I am also working on mathematical foundations of quantum information theory. In particular, I want to develop novel linear and non-linear positive maps that characterize entanglement and the space of quantum states. I have been successful in describing several families of such linear maps in even dimension. A rigorous proof of the behavior of their non-linear counterparts remains a challenging open issue in mathematical physics. Currently I am examining the constructions of maps in arbitrary dimensions, nonlinear extension and the nature of detectable entangled states.