Entanglement and Quantum Groups

TL;DR

This paper explores the relationship between quantum entanglement and compact quantum groups, establishing criteria and theorems analogous to classical entanglement detection methods.

Contribution

It introduces a framework linking quantum entanglement with quantum groups and proves key criteria similar to PPT and Horodecki theorems.

Findings

Established a PPT-like positivity criterion for quantum groups.

Formulated a Horodecki-type theorem within this framework.

Provided a new perspective on quantum entanglement using algebraic structures.

Abstract

We describe quantum mechanical entanglement in terms of compact quantum groups. We prove an analog of positivity of partial transpose (PPT) criterion and formulate a Horodecki-type Theorem.