Single-Shot Holographic Compression from the Area Law

Wilming H, Eisert J (2019)

Publication Type: Journal article

Publication year: 2019

Journal

Physical Review Letters American Physical Society

Book Volume: 122

Article Number: 190501

Journal Issue: 19

DOI: 10.1103/PhysRevLett.122.190501

Abstract

The area law conjecture states that the entanglement entropy of a region of space in the ground state of a gapped, local Hamiltonian only grows like the surface area of the region. We show that, for any state that fulfills an area law, the reduced quantum state of a region of space can be unitarily compressed into a thickened boundary of the region. If the interior of the region is lost after this compression, the full quantum state can be recovered to high precision by a quantum channel only acting on the thickened boundary. The thickness of the boundary scales inversely proportional to the error for arbitrary spin systems and logarithmically with the error for quasifree bosonic systems. Our results can be interpreted as a single-shot operational interpretation of the area law. The result for spin systems follows from a simple inequality showing that any probability distribution with entropy S can be approximated to error Ïby a distribution with support of size exp(S/Ï), which we believe to be of independent interest. We also discuss an emergent approximate correspondence between bulk and boundary operators and the relation of our results to tensor network states.

Involved external institutions

Eidgenössische Technische Hochschule Zürich (ETHZ) / Swiss Federal Institute of Technology in Zurich

Switzerland (CH) Freie Universität Berlin

Germany (DE)

How to cite

APA:

Wilming, H., & Eisert, J. (2019). Single-Shot Holographic Compression from the Area Law. Physical Review Letters, 122(19). https://doi.org/10.1103/PhysRevLett.122.190501

MLA:

Wilming, Henrik, and Jens Eisert. "Single-Shot Holographic Compression from the Area Law." Physical Review Letters 122.19 (2019).

BibTeX: Download