Construction of Three-Qubit Kochen-Specker Sets

TL;DR

This paper introduces a simple manual method to construct Kochen-Specker sets for three-qubit systems, aiding the parity proof of quantum contextuality without extensive computer calculations.

Contribution

It presents the first straightforward manual approach to generate KS sets in an eight-dimensional three-qubit space based on the Mermin pentagram.

Findings

Successfully constructed KS sets manually for three-qubit systems.

The method simplifies the process of generating KS sets for parity proofs.

Provides a new tool for studying quantum contextuality in multi-qubit systems.

Abstract

Contextuality is one of the fundamental deviations of quantum mechanics from classical physics. The Kochen-Specker (KS) theorem shows that non-contextual classical physics with hidden variables is inconsistent with the predictions of quantum mechanics. Parity proof is one of the many different approaches applied to prove KS theorem for quantum system with different dimensionality. This method of proof requires KS sets that composed of an odd number of bases and an even number of projectors. In most of the cases, the number of KS sets produced is large and its production is generally aided by computer calculation. However, manually generation of KS sets are also reported previously for qutrit and two-qubit systems. We put forward the first and surprisingly simple method to generate manually KS sets, with respect to Mermin pentagram, that can be used for the parity proof of KS theorem in a state space of eight-dimensional three-qubit system .