STU attractors from vanishing concurrence

TL;DR

This paper links black hole attractor equations in supergravity to the vanishing of bipartite entanglement measures in a three-qubit state, providing a quantum information perspective on black hole entropy.

Contribution

It establishes a novel correspondence between black hole attractor equations and the vanishing of bipartite concurrences in a three-qubit framework, connecting supergravity and quantum entanglement.

Findings

Vanishing bipartite concurrences on the horizon correspond to attractor equations.

Black hole entropy can be interpreted as a linear entropy of a pure state.

Explicit concurrence expressions are derived for BPS and non-BPS cases.

Abstract

Concurrence is an entanglement measure characterizing the {\it mixed} state bipartite correlations inside of a pure state of an $n$-qubit system. We show that after organizing the charges and the moduli in the STU model of $N=2$, $d=4$ supergravity to a three-qubit state, for static extremal spherically symmetric BPS black hole solutions the vanishing condition for all of the bipartite concurrences on the horizon is equivalent to the attractor equations. As a result of this the macroscopic black hole entropy given by the three-tangle can be reinterpreted as a linear entropy characterizing the {\it pure} state entanglement for an arbitrary bipartite split. Both for the BPS and non-BPS cases explicit expressions for the concurrences are obtained, with their vanishing on the horizon is demonstrated.