Entanglement witnesses for families of the bound entangled three-qubit states

Abstract

Entanglement witnesses are of special interest for distinguishing between separable and entangled states. For three-qubit states, a family of optimal entanglement witnesses has been introduced by Jafarizadeh et al. [Eur. Phys. J. D 50 (2008) 107]. We give an alternative demonstration for some elements of this family and show that they are able to detect bound entangled states. To illustrate this fact, we consider two families of bound entangled three-qubit states, introduced by Kay [Phys. Rev. A 83 (2011) 020303] and Kye [J. Phys. A, Math. Theor. 48 (2015) 235303], and show that these witnesses detect the entanglement of all states of these two families.