论文标题
SYK和散装出现的量子误差校正
Quantum Error Correction in SYK and Bulk Emergence
论文作者
论文摘要
我们分析了Sachdev-ye-Kitaev模型的误差纠正属性，其误差对应于费米子亚集的擦除。我们研究限制的限制，与费米子总数相比，抹杀的费米数较大但很少。我们计算量子误差校正代码的价格，该代码定义为重建是否已在热状态下作用的物理量子数量。通过考虑通过量子传送的重建，我们主张将价格与普通运营商大小相关联的系统中，这些系统显示了Nezami等人的所谓详细尺寸绕组。 （2021）。然后，我们发现在Syk中，价格大致饱和。计算价格需要计算模块化的相关器相对于与费米子的子集相关的密度矩阵。我们将这些相关因子解释为探测Syk的广告中的量子极端表面。在大的$ n $限制中，与Syk中的费米子集相关的操作员代数满足半侧模块化包含，这表明了新兴类型III $ _1 $ _1 $ von Neumann代数。我们讨论了半侧模块化夹杂物的紧急代数与散装对称发生器之间的关系。
We analyze the error correcting properties of the Sachdev-Ye-Kitaev model, with errors that correspond to erasures of subsets of fermions. We study the limit where the number of fermions erased is large but small compared to the total number of fermions. We compute the price of the quantum error correcting code, defined as the number of physical qubits needed to reconstruct whether a given operator has been acted upon the thermal state or not. By thinking about reconstruction via quantum teleportation, we argue for a bound that relates the price to the ordinary operator size in systems that display so-called detailed size winding of Nezami et al. (2021). We then find that in SYK the price roughly saturates this bound. Computing the price requires computing modular flowed correlators with respect to the density matrix associated to a subset of fermions. We offer an interpretation of these correlators as probing a quantum extremal surface in the AdS dual of SYK. In the large $N$ limit, the operator algebras associated to subsets of fermions in SYK satisfy half-sided modular inclusion, which is indicative of an emergent Type III$_1$ von Neumann algebra. We discuss the relationship between the emergent algebra of half-sided modular inclusions and bulk symmetry generators.
