Grassmannian Connection Between Three- and Four-Qubit Observables, Mermin's Contextuality and Black Holes

Peter Levay (1) , Michel Planat (2) , Metod Saniga (3)

1 BME - Budapest University of Technology and Economics [Budapest]
2 FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174)
3 Astronomical Institute of the Slovak Academy of Sciences

We invoke some ideas from finite geometry to map bijectively 135 heptads of mutually commuting three-qubit observables into 135 symmetric four-qubit ones. After labeling the elements of the former set in terms of a seven-dimensional Clifford algebra, we present the bijective map and most pronounced actions of the associated symplectic group on both sets in explicit forms. This formalism is then employed to shed novel light on recently-discovered structural and cardinality properties of an aggregate of three-qubit Mermin's ''magic'' pentagrams. Moreover, some intriguing connections with the so-called black-hole--qubit correspondence are also pointed out.

Domains: Mathematical Physics [math-ph]; Mathematical Physics [math-ph]; Quantum Physics [quant-ph]; High Energy Physics - Theory [hep-th]; Combinatorics [math.CO]

Peter Levay, Michel Planat, Metod Saniga. Grassmannian Connection Between Three- and Four-Qubit Observables, Mermin's Contextuality and Black Holes. Journal of High Energy Physics, 2013, pp.037. ⟨10.1007/JHEP09(2013)037⟩. ⟨hal-00825701v2⟩