Entanglement distillation towards minimal bond cut surface in tensor networks

Abstract

We propose that a minimal bond cut surface is characterized by entanglement distillation in tensor networks. Our proposal is not only consistent with the holographic models of perfect or tree tensor networks, but also can be applied for several different classes of tensor networks including matrix product states and multi-scale entanglement renormalization ansatz. We confirmed our proposal by a numerical simulation based on the random tensor network. The result sheds new light on a deeper understanding of the Ryu-Takayanagi formula for entanglement entropy in holography.Comment: 8 pages, 9 figure