论文标题
无限维度的快乐代码：纠缠楔重建和动态
The infinite-dimensional HaPPY code: entanglement wedge reconstruction and dynamics
论文作者
论文摘要
我们构建了快乐代码的无限二维类似物，作为一系列稳定器代码，这些稳定器代码定义为他们的希尔伯特空间。希尔伯特的空间通过等距图关联，我们明确定义。我们构建了一种与无限维的快乐代码兼容的哈密顿量，并进一步研究了我们的代码的稳定器，该代码具有固有的分形结构。我们使用此结果来研究代码的动力学，并将非平凡的散装哈密顿量映射到边界。我们发现映射的图像是比例不变的，但在边界中没有产生任何远程纠缠，因此未能重现CFT的特征。该结果显示了快乐代码作为AD/CFT对应的模型的限制，但也暗示量子误差校正在量子重力中的相关性可能不限于CFT上下文。
We construct an infinite-dimensional analog of the HaPPY code as a growing series of stabilizer codes defined respective to their Hilbert spaces. The Hilbert spaces are related by isometric maps, which we define explicitly. We construct a Hamiltonian that is compatible with the infinite-dimensional HaPPY code and further study the stabilizer of our code, which has an inherent fractal structure. We use this result to study the dynamics of the code and map a nontrivial bulk Hamiltonian to the boundary. We find that the image of the mapping is scale invariant, but does not create any long-range entanglement in the boundary, therefore failing to reproduce the features of a CFT. This result shows the limits of the HaPPY code as a model of the AdS/CFT correspondence, but also hints that the relevance of quantum error correction in quantum gravity may not be limited to the CFT context.
