The Ryu–Takayanagi Formula from Quantum Error Correction

  title={The Ryu–Takayanagi Formula from Quantum Error Correction},
  author={Daniel Harlow},
  journal={Communications in Mathematical Physics},
  • D. Harlow
  • Published 13 July 2016
  • Mathematics
  • Communications in Mathematical Physics
I argue that a version of the quantum-corrected Ryu–Takayanagi formula holds in any quantum error-correcting code. I present this result as a series of theorems of increasing generality, with the final statement expressed in the language of operator-algebra quantum error correction. In AdS/CFT this gives a “purely boundary” interpretation of the formula. I also extend a recent theorem, which established entanglement-wedge reconstruction in AdS/CFT, when interpreted as a subsystem code, to the… 
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