Entanglement conditions for tripartite systems via indeterminacy relations

TL;DR

This paper introduces new inequalities based on S-R indeterminacy relations and partial transposition that effectively detect entanglement in various tripartite quantum systems, surpassing traditional Heisenberg-based methods.

Contribution

It develops a novel class of entanglement detection inequalities using indeterminacy relations and partial transposition applicable to multiple tripartite quantum systems.

Findings

Inequalities are generally stronger than Heisenberg-based criteria.

Applicable to bosonic, SU(2), and SU(1,1) systems.

Framework extends to multipartite systems.

Abstract

Based on the S-R indeterminacy relations in conjugation with the partial transposition, we derive a class of inequalities for detecting entanglement in several tripartite systems, including bosonic, SU(2), and SU(1,1) systems. These inequalities are in general stronger than those based on the usual Heisenberg relations for detecting entanglement. We also discuss the reduction from SU(2) and SU(1,1) to bosonic systems and the generalization to multipartite case.