Detecting three-qubit bound MUB diagonal entangled states via Nonlinear optimal entanglement witnesses

TL;DR

This paper develops nonlinear optimal entanglement witnesses from linear ones to effectively detect bound entangled states in three-qubit MUB diagonal systems, providing a practical method for distinguishing entangled from separable states.

Contribution

It introduces a novel approach to construct nonlinear optimal entanglement witnesses from linear ones, enhancing detection of bound entangled states in three-qubit MUB diagonal systems.

Findings

Nonlinear EWs can detect PPT entangled states.

The method separates bound entangled regions from separable states.

Numerical examples confirm practical applicability.

Abstract

One of the important approaches to detect quantum entanglement is using linear entanglement witnesses EWs. In this paper, by determining the envelope of the boundary hyper-planes defined by a family of linear EWs, a set of powerful nonlinear optimal EWs is manipulated. These EWs enable us to detect some three qubits bound MUB (mutually unbiased bases) diagonal entangled states, i.e., the PPT (positive partial transpose) entangled states. Also, in some particular cases, the introduced nonlinear optimal EWs are powerful enough to separate the bound entangled regions from the separable ones. Finally, we present numerical examples to demonstrate the practical accessibility of this approach. Keywords :nonlinear optimal entanglement witnesses, mutually unbiased bases, MUB diagonal states