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. 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. 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. Harlow’s key insight was that the realistic and accurate treatment of the code space is using Von Neumann algebras. 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. I present this result as a series of theorems. 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. I argue that a version of the quantum-corrected Ryu-Takayanagi formula holds in any quantum error-correcting code. 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. 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. Presenting Author: Helia Kamal, University of California BerkeleyĬontributing Author(s): Geoffrey Penington Traditional versions of QEC as special cases.The Ryu-Takayanagi formula from quantum error correction: An algebraic treatment of the boundary CFT ![]() Independent interest as a very broad generalization of QEC it includes most This definition captures the quantum errorĬorrection (QEC) properties present in holographic codes and has potential Subsystems, and argue that this definition is "functionally unique." We alsoįormalize a definition of bulk reconstruction that we call "state-specific General quantum codes, defining "areas" associated to arbitrary logical In developing this theorem, we construct an emergent bulk geometry for Not require the entanglement wedge to be the same for all states in the code For example, if we can correct a Zerror, we can also correct ei Z cos + isin Z for arbitrary. The basic idea of any error-correcting code, quantum or classical, is to store the information redundantly. This fact is what hinted to Almheiri, Dong and Harlow in 2014 that quantum error correction might be related to the way anti-de Sitter space-time arises from quantum entanglement. This significantly generalizesīoth sides of an equivalence previously shown by Harlow in particular, we do IBM has made 18 quantum computers available for use. Prescription for physical (boundary) entropies. IBM researchers Hanhee Paik (left) and Sarah Sheldon (right) work on a quantum computer that is cooled by a hanging dilution refrigerator. ![]() Operators is equivalent to the existence of a quantum minimal surface Download a PDF of the paper titled Quantum minimal surfaces from quantum error correction, by Chris Akers and Geoff Penington Download PDF Abstract: We show that complementary state-specific reconstruction of logical (bulk)
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