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 (2)

• Strings, black holes, the tripartite entanglement of seven qubits and the Fano plane
• Multipartite Entanglement and Hyperdeterminants

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• Black Hole Entropy and Finite Geometry
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• Attractor Horizon Geometries of Extremal Black Holes
• More on N=8 Attractors
• Extremal Black Holes in Supergravity
• The Effective Action of N=8 Supergravity
• Twin "Fano-Snowflakes" Over the Smallest Ring of Ternions
• Polynomial Representation of $E_7$ and Its Combinatorial and PDE Implications
• Black hole entropy and quantum information