Southwest Quantum Information and Technology

The Ryu-Takayanagi formula from quantum error correction: An algebraic treatment of the boundary CFT

Presenting Author: Helia Kamal, University of California Berkeley
Contributing Author(s): Geoffrey Penington

In recent years, an interpretation of the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence in the language of quantum error correction has been developed. This language shines light on several puzzling features of the correspondence and has therefore played a crucial role in advancing our understanding of AdS/CFT. In particular, in a recent work by Daniel Harlow, it is shown that sub-algebra quantum erasure-correcting codes with complementary recovery naturally give rise to a version of quantum-corrected Ryu-Takayanagi formula that captures the physics of AdS/CFT. Harlow’s key insight was that the realistic and accurate treatment of the code space is using Von Neumann algebras. In his interpretation of AdS/CFT, a Von Neumann algebra is defined on the bulk, while a simple tensor product structure is assumed for the boundary Hilbert space. In this work, we develop the mathematical framework for extending Harlow's results to the more physical case where a Von Neumann algebra is also given on the boundary CFT. By obtaining an algebraic version of Ryu-Takayanagi that very closely resembles the original formula, we show that our code more accurately captures the properties of AdS/CFT.

(Session 5 : Sunday from 5:00pm - 7:00pm)