Grassmannian connection between three- and four-qubit observables, mermin's contextualities and black holes

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Date
2013-07-23MFO Scientific Program
Research in Pairs 2013Series
Oberwolfach Preprints;2013,17Author
Lévay, Péter
Planat, Michel
Saniga, Metod
Metadata
Show full item recordOWP-2013-17
Abstract
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.