Entanglement Wedge Reconstruction Beyond the Large N Limit via the Twirled Petz Map

RESUMO

Entanglement wedge reconstruction provides the sharpest formulation of bulk locality in AdS/CFT, identifying the entanglement wedge as the largest bulk region reconstructible from a boundary subregion. While this statement is well understood at leading order in the large N expansion through both modular flow and Petz map reconstruction, its extension beyond the semiclassical regime has remained unclear. In this work, we show that quantum error correction provides the natural framework for addressing this problem. At leading order, we reproduce the known leading-order reconstruction formulas, and by employing the twirled Petz map, we obtain a systematic and explicit method for incorporating subleading 1/N corrections. Beyond the leading approximation, we have obtained an explicit bi-local correction controlled by a subleading Petz kernel. Our results establish a controlled approach to bulk reconstruction beyond large N and sharpening the role of quantum error correction in holography. This framework provides a controlled path toward understanding bulk reconstruction in fully quantum gravitational settings.