Decoherence and the Classes of Maximally Entangled States

TL;DR

This paper explores how decoherence drives quantum systems toward maximally entangled states, which can be classified by entanglement invariants, and investigates the dynamics of these states through random walks in entanglement space.

Contribution

It introduces a classification of maximally entangled states using entanglement invariants and analyzes their behavior under decoherence in various quantum systems.

Findings

Maximally entangled states can be uniquely classified by entanglement invariants.

Constructed compact states in the most entangled classes for tripartite systems.

Studied random walks in entanglement space to model decoherence effects.

Abstract

Self-interactions and interaction with the environment tend to push quantum systems toward states of maximal entanglement. This is a definition of decoherence. We argue that these maximally entangled states fall into the well-defined classes that can be uniquely described by the values of certain entanglement invariants. After discussing these ideas we present examples of maximally entangled states for a number of generic systems, construct compact states in the most entangled classes for tripartite systems, and suggest how they may be constructed for other $n$-partite systems. We study random walks through the space of entanglement classes to see how decoherence might work in practice.