E_7 and the tripartite entanglement of seven qubits

Details E_7 and the tripartite entanglement of seven qubits E_7 and the tripartite entanglement of seven qubits

2006-09-29

arxiv.org/abs/quant-ph/0609227v4

Phys.Rev.D76:025018,2007

Physics

Quantum Physics

Minor improvements. 15 page latex

Scientific paper

10.1103/PhysRevD.76.025018

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.

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