Systematic Construction of Genuine Multipartite Entanglement Criteria using Uncertainty Relations

TL;DR

This paper introduces a systematic method for constructing practical criteria to detect genuine multipartite continuous variable entanglement using uncertainty relations, unifying and strengthening previous approaches.

Contribution

It provides a general, computable framework for entanglement detection based on global operators and the positive partial transpose criterion, extending prior work by van Loock and Furusawa.

Findings

Criteria are single inequalities that are experimentally feasible.

Violations of criteria are sufficient for genuine multipartite entanglement.

The method unifies and generalizes previous entanglement detection approaches.

Abstract

A general procedure to construct criteria for identifying genuine multipartite continuous variable entanglement is presented. It relies on the proper definition of adequate global operators describing the multipartite system, the positive partial transpose criterion of separability, and quantum mechanical uncertainty relations. As a consequence, each criterion encountered consists of a single inequality that is nicely computable and experimentally feasible, and that when violated is sufficient condition for genuine multipartite entanglement. Additionally we show that the previous work of van Loock and Furusawa [Phys. Rev. A, 67, 052315 (2003)] is a special case of our result that includes strongest criteria to detect entanglement.