Complete positivity conditions for quantum qutrit channels

Abstract

We present an analysis of complete positivity constraints on qutrit-qubit and qutrit-qutrit quantum channels that have a form of affine transformations of a generalized Bloch vector. We show that, in general, the complete positivity constraints for qutrit channels' parameters reveal nonlinearities and cannot be reduced to piecewise linear conditions defining a convex simplex. We discuss qutrit-qubit entanglement breaking channels and show Kraus representation for qutrit-qutrit damping channels.