From qubits to E7

Abstract

There is a intriguing relation between quantum information theory and super gravity, discovered by M.J. Duff and S. Ferrara. It relates entanglement measures for qubits to black hole entropy, which in a certain case involves the quartic invariant on the 56-dimensional representation of the Lie group E7. In this paper we recall the relatively straightforward manner in which three-qubits lead to E7, or at least to the Weyl group of E7. We also show how the Fano plane emerges in this context.

29 pages

References in corpus (4)

• E_7 and the tripartite entanglement of seven qubits
• Three-Qubit Operators, the Split Cayley Hexagon of Order Two and Black Holes
• E_6 and the bipartite entanglement of three qutrits
• The Veldkamp space of multiple qubits

Cited by in corpus (13)

• The black-hole/qubit correspondence: an up-to-date review
• Grassmannian Connection Between Three- and Four-Qubit Observables, Mermin's Contextuality and Black Holes
• Hitchin functionals are related to measures of entanglement
• The magic three-qubit Veldkamp line: A finite geometric underpinning for form theories of gravity and black hole entropy
• Mermin pentagrams arising from Veldkamp lines for three qubits
• A finite geometric toy model of space-time as an error correcting code
• Classification of multipartite systems featuring only $|W⟩$ and $|GHZ⟩$ genuine entangled states
• Sextonions, Zorn Matrices, and ${\mathbf{e}}_{7\frac{1}{2}}$
• The role of PSL(2,7) in M-theory: M2-branes, Englert equation and the septuples
• Multi-Centered Invariants, Plethysm and Grassmannians
• Adams-Iwasawa N=8 Black Holes
• BPS Black Hole Entropy and Attractors in Very Special Geometry. Cubic Forms, Gradient Maps and their Inversion
• Orthogonal roots, Macdonald representations, and quasiparabolic sets