Entanglement island, miracle operators and the firewall
Xiao-Liang Qi

TL;DR
This paper explores how entanglement islands and miracle operators influence information retrieval from black holes, revealing contradictions in state reconstruction and proposing a breakdown of smooth geometry assumptions to resolve the firewall paradox.
Contribution
It introduces miracle operators that challenge the smooth replica geometry assumption and provides a new perspective on the firewall paradox through these operators.
Findings
Contradiction in state reconstruction when applying certain measurements.
Introduction of miracle operators that simulate interior information retrieval.
Breakdown of smooth replica geometry due to extra wormholes.
Abstract
In this paper, we obtain some general results on information retrieval from the black hole interior, based on the recent progress on quantum extremal surface formula and entanglement island. We study an AdS black hole coupled to a bath with generic dynamics, and ask whether it is possible to retrieve information about a small perturbation in the interior from the bath system. We derive a state reconstruction formula based on one norm. However, we show that a contradiction arises if we apply this result to a special situation when the bath dynamics includes a unitary operation that carries a particular measurement to a region and send the result to another region . Physically, the contradiction arises between transferability of classical information during the measurement, and non-transferability of quantum information which determines the entanglement island. We propose that the…
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