# The Ryu–Takayanagi Formula from Quantum Error Correction

@article{Harlow2016TheRF, title={The Ryu–Takayanagi Formula from Quantum Error Correction}, author={Daniel Harlow}, journal={Communications in Mathematical Physics}, year={2016}, volume={354}, pages={865-912} }

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…

## 224 Citations

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Abstract
We first show that a class of operators acting on a given bipartite pure state on ℋ
A
⊗ ℋ
B
can shrink its supports on ℋ
A
⊗ ℋ
B
to only ℋ
A
or ℋ
B
while keeping its mappings.…

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