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

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