Beyond toy models: distilling tensor networks in full AdS/CFT
Beyond toy models: distilling tensor networks in full AdS/CFT
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DOI：
10.1007/jhep11(2019)069
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发表时间：
2018-12
影响因子：
5.4
通讯作者：
N. Bao;Geoffrey Penington;J. Sorce;Aron C. Wall
中科院分区：
文献类型：
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作者：
N. Bao;Geoffrey Penington;J. Sorce;Aron C. Wall
我们提出了一个一般的程序，用于构建张量网络，准确地再现共形场论（CFTs）中的全息态。给定一个静态半经典引力对偶的大N CFT中的状态，我们通过一系列迭代近似来建立张量网络，这些近似消除了冗余的自由度，并最小化了所得网络的键尺寸。我们认为，张量网络的键尺寸将匹配相应的散装表面的面积。对于“树”张量网络（即那些通过不相交的Ryu-Takayanagi表面离散时空而构建的网络），我们的论点可以在CFT中使用一次纠缠蒸馏的版本来进行严格的论证。利用AdS/CFT已知的量子纠错特性，我们证明了可以将大块腿添加到张量网络中以创建全息量子纠错码。这些代码的行为类似于以前的全息张量网络玩具模型，但描述了连续体AdS/CFT中的实际体激发。通过假设“全息纠缠纯化”猜想的一些自然概括，我们能够为更一般的批量离散化构建张量网络，从而形成更细粒度的网络，将Ryu-Takayanagi表面的信息内容划分为张量分解的子区域。虽然这样的张量网络的粒度必须设置为大于弦/普朗克尺度，但我们希望它可以选择远低于AdS尺度。然而，我们也证明了一个不去定理，这表明体积到边界的映射不能都是等距的张量网络相交Ryu-Takayanagi表面。
We present a general procedure for constructing tensor networks that accurately reproduce holographic states in conformal field theories (CFTs). Given a state in a large-N CFT with a static, semiclassical gravitational dual, we build a tensor network by an iterative series of approximations that eliminate redundant degrees of freedom and minimize the bond dimensions of the resulting network. We argue that the bond dimensions of the tensor network will match the areas of the corresponding bulk surfaces. For “tree” tensor networks (ie, those that are constructed by discretizing spacetime with non intersecting Ryu-Takayanagi surfaces), our arguments can be made rigorous using a version of one-shot entanglement distillation in the CFT. Using the known quantum error correcting properties of AdS/CFT, we show that bulk legs can be added to the tensor networks to create holographic quantum error correcting codes. These codes behave similarly to previous holographic tensor network toy models, but describe actual bulk excitations in continuum AdS/CFT. By assuming some natural generalizations of the “holographic entanglement of purification” conjecture, we are able to construct tensor networks for more general bulk discretizations, leading to finer-grained networks that partition the information content of a Ryu-Takayanagi surface into tensor-factorized subregions. While the granularity of such a tensor network must be set larger than the string/Planck scales, we expect that it can be chosen to lie well below the AdS scale. However, we also prove a no-go theorem which shows that the bulk-to-boundary maps cannot all be isometries in a tensor network with intersecting Ryu-Takayanagi surfaces.