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 (EW s). In this paper, by determining the envelope of the boundary hyper-planes defined by a family of linear EW s, a set of powerful nonlinear optimal EW s is manipulated. These EW s 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 EW s 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.