# Black hole entropy and quantum information

**Authors:** M. J. Duff, S. Ferrara  
**arXiv:** [hep-th/0612036](https://arxiv.org/abs/hep-th/0612036)  
**Date:** 2006-12-05  
**Summary page:** https://www.summarizepaper.com/en/paper/hep-th--0612036v3/

## Key points

- Authors M. J. Duff and S. Ferrara explore connections between black hole entropy in string theory and multipartite entanglement in quantum information theory.
- Study focuses on N=2 black holes with three-qubit entanglement and N=8 black holes with seven-qubit entanglement.
- Mathematical constructs, such as Cayley's hyperdeterminant for N=2 black holes and the E_7 invariant of Cartan for N=8 black holes, play a crucial role in determining black hole entropy and measuring tripartite entanglement.
- Invariants quantify black hole entropy and capture specific forms of tripartite entanglement encoded within the Fano plane.
- Bridging fields of mathematics, physics, and information science offers new insights into the fundamental nature of black holes and quantum entanglement.

## Summary

In their paper "Black hole entropy and quantum information," authors M. J. Duff and S. Ferrara explore the intriguing connections between black hole entropy in string theory and multipartite entanglement in quantum information theory. The study focuses on two specific scenarios: N=2 black holes with three-qubit entanglement, and N=8 black holes with seven-qubit entanglement. In both cases, mathematical constructs play a crucial role in determining the black hole entropy as well as measuring tripartite entanglement within the system. For N=2 black holes, the quartic [SL(2)]^3 invariant known as Cayley's hyperdeterminant is key, while for N=8 black holes, the quartic E_7 invariant of Cartan takes center stage. These invariants not only quantify the black hole entropy but also capture specific forms of tripartite entanglement that are intricately encoded within the Fano plane. By bridging seemingly disparate fields, Duff and Ferrara offer new insights into the fundamental nature of black holes and quantum entanglement while highlighting the deep interplay between mathematics, physics, and information science.