Reconstruction wedges in AdS/CFT with boundary fractallike structures

Ning Bao (Computational Science Initiative, Brookhaven National Laboratory, Upton, New York 11973, USA) ; Joydeep Naskar (Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA)

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-setlike erasure in the boundary in AdS3/CFT2, the code distance is independent of the mixed-state entropy in the bulk in the m limit. We also show that for a Sierpinski triangle shaped boundary subregion with fractal boundary erasures in AdS4/CFT3, bulk reconstruction is possible in the presence of highly entropic mixed states in the bulk in the large m regime.

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      "title": "Reconstruction wedges in <math><mrow><mi>AdS</mi><mo>/</mo><mi>CFT</mi></mrow></math> with boundary fractallike structures"
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      "source": "APS", 
      "value": "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-setlike erasure in the boundary in <math><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>/</mo><msub><mrow><mi>CFT</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math>, the code distance is independent of the mixed-state entropy in the bulk in the <math><mi>m</mi><mo>\u2192</mo><mi>\u221e</mi></math> limit. We also show that for a Sierpinski triangle shaped boundary subregion with fractal boundary erasures in <math><msub><mi>AdS</mi><mn>4</mn></msub><mo>/</mo><msub><mi>CFT</mi><mn>3</mn></msub></math>, bulk reconstruction is possible in the presence of highly entropic mixed states in the bulk in the large <math><mi>m</mi></math> regime."
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Published on:
17 March 2023
Publisher:
APS
Published in:
Physical Review D , Volume 107 (2023)
Issue 6
DOI:
https://doi.org/10.1103/PhysRevD.107.066014
arXiv:
2209.15026
Copyrights:
Published by the American Physical Society
Licence:
CC-BY-4.0

Fulltext files: