An introduction to entanglement measures

TL;DR

This paper reviews various entanglement measures in quantum information theory, focusing on finite-dimensional bipartite systems, and discusses their properties, manipulation, and related theorems.

Contribution

It provides a comprehensive overview of entanglement measures, including recent developments and key theorems, in a unified framework for finite-dimensional systems.

Findings

Summarizes key entanglement measures like entanglement of formation and distillable entanglement.

Discusses properties and extremality theorems of entanglement measures.

Briefly addresses infinite-dimensional and multi-party systems.

Abstract

We review the theory of entanglement measures, concentrating mostly on the finite dimensional two-party case. Topics covered include: single-copy and asymptotic entanglement manipulation; the entanglement of formation; the entanglement cost; the distillable entanglement; the relative entropic measures; the squashed entanglement; log-negativity; the robustness monotones; the greatest cross-norm; uniqueness and extremality theorems. Infinite dimensional systems and multi-party settings will be discussed briefly.