Tensor Networks for Entanglement Evolution

TL;DR

This paper develops a tensor network framework to unify and analyze the evolution of quantum entanglement, revealing topological equivalences and enabling new computational approaches.

Contribution

It introduces a tensor network-based theory for entanglement evolution, connecting recent equations of motion with topological and graphical methods.

Findings

Unified entanglement evolution theory in arbitrary dimensions

Revealed topological equivalence of entanglement monotones

Enabled application of tensor network methods to entanglement dynamics

Abstract

The intuitiveness of the tensor network graphical language is becoming well known through its use in numerical simulations using methods from tensor network algorithms. Recent times have also seen rapid progress in developing equations of motion to predict the time evolution of quantum entanglement [Nature Physics, 4(\textbf{4}):99, 2008]. Here we cast these recent results into a tensor network framework and in doing so, construct a theory which exposes the topological equivalence of the evolution of a family of entanglement monotones in arbitrary dimensions. This unification was accomplished by tailoring a form of channel state duality through the interpretation of graphical tensor network rewrite rules. The introduction of tensor network methods to the theory of entanglement evolution opens the door to apply methods from the rapidly evolving area known as tensor network states.