The thread embodiment of holographic quantum entanglement

TL;DR

This paper introduces the concept of entanglement threads as a visual and structural tool to understand holographic quantum entanglement, linking tensor networks, quantum circuits, and holographic complexity.

Contribution

It develops a new framework of entanglement threads to characterize holographic entanglement structure, connecting it with quantum circuits and complexity measures.

Findings

Entanglement threads visualize holographic entanglement.

A circuit interpretation of holographic complexity is proposed.

Clarifies the relation between entanglement threads and bit threads.

Abstract

This paper systematically develops the concept of entanglement threads that characterize the entanglement structure of holographic duality. Behind this framework lies a simple philosophy: holographic quantum entanglement can be visualized using thread-like objects. Inspired by the fact that tensor network models can be deformed into a quantum circuit form with flow-conserving features, we abstract the concept of entanglement threads. These entanglement threads can be understood as a pre-set ensemble of wires in a holographic quantum circuit, and we propose that they characterize the underlying partially ordered structure of holographic quantum entanglement. Combining the concepts of entanglement threads and kinematic space, a elegant circuit interpretation for the holographic complexity is provided. We also clarify the connection and distinction between entanglement threads and the previously proposed concept of bit threads.