Distinguishing Black Hole Microstates using Holevo Information

TL;DR

This paper investigates how quantum corrections affect the ability to distinguish black hole microstates from thermal states using Holevo information in a 2D CFT, revealing that higher-order effects spoil previous indistinguishability results.

Contribution

It demonstrates that including $1/c$ corrections in holographic calculations lifts the plateau behaviors, altering the distinguishability of black hole microstates.

Findings

Plateaus in Holevo information are lifted by $1/c$ corrections.

Higher order quantum gravity effects spoil microstate indistinguishability.

Results apply to both canonical and microcanonical ensembles.

Abstract

We use the Holevo information in a two-dimensional conformal field theory (CFT) with a large central charge $c$ to distinguish microstates from the underlying thermal state. Holographically, the CFT microstates of a thermal state are dual to black hole microstate geometries in three-dimensional anti-de Sitter space. It was found recently that the holographic Holevo information shows plateau behaviors at both short and long interval regions. This indicates that the black hole microstates are indistinguishable from the thermal state by measuring over a small region, and perfectly distinguishable over a region with its size comparable to the whole system. In this letter, we demonstrate that the plateaus are lifted by including the $1/c$ corrections from both the vacuum and non-vacuum conformal families of CFT in either the canonical ensemble or microcanonical ensemble thermal state. Our results imply that the aforementioned indistinguishability and distinguishability of black hole microstate geometries from the underlying black hole are spoiled by higher order Newton constant $G_N$ corrections of quantum gravity.