A cross-ratio threshold relation η'/η = e^{ΔH/2} governs entanglement-wedge phase transitions on pure-state holographic geometries, and uberholography's fractal dimension α ≈ 0.786 persists on asymptotic boundaries but not on RT-boundary geodesics.
Code properties from holographic geometries
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abstract
Almheiri, Dong, and Harlow [arXiv:1411.7041] 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.
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The paper organizes important open questions in quantum gravity and quantum information into four themes without presenting new results or derivations.
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Phase transitions and uberholography of holographic pure-state geometries
A cross-ratio threshold relation η'/η = e^{ΔH/2} governs entanglement-wedge phase transitions on pure-state holographic geometries, and uberholography's fractal dimension α ≈ 0.786 persists on asymptotic boundaries but not on RT-boundary geodesics.
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Rethinking quantum information in gravity and fields
The paper organizes important open questions in quantum gravity and quantum information into four themes without presenting new results or derivations.