论文标题
在张量网络中向最小键切面表面的纠缠蒸馏
Entanglement distillation toward minimal bond cut surface in tensor networks
论文作者
论文摘要
在张量网络中，将键切面表面推向最小表面的几何操作对应于纠缠蒸馏。切割键定义了键切面上的降低过渡矩阵，而相关的量子状态自然而然地从中出现。我们通过评估最大纠缠状态与键切面的状态之间的痕量距离在多尺度纠缠重归于ANSATZ（MERA）（MERA）和矩阵乘积状态状态下的痕量距离，以定量的方式证明了这张图。随机MERA的数值结果与我们的建议达成了合理的协议。该结果为对全息图和纠缠结构的几何形状的纠缠熵的Ryu-takayanagi公式有了更深入的了解。
In tensor networks, a geometric operation of pushing a bond cut surface toward a minimal surface corresponds to entanglement distillation. Cutting bonds defines a reduced transition matrix on the bond cut surface and the associated quantum state naturally emerges from it. We justify this picture quantitatively by evaluating the trace distance between the maximally entangled states and the states on bond cut surfaces in the multi-scale entanglement renormalization ansatz (MERA) and matrix product states in a canonical form. Our numerical result for the random MERA is in a reasonable agreement with our proposal. The result sheds new light on a deeper understanding of the Ryu-Takayanagi formula for entanglement entropy in holography and the emergence of geometry from the entanglement structure.
