E_6 and the bipartite entanglement of three qutrits

Details E_6 and the bipartite entanglement of three qutrits E_6 and the bipartite entanglement of three qutrits

2007-04-04

arxiv.org/abs/0704.0507v2

Phys.Rev.D76:124023,2007

Physics

High Energy Physics

High Energy Physics - Theory

15 pages latex, 3 figures, minor corrections

Scientific paper

10.1103/PhysRevD.76.124023

Recent investigations have established an analogy between the entropy of four-dimensional supersymmetric black holes in string theory and entanglement in quantum information theory. Examples include: (1) N=2 STU black holes and the tripartite entanglement of three qubits (2-state systems), where the common symmetry is [SL(2)]^3 and (2) N=8 black holes and the tripartite entanglement of seven qubits where the common symmetry is E_7 which contains [SL(2)]^7. Here we present another example: N=8 black holes (or black strings) in five dimensions and the bipartite entanglement of three qutrits (3-state systems), where the common symmetry is E_6 which contains [SL(3)]^3. Both the black hole (or black string) entropy and the entanglement measure are provided by the Cartan cubic E_6 invariant. Similar analogies exist for ``magic'' N=2 supergravity black holes in both four and five dimensions.

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