A general algorithm for manipulating non-linear and linear entanglement witnesses by using exact convex optimization

A generic algorithm is developed to reduce the problem of obtaining linear and nonlinear entanglement witnesses of a given quantum system, to convex optimization problem. This approach is completely general and can be applied for the entanglement detection of any N-partite quantum system. For this purpose, a map from convex space of separable density matrices to a convex region called feasible region is defined, where by using exact convex optimization method, the linear entanglement witnesses can be obtained from polygonal shape feasible regions, while for curved shape feasible regions, envelope of the family of linear entanglement witnesses can be considered as nonlinear entanglement witnesses. This method proposes a new methodological framework within which most of previous EWs can be studied. To conclude and in order to demonstrate the capability E-mail:[email protected] E-mail:[email protected] E-mail:[email protected]