Order indices and entanglement production in quantum systems

TL;DR

This review discusses order indices and entanglement production in many-body quantum systems, highlighting their definitions, differences, and the relationship between order classification and entanglement quantification.

Contribution

It provides a comprehensive overview of order indices and entanglement production, emphasizing their applicability to finite systems and their interconnected roles.

Findings

Order indices classify all types of order in finite systems.

Entanglement production quantifies entanglement generated by quantum operations.

A close relationship exists between order indices and entanglement measures.

Abstract

The review is devoted to two important quantities characterizing many-body systems, order indices and the measure of entanglement production. Order indices describe the type of order distinguishing statistical systems. Contrary to the order parameters characterizing systems in the thermodynamic limit and describing long-range order, the order indices are applicable to finite systems and classify all types of orders, including long-range, mid-range, and short-range orders. The measure of entanglement production quantifies the amount of entanglement produced in a many-partite system by a quantum operation. Despite that the notions of order indices and entanglement production seem to be quite different, there is an intimate relation between them, which is emphasized in the review.