State-independent proof of Kochen-Specker theorem with 13 rays

TL;DR

This paper presents a simplified, experimentally testable inequality involving only 13 observables that demonstrates quantum contextuality in a qutrit system, providing a new, practical proof of the Kochen-Specker theorem.

Contribution

It introduces a minimal, experimentally feasible inequality for state-independent quantum contextuality testing in qutrits, simplifying previous complex approaches.

Findings

The inequality is satisfied by all non-contextual models.

All qutrit states violate the inequality, confirming contextuality.

Provides a record-breaking proof with only 13 directions.

Abstract

Quantum contextuality, as proved by Kochen and Specker, and also by Bell, should manifest itself in any state in any system with more than two distinguishable states and recently has been experimentally verified on various physical systems. However for the simplest system capable of exhibiting contextuality, a qutrit, the quantum contextuality is verified only state-dependently in experiment because too many (at least 31) observables are involved in all the known state-independent tests. Here we report an experimentally testable inequality involving only 13 observables that is satisfied by all non-contextual realistic models while being violated by all qutrit states. Thus our inequality will practically facilitate a state-independent test of the quantum contextuality for an indivisible quantum system. We provide also a record-breaking state-independent proof of the Kochen-Specker theorem with 13 directions determined by 26 points on the surface of a three by three magic cube.