Entanglement witnesses for $d \otimes d$ systems and new classes of entangled qudit states

TL;DR

This paper introduces new entanglement witnesses for bipartite qudit systems and identifies classes of entangled states that these witnesses can detect, expanding the tools for quantum entanglement analysis.

Contribution

The authors develop a generalized construction of entanglement witnesses for $d imes d$ systems using semidefinite programming, extending previous methods for specific dimensions.

Findings

New entanglement witnesses for $d imes d$ systems.

Detection of new classes of PPT entangled states.

Generalization of previous entanglement detection methods.

Abstract

We provide a new class of entanglement witnesses for $d \ot d$ systems (two qudits). Our construction generalizes the one proposed recently by Jafarizadeh et al. for $d=3$ and $d=4$ on the basis of semidefinite linear programming. Moreover, we provide a new class of PPT entangled states detected by our witnesses which generalizes well known family of states constructed by Horodecki et al. for $d=3$.