# E_6 and the bipartite entanglement of three qutrits

## TL;DR

This paper explores the analogy between black hole entropy in string theory and bipartite entanglement in quantum information, focusing on three qutrits and the E_6 symmetry group.

## Contribution

It introduces a new example linking five-dimensional N=8 black holes to bipartite entanglement of three qutrits with E_6 symmetry, expanding the black hole-entanglement analogy.

## Key findings

- Black hole entropy relates to E_6 invariant.
- Bipartite entanglement of three qutrits exhibits E_6 symmetry.
- Analogies extend to other supergravity black holes.

## 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 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.