  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.
