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

Michel Planat (1) , Metod Saniga (2)

1 FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174)
2 Astronomical Institute of the Slovak Academy of Sciences

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 $W(9,2)$.

Domains: Quantum Physics [quant-ph]; Mathematical Physics [math-ph]; Mathematical Physics [math-ph]

Michel Planat, Metod Saniga. Five-Qubit Contextuality, Noise-Like Distribution of Distances Between Maximal Bases and Finite Geometry. Physics Letters A, 2012, 376, pp.3485-3490. ⟨10.1016/j.physleta.2012.10.020⟩. ⟨hal-00703166⟩