Kochen-Specker Sets with Thirty Rank-Two Projectors in Three-Qubit System

TL;DR

This paper introduces a straightforward scheme to generate Kochen-Specker sets with 30 rank-two projectors in a three-qubit system, providing a state-independent proof of the KS theorem and enabling manual creation of diverse KS sets.

Contribution

It presents a simple, step-by-step method to produce Kochen-Specker sets with specific projectors, advancing the construction of KS sets in quantum systems.

Findings

Successfully generated KS sets with 30 rank-2 projectors

Scheme allows manual creation of diverse KS sets with mixed projectors

Provides a state-independent proof of the KS theorem in three-qubit systems

Abstract

A simple three rules supplemented by five steps scheme is proposed to produce Kochen-Specker (KS) sets with 30 rank-2 projectors that occur twice each. The KS sets provide state-independent proof of KS theorem based on a system of three qubits. A small adjustment of the scheme enables us to manually generate a large number of KS sets with a mixture of rank-1 and rank-2 projectors.