E_7 and the tripartite entanglement of seven qubits

Abstract

In quantum information theory, it is well known that the tripartite entanglement of three qubits is described by the group [SL(2,C)]^3 and that the entanglement measure is given by Cayley's hyperdeterminant. This has provided an analogy with certain N=2 supersymmetric black holes in string theory, whose entropy is also given by the hyperdeterminant. In this paper, we extend the analogy to N=8. We propose that a particular tripartite entanglement of seven qubits, encoded in the Fano plane, is described by the exceptional group E_7(C) and that the entanglement measure is given by Cartan's quartic E_7 invariant.

Minor improvements. 15 page latex

References in corpus (23)

• Distributed Entanglement
• N=2 Extremal Black Holes
• Solitonic Strings and BPS Saturated Dyonic Black Holes
• Four Dimensional String/String/String Triality
• Orbits of Exceptional Groups, Duality and BPS States in String Theory
• STU Black Holes and String Triality
• E(7) Symmetric Area of the Black Hole Horizon
• General Static Spherically Symmetric Black Holes of Heterotic String on a Six Torus
• Black Rings in Taub-NUT
• Microscopic Description of Black Rings in AdS/CFT
• Massive String States as Extreme Black Holes
• Conformal and Quasiconformal Realizations of Exceptional Lie Groups
• Branes, central charges and U-duality invariant BPS conditions
• String triality, black hole entropy and Cayley's hyperdeterminant
• On N=8 attractors
• Strings, Black Holes, and Quantum Information
• Stringy Black Holes and the Geometry of Entanglement
• Branes at Angles and Black Holes
• Bound States of Black Holes and Other $P$-Branes
• Strings, black holes, the tripartite entanglement of seven qubits and the Fano plane
• Multiplet Structures of BPS Solitons
• Hidden symmetries of the Nambu-Goto action
• Multipartite Entanglement and Hyperdeterminants

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