Proofs of the Kochen-Specker theorem based on a system of three qubits

TL;DR

This paper presents new, visually intuitive proofs of the Kochen-Specker theorem using three-qubit Pauli group observables, leading to numerous parity proofs and potential applications.

Contribution

It introduces novel observable-based proofs of the Kochen-Specker theorem using three-qubit systems, with diagrams that make the proofs straightforward to verify.

Findings

Multiple new proofs of the Kochen-Specker theorem are provided.

The proofs generate large systems of projectors and bases for parity proofs.

Applications of these proofs are discussed.

Abstract

A number of new proofs of the Kochen-Specker theorem are given based on the observables of the three-qubit Pauli group. Each proof is presented in the form of a diagram from which it is obvious by inspection. Each of our observable-based proofs leads to a system of projectors and bases that generally yields a large number of "parity proofs" of the Kochen-Specker theorem. Some examples of such proofs are given and some of their applications are discussed.