This paper studies whether actions on the Hawking radiation can change the quantum information inside a black hole. According to the “island formula,” after the Page time (the stage of evaporation when the black hole is roughly maximally entangled with its radiation), information that lived in the black hole interior can be viewed as encoded in the radiation. That encoding raises a puzzle: could an operation on the radiation, far from the hole and not causally connected to the interior, actually alter the interior state and so violate causality?

The authors test this question in two simple two-dimensional gravity models. They set up the problem as one of quantum error correction. The interior degrees of freedom play the role of a code subspace. The Hawking radiation and black hole microstates form the larger physical system. They model errors on the radiation as quantum channels (described by Kraus operators) and use a diagnostic called the Rényi-2 mutual information. This mutual information is a concrete measure of correlations that signals whether the interior state is “decoupled” from the environment — that is, protected from the error.

In the first model, called the West Coast model, gravity is included only through topological ingredients. There the authors reproduce an earlier finding: when the error is large, decoupling can fail for a short time after the Page time. In physical terms, a particular spacetime configuration — a fully connected wormhole that links replicas of the radiation, the black hole, and their copies — can dominate the gravitational path integral. That dominance produces a nonzero Rényi-2 mutual information, which indicates that the radiation operation could in principle affect the interior.

Next they study Jackiw–Teitelboim (JT) gravity, a two-dimensional model that includes dynamical gravitational degrees of freedom. In this case the operations on the radiation carry energy and produce gravitational backreaction. The backreaction changes which spacetime configurations dominate the path integral. The authors find that the fully connected wormhole becomes energetically costly and no longer dominates. As a result the Rényi-2 mutual information vanishes and the decoupling condition holds. In other words, once gravity acting on the radiation is included, even large errors cannot alter the interior in these models.