Witness for an entangled state with positive partial transpose

TL;DR

This paper investigates a specific entangled state with positive partial transpose in a 3x3 system, demonstrating it as an edge state and explicitly constructing a witness operator to detect its entanglement.

Contribution

The work explicitly constructs a witness operator for a PPT entangled state in a 3x3 system, identifying it as an edge state and advancing entanglement detection methods.

Findings

Identified a PPT entangled state as an edge state.

Constructed an explicit entanglement witness operator.

Enhanced understanding of entanglement detection in higher-dimensional systems.

Abstract

In this letter we have analyzed an entangled state in $C^{3} \bigotimes C^{3}$ having a positive partial transposition and have shown that it is an edge state. Further we have constructed explicitly a witness operator $W$ which detects the entanglement.