On Quantum Information Before the Page Time

TL;DR

This paper shows that the quantum state of Hawking radiation before the Page time contains significant information about the black hole's microstructure, challenging the notion of purely thermal early radiation.

Contribution

It introduces a method to detect quantum information in early Hawking radiation using fidelity calculations in 2D BCFT models, applicable to various conformal field theories.

Findings

Quantum information is present in Hawking radiation prior to the Page time.

An observer can distinguish different black holes via measurements of early radiation, given enough measurements.

The techniques are universal and applicable to a broad class of 2D conformal field theories.

Abstract

While recent progress in the black hole information problem has shown that the entropy of Hawking radiation follows a unitary Page curve, the quantum state of Hawking radiation prior the Page time is still treated as purely thermal, containing no information about the microstructure of the black hole. We demonstrate that there is significant quantum information regarding the quantum state of the black hole in the Hawking radiation prior to the Page time. By computing of the quantum fidelity in a 2D boundary conformal field theory (BCFT) model of black hole evaporation, we demonstrate that an observer outside of an evaporating black hole may distinguish different black holes via measurements of the Hawking radiation at \textit{any} time during the evaporation process, albeit with an exponentially large number of measurements. Furthermore, our results are universal, applicable to general BCFTs including those with large central charge and rational BCFTs. The techniques we develop for computing the fidelity are more generally applicable to excited states in CFT. As such, we are able to characterize more general aspects of thermalization in 2D conformal field theory.