E_7 and the tripartite entanglement of seven qubits
Quantum Physics
2008-11-26 v4 General Relativity and Quantum Cosmology
High Energy Physics - Theory
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.
Cite
@article{arxiv.quant-ph/0609227,
title = {E_7 and the tripartite entanglement of seven qubits},
author = {M. J. Duff and S. Ferrara},
journal= {arXiv preprint arXiv:quant-ph/0609227},
year = {2008}
}
Comments
Minor improvements. 15 page latex