Entanglement Wedge Reconstruction Fidelity

김정욱

Chris Akers, Adam Levine, Stefan Leichenauer

We show that the bulk region reconstructable from a given boundary subregion---which we term the reconstruction wedge---can be much smaller than the entanglement wedge even when backreaction is small. We find arbitrarily large separations between the reconstruction and entanglement wedges in near-vacuum states for regions close to an entanglement phase transition, and for more general regions in states with large energy (but very low energy density). Our examples also illustrate situations for which the quantum extremal surface is macroscopically different from the Ryu-Takayanagi surface.

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.

Vahid Azimi Mousolou

Yu Jing Guo, Lin Zhang, Huting Yuan

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.