The attractor mechanism as a distillation procedure

TL;DR

This paper explores the attractor mechanism in black hole solutions through the lens of three-qubit entangled states, revealing how moduli stabilization and entropy relate to quantum state distillation in both BPS and non-BPS cases.

Contribution

It introduces a detailed analysis of the attractor flow as a three-qubit state distillation process, extending previous work to non-BPS solutions and linking quantum entanglement properties to black hole entropy.

Findings

Non-BPS solutions exhibit a transition from complex to GHZ states at the horizon.

The amplitude magnitudes correlate with black hole entropy.

Flat directions cause errors that disrupt the uniform entanglement structure.

Abstract

In a recent paper it has been shown that for double extremal static spherically symmetric BPS black hole solutions in the STU model the well-known process of moduli stabilization at the horizon can be recast in a form of a distillation procedure of a three-qubit entangled state of GHZ-type. By studying the full flow in moduli space in this paper we investigate this distillation procedure in more detail. We introduce a three-qubit state with amplitudes depending on the conserved charges the warp factor, and the moduli. We show that for the recently discovered non-BPS solutions it is possible to see how the distillation procedure unfolds itself as we approach the horizon. For the non-BPS seed solutions at the asymptotically Minkowski region we are starting with a three-qubit state having seven nonequal nonvanishing amplitudes and finally at the horizon we get a GHZ state with merely four nonvanishing ones with equal magnitudes. The magnitude of the surviving nonvanishing amplitudes is proportional to the macroscopic black hole entropy. A systematic study of such attractor states shows that their properties reflect the structure of the fake superpotential. We also demonstrate that when starting with the very special values for the moduli corresponding to flat directions the uniform structure at the horizon deteriorates due to errors generalizing the usual bit flips acting on the qubits of the attractor states.