Reconstruction wedges in $AdS/CFT$ with boundary fractallike structures

TL;DR

This paper demonstrates that the robustness of holographic quantum error correction persists even with complex fractal boundary erasures and highly entropic mixed states in the bulk, across different AdS/CFT setups.

Contribution

It extends the understanding of holographic error correction to fractal boundary structures and shows its resilience against bulk mixed states in the large limit.

Findings

Code distance remains unaffected by bulk entropy in certain fractal erasures.

Bulk reconstruction is possible despite high entropy in fractal boundary erasures.

Robustness of holographic codes extends to complex boundary geometries.

Abstract

In this work, we show the robustness of uberholography and its associated quantum error correcting code against the breakdown of entanglement wedge in the presence of highly entropic mixed states in the bulk. We show that for Cantor-set-like erasure in the boundary in $AdS_3/CFT_2$, the code distance is independent of the mixed-state entropy in the bulk in the $m\rightarrow\infty$ limit. We also show that for a Sierpinski triangle shaped boundary subregion with fractal boundary erasures in $AdS_4/CFT_3$, bulk reconstruction is possible in the presence of highly entropic mixed states in the bulk in the large $m$ regime.