Depolarizing channel as a completely positive map with memory

The master equations that possess a memory kernel leading to a replacement of white noise by colored noise were discussed. The canonical form of the generator that leads to the quantum Markovian master equation for the system density operator was reviewed. It was found that the loss of complete positivity when the memory kernel was present was a feature of the colored noise. An example of a completely positive, trace-preserving map that results from a system-environment coupling that was essentially non-Markovian was also presented.