E-6 and the bipartite entanglement of three qutrits

Abstract

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 E7⊃[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 E6⊃[SL(3)]3. Both the black hole (or black string) entropy and the entanglement measure are provided by the Cartan cubic E6 invariant. Similar analogies exist for magic N=2 supergravity black holes in both four and five dimensions.