Grassmannian connection between three- and four-qubit observables, Mermin's contextuality and black holes

P. Lévay, Michel Planat, Metod Saniga

Research output: Contribution to journalArticle

10 Citations (Scopus)

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.

Original languageEnglish
Article number037
JournalJournal of High Energy Physics
Volume2013
Issue number9
DOIs
Publication statusPublished - 2013

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algebra
formalism
geometry

Keywords

  • Black Holes in String Theory
  • Differential and Algebraic Geometry
  • Discrete and Finite Symmetries

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

Cite this

Grassmannian connection between three- and four-qubit observables, Mermin's contextuality and black holes. / Lévay, P.; Planat, Michel; Saniga, Metod.

In: Journal of High Energy Physics, Vol. 2013, No. 9, 037, 2013.

Research output: Contribution to journalArticle

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