Five-Qubit Contextuality, Noise-Like Distribution of Distances Between Maximal Bases and Finite Geometry

TL;DR

This paper presents new state proofs of the Bell-Kochen-Specker and Bell's theorems using five-qubit observables, revealing a noise-like distribution of basis distances and linking the structure to finite geometry.

Contribution

It introduces specific state proofs of fundamental quantum theorems using five-qubit observables and connects their geometric structure to symplectic polar space.

Findings

Histogram of basis distances shows noise-like behaviour

Proposes new state proofs of Bell and Kochen-Specker theorems

Links quantum structures to finite geometry

Abstract

Employing five commuting sets of five-qubit observables, we propose specific 160-661 and 160-21 state proofs of the Bell-Kochen-Specker theorem that are also proofs of Bell's theorem. A histogram of the 'Hilbert-Schmidt' distances between the corresponding maximal bases shows in both cases a noise-like behaviour. The five commuting sets are also ascribed a finite-geometrical meaning in terms of the structure of symplectic polar space W(9,2).