Stringy Black Holes and the Geometry of Entanglement

TL;DR

This paper explores deep mathematical connections between black hole entropy in string theory and quantum entanglement, revealing new insights into both fields through geometric and informational perspectives.

Contribution

It establishes a novel link between black hole moduli stabilization and three-qubit entanglement canonical forms, using twistors and entanglement measures.

Findings

Relation between black hole entropy and three-qubit entanglement forms

Connection between moduli stabilization and GHZ state distillation

Geometric classification of black holes using twistors

Abstract

Recently striking multiple relations have been found between pure state 2 and 3-qubit entanglement and extremal black holes in string theory. Here we add further mathematical similarities which can be both useful in string and quantum information theory. In particular we show that finding the frozen values of the moduli in the calculation of the macroscopic entropy in the STU model, is related to finding the canonical form for a pure three-qubit entangled state defined by the dyonic charges. In this picture the extremization of the BPS mass with respect to moduli is connected to the problem of finding the optimal local distillation protocol of a GHZ state from an arbitrary pure three-qubit state. These results and a geometric classification of STU black holes BPS and non-BPS can be described in the elegant language of twistors. Finally an interesting connection between the black hole entropy and the average real entanglement of formation is established.