Entanglement criteria and nonlocality for multi-mode continuous variable systems

TL;DR

This paper develops a comprehensive method for deriving entanglement inequalities in multi-mode continuous variable systems, confirming that nonlocality implies negative partial transpose entanglement, thus advancing quantum entanglement detection.

Contribution

It introduces a general approach combining partial transposition with necessary conditions to derive entanglement inequalities, supporting Peres' conjecture fully.

Findings

Derived broad class of entanglement inequalities

Supported Peres' conjecture in multipartite systems

Unified previous inequalities as special cases

Abstract

We demonstrate how to efficiently derive a broad class of inequalities for entanglement detection in multi-mode continuous variable systems. The separability conditions are established from partial transposition (PT) in combination with several distinct necessary conditions for a quantum physical state, which include previously established inequalities as special cases. Remarkably, our method enables us to support Peres' conjecture to its full generality within the framework of Cavalcanti-Foster-Reid-Drummond multipartite Bell inequality [Phys. Rev. Lett. 99}, 210405 (2007)] that the nonlocality necessarily implies negative PT entangled states.