MIXING DOUBLY STOCHASTIC QUANTUM CHANNELS WITH THE COMPLETELY DEPOLARIZING CHANNEL
It is proved that every double stochastic quantum channel that is properly averaged with the completely depolarizing channel can be written as a convex combination of unitary channels. It follows that within the space of doubly stochastic quantum channels, there is a ball with positive radius around the completely depolarizing channel within which all channels are convex combinations of unitary channels.
doubly stochastic quantum channels random unitary channels mixed unitary channels theory of quantum information