Code properties from holographic geometries
Code properties from holographic geometries
复制标题
全息几何的代码属性
DOI：
10.1103/physrevx.7.021022
复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
J. Preskill
中科院分区：
文献类型：
--
作者：
F. Pastawski;J. Preskill
AlMheiri，Dong和Harlow[arxiv：1411.7041]提出了ADS/CFT全息对应和算符代数量子纠错之间的一种极具启发性的联系。在这里，我们将进一步探讨这种联系。我们得到了一些关于OAQEC的一般性结果，以及特别适用于允许全息解释的量子码的结果。我们引入了一个新的量，称为‘价格’，它刻画了受保护逻辑系统的支持度，并找到了对量子码逻辑子代数的价格和距离的约束。我们证明了定义在具有渐近负曲率的体流形上的全息码表现出‘超全息’，这意味着体逻辑代数可以被支持在具有分形结构的边界区域上。我们认为，对于定义在具有渐近平坦或正曲率的体流形上的全息码，边界物理必须是高度非局域的，这对黑洞和ADS空间中的量子引力具有潜在的影响，与ADS曲率半径相比，距离尺度很小。
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.