Explicit reconstruction of the entanglement wedge

Eyoab Bahiru, Niloofar Vardian

Abstract We revisit entanglement wedge reconstruction in AdS/CFT using the Petz recovery channel. In the case of a spherical region on the boundary, we show that the Petz map reproduces the AdS-Rindler HKLL reconstruction. Moreover, for a generic subregion of the boundary, we could obtain the same boundary representation of a local bulk field lies in the entanglement wedge as the one proposed earlier in [1, 2] using properties of the modular flow.

Justin H. Wilson, Joe Mitchell, Victor M. Galitski

Arash Alipour Shahmiri, Maryam Sharifian, Niloofar Vardian

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 a 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.

Vic Vander Linden

The AdS/CFT correspondence is an explicit realization of the holographic principle relating a theory of gravity in a volume of space to a lower dimensional quantum field theory on its boundary. By exploiting elements of quantum error correction, qubit toy models of this correspondence have been constructed for which the bulk logical operators are representable by operators acting on the boundary. Given a boundary subregion, wedges in the volume space are used to enclose the bulk qubits for which logical operators are reconstructable on that boundary subregion. In this thesis a number of different wedges, such as the causal wedge, greedy entanglement wedge and minimum entanglement wedge, are examined. More specifically, Monte-Carlo simulations of boundary erasure are performed with various toy models to study the differences between wedges and the effect on these wedge by the type of the model, non-uniform boundaries and stacking of models. It has been found that the minimum entanglement wedge is the best approximate for the true geometric wedge. This is illustrated by an example toy model for which an operator beyond the greedy entanglement wedge was also reconstructed. In addition, by calculating the entropy of these subregions, the viability of a mutual information wedge is rejected. Only for particular connected boundary subregions was the inclusion of the central tensor by the geometric wedge associated to a rise in mutual information.

Shahabeddin Mostafanazhad aslmarand, Warner A. Miller, Doyeol Ahn +1 more