发表机构
Sharif University of Technology; Research Center for High Energy Physics, Department of Physics, Sharif University of Technology（谢里夫理工大学; 谢里夫理工大学物理系高能物理研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究利用代数Petz映射构建黑洞岛重构协议，证明可通过模理论将黑洞内部算符映射到辐射代数，得到镜像算符结构，为岛公式提供操作字典，证实黑洞内信息可解码。
AI 中文摘要
岛方案保证了蒸发黑洞的幺正Page曲线，这意味着视界深处的算符必须能从渐近霍金辐射中完全重构。然而，由于内部区域在因果上不连通且动力学性极强，依赖全局等距变换或连续模流的标准纠缠楔重构方法无法提供这种映射。我们通过构建利用代数Petz映射的岛重构协议解决了这一问题。借助模理论，我们将岛算符反射到可及的补集，传输到边界，并映射到辐射代数中。此外，我们证明这种纯代数推导自然产生了Papadodimas-Raju镜像算符的结构。该框架为岛公式提供了严格的操作字典，证明了被困在黑洞内部的信息可以被解码。
英文摘要
The island proposal guarantees a unitary Page curve for evaporating black holes, implying that operators deep behind the horizon must be fully reconstructable from asymptotic Hawking radiation. However, because the interior is causally disconnected and highly dynamical, standard entanglement wedge reconstruction methods, relying on global isometries or continuous modular flow, fail to provide this mapping. We resolve this by constructing a protocol for island reconstruction using the algebraic Petz map. By using modular theory, we reflect island operators into the accessible complement, transport them to the boundary, and map them into the radiation algebra. Furthermore, we demonstrate that this purely algebraic derivation naturally yields the structure of Papadodimas-Raju mirror operators. This framework provides a rigorous operational dictionary for the island formula, proving that information trapped inside a black hole can be decoded.
Comments6 pages + Appendix
