Alladi Ramakrishnan Hall

Parallels between Quantum Error Correction and Holography

Adarsh Sudhakar

My talk will be based on Daniel Harlow's paper "The Ryu-Takayanagi Formula from Quantum Error Correction." Under the framework of AdS/CFT, it has been recently proposed that in the limit of vanishing Newton's constant, modes of the bulk gravitational theory can be mapped to certain subspaces of the boundary CFT's Hilbert space via quantum error correction codes. By examining models of increasing generality, we characterise the capacity of a code subspace to compensate for erasures of a physical subsystem. We will then see that generic quantum error correcting codes that meet certain complementary recovery properties akin to those in AdS/CFT will satisfy a Ryu-Takayanagi like formula and allow for operator algebras acting on the code subspace to be replicated onto various other subspaces of the Hilbert space in a manner reminiscent of bulk reconstruction.