Fluctuation in the Fidelity of Information Recovery from Hawking Radiation

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Miyaji, Masamichi, Yano, Kazuyoshi
Format: Preprint
Published: 2023
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866910304089145344
author Miyaji, Masamichi
Yano, Kazuyoshi
author_facet Miyaji, Masamichi
Yano, Kazuyoshi
contents The interior of a pure-state black hole is known to be reconstructed from the Petz map by collecting a sufficiently large amount of the emitted Hawking radiation. This was established based on the Euclidean replica wormhole, which comes from an ensemble averaging over gravitational theories. On the other hand, this means that the Page curve and the interior reconstruction are both ensemble averages; thus, there is a possibility of large errors. In the previous study [Bousso, Miyaji (2023)], it was shown that the entropy of the Hawking radiation has fluctuation of order $e^{-S_{\mathbf{BH}}}$, thus is typical in the ensemble. In the present article, we show that the fluctuations of the relative entropy difference in the encoding map and the entanglement fidelity of the Petz map are both suppressed by $e^{-S_{\mathbf{BH}}}$ compared to the signals, establishing the typicality in the ensemble. In addition, we also compute the entanglement loss of the encoding map.
format Preprint
id arxiv_https___arxiv_org_abs_2311_02881
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Fluctuation in the Fidelity of Information Recovery from Hawking Radiation
Miyaji, Masamichi
Yano, Kazuyoshi
High Energy Physics - Theory
Statistical Mechanics
General Relativity and Quantum Cosmology
Quantum Physics
The interior of a pure-state black hole is known to be reconstructed from the Petz map by collecting a sufficiently large amount of the emitted Hawking radiation. This was established based on the Euclidean replica wormhole, which comes from an ensemble averaging over gravitational theories. On the other hand, this means that the Page curve and the interior reconstruction are both ensemble averages; thus, there is a possibility of large errors. In the previous study [Bousso, Miyaji (2023)], it was shown that the entropy of the Hawking radiation has fluctuation of order $e^{-S_{\mathbf{BH}}}$, thus is typical in the ensemble. In the present article, we show that the fluctuations of the relative entropy difference in the encoding map and the entanglement fidelity of the Petz map are both suppressed by $e^{-S_{\mathbf{BH}}}$ compared to the signals, establishing the typicality in the ensemble. In addition, we also compute the entanglement loss of the encoding map.
title Fluctuation in the Fidelity of Information Recovery from Hawking Radiation
topic High Energy Physics - Theory
Statistical Mechanics
General Relativity and Quantum Cosmology
Quantum Physics
url https://arxiv.org/abs/2311.02881