E7and 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.