Hall puzzle: a coherent "discard" procedure followed by a projective measurement. In any NCHV theory that respects the Monty Hall condition (the discard never eliminates the true state), the probability of obtaining a chosen state after the discard is exactly 1/3. In contrast, quantum mechanics predicts 1/6, due to the preparation of coherent superpositions. Quantum mechanics thus violates the deterministic bound by a factor of two, providing a state-dependent non-contextuality inequality with a novel operational interpretation. Unlike standard Kochen-Specker proofs, which require 117 rays or 33 observables, our test uses only a single qutrit and two sequential measurements. An experimental implementation with photonic qutrits is proposed, including an analysis of experimental imperfections.
Keywords
Cite
@article{arxiv.2604.25953,
title = {A Monty-Hall test of non-contextual determinism with a single qutrit},
author = {Jorge Meza-Domínguez},
journal= {arXiv preprint arXiv:2604.25953},
year = {2026}
}
Comments
New version, more rigourous