Black Hole Interior and Quantum Error Correction with Dynamical Gravity

TL;DR

This work investigates how gravity acting on Hawking radiation affects the quantum error-correcting structure of black hole interiors. Using the West Coast (topological) model and dynamical JT gravity, it shows that backreaction from gravitating radiation can suppress replica wormholes that previously allowed interior information to be disturbed by radiation-based errors. The main finding is that for errors with scaling dimension above a critical value, the Rényi-2 mutual information between interior references and radiation sectors vanishes, preserving interior causality. This suggests gravitational dynamics stabilizes the entanglement wedge structure and supports causality in evaporating black holes, with potential implications for island physics and holographic quantum error correction.

Abstract

According to the island formula, information in the code subspace defined in the black hole interior is embedded in the Hawking radiation after the Page time. At first sight, this embedding suggests that operations acting on the Hawking radiation could modify the information in the code subspace, potentially leading to an apparent violation of causality. Indeed, in previous studies based on the PSSY model, which incorporates only the topological degrees of freedom of gravity, it was shown that when the error is sufficiently large, a violation of causality can arise, as indicated by a nonvanishing mutual information. In this paper, we investigate the situation in which dynamical gravity also acts on the Hawking radiation. In this case, operations on the Hawking radiation induce nontrivial backreaction on the bulk spacetime appearing in the gravitational path integral for the mutual information -- an effect that is absent when the Hawking radiation is non-gravitating. We find that this backreaction renders the relevant mutual information vanishing. This result implies that, in theories with dynamical gravity, the apparent violation of causality is resolved.

Figures (26)

• Figure 1: Diagrammatic representation of the boundary condition for the state $\left|\psi_{i, i^{\prime}}^\alpha\right\rangle_A^{*} \otimes\left|\psi^\beta\right\rangle_B$ and its naive bulk dual. The red solid lines denote the EoW branes, and the green and blue solid lines are bulk branes corresponding to exterior and interior code excitations. The red, blue and green dashed lines denote the labels of states for the EoW brane, interior and exterior code excitations respectively. The star $*$ denotes the CPT conjugation acting on the universe $A$ to keep the orientation of the total system $AB$. We refer to it as the naive bulk dual because there is another possibility for bulk geometry where the two branes are connected.
• Figure 2: Fully disconnected saddle
• Figure 3: Fully connected saddle
• Figure 5: Diagrammatic representation of the boundary condition for $\mathop{\mathrm{tr}}\nolimits \left(\rho_{ref(in)}' \right)^{2}$, (\ref{['eq:renyiTwoOnesystem']}).
• Figure 6: Diagrammatic representation of boundary conditions (\ref{['eq:renyiTwoThreesystem']}) and (\ref{['eq:renyiTwoTwosystem']}), which include the Kraus operators. Only the difference between $(a)$ and $(b)$ is the way the dotted blue lines (indices of the interior code subspace) are contracted.