Common entanglement witnesses and their characteristics

TL;DR

This paper explores methods for constructing common entanglement witnesses, including Schmidt number witnesses, especially for states with positive partial transpose, using examples from qutrit systems.

Contribution

It introduces the concept of common decomposable and non-decomposable witnesses, extending entanglement detection techniques for complex quantum states.

Findings

Developed methods for common entanglement witness construction

Extended to Schmidt number witnesses for broader applicability

Illustrated with qutrit system examples

Abstract

We investigate the issue of finding common entanglement witness for certain class of states and extend this study to the case of Schmidt number witnesses. We also introduce the notion of common decomposable and non-decomposable witness operators which is specially useful for constructing a common witness where one of the entangled states is with a positive partial transpose. Our approach is illustrated with the help of suitable examples of qutrit systems.