论文标题
真实空间RG，错误校正和PETZ地图
Real-space RG, error correction and Petz map
论文作者
论文摘要
这项工作有两个部分： 首先，我们研究真实空间重新归一化组（RG）的误差校正性能。长距离操作员是在短距离运算符的物理代数中编码的（大约）可更正的运算符。这与将全息图建模为量子误差校正代码密切相关。与全息图相反，多体量子系统的真实空间RG没有互补的恢复属性。我们讨论了大型$ n $的作用和在互补恢复的出现中在运营商范围中的巨大差距。 其次，我们研究了任何von Neumann代数的操作员代数确切的量子误差校正。我们表明，与有限维度的情况相似，对于von Neumann代数之间的任何误差映射，误差图的PETZ双重图是一个恢复图，如果包含操作员的可更正子代数为有限索引。
There are two parts to this work: First, we study the error correction properties of the real-space renormalization group (RG). The long-distance operators are the (approximately) correctable operators encoded in the physical algebra of short-distance operators. This is closely related to modeling the holographic map as a quantum error correction code. As opposed to holography, the real-space RG of a many-body quantum system does not have the complementary recovery property. We discuss the role of large $N$ and a large gap in the spectrum of operators in the emergence of complementary recovery. Second, we study the operator algebra exact quantum error correction for any von Neumann algebra. We show that similar to the finite dimensional case, for any error map in between von Neumann algebras the Petz dual of the error map is a recovery map if the inclusion of the correctable subalgebra of operators has finite index.
