E7and the tripartite entanglement of seven qubits

In quantum information theory, it is well known that the tripartiteentanglement of three qubits is described by the group [SL(2,C)]^3 and that theentanglement measure is given by Cayley's hyperdeterminant. This has providedan analogy with certain N=2 supersymmetric black holes in string theory, whoseentropy is also given by the hyperdeterminant. In this paper, we extend theanalogy to N=8. We propose that a particular tripartite entanglement of sevenqubits, 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.Comment: Minor improvements. 15 page late