Mainz 2017 – wissenschaftliches Programm
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Q: Fachverband Quantenoptik und Photonik
Q 8: Quantum Information: Concepts and Methods II
Q 8.8: Vortrag
Montag, 6. März 2017, 18:45–19:00, P 2
Code properties from holographic geometries — •Fernando Pastawski1 and John Preskill2 — 1Freie Universität Berlin — 2California Institute of Technology
Almheiri, Dong, and Harlow proposed a highly illuminating connection between the AdS/CFT holographic correspondence and operator algebra quantum error correction (OAQEC). Here we explore this connection further. We derive some general results about OAQEC, as well as results that apply specifically to quantum codes which admit a holographic interpretation. We introduce a new quantity called price, which characterizes the support of a protected logical system, and find constraints on the price and the distance for logical subalgebras of quantum codes. We show that holographic codes defined on bulk manifolds with asymptotically negative curvature exhibit uberholography, meaning that a bulk logical algebra can be supported on a boundary region with a fractal structure. We argue that, for holographic codes defined on bulk manifolds with asymptotically flat or positive curvature, the boundary physics must be highly nonlocal, an observation with potential implications for black holes and for quantum gravity in AdS space at distance scales small compared to the AdS curvature radius.