# Distinguishing Black Hole Microstates using Holevo Information

Guo, Wu-zhong (Physics Division, National Center for Theoretical Sciences, National Tsing Hua University, No. 101, Sec. II, Kuang Fu Road, Hsinchu 30013, Taiwan) ; Lin, Feng-Li (Department of Physics, National Taiwan Normal University, No. 88, Sec. IV, Ting-Chou Road, Taipei 11677, Taiwan) ; Zhang, Jiaju (Dipartimento di Fisica G. Occhialini, Università degli Studi di Milano-Bicocca, Piazza della Scienza 3, 20126 Milano, Italy) (INFN, Sezione di Milano-Bicocca, Piazza della Scienza 3, 20126 Milano, Italy)

21 December 2018

Abstract: We use Holevo information in the 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 anti–de Sitter space. It was found recently that 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 nonvacuum 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.

Published in: Physical Review Letters 121 (2018)