  We propose a new characterization of non-Markovian quantum evolution based on
the concept of non-Markovianity degree. It provides an analog of a Schmidt
number in the entanglement theory and reveals the formal analogy between
quantum evolution and the entanglement theory: Markovian evolution corresponds
to a separable state and non-Markovian one is further characterized by its
degree. It enables one to introduce a non-Markovinity witness -- an analog of
an entanglement witness -- and a family of measures -- an analog of Schmidt
coefficients -- and finally to characterize maximally non-Markovian evolution
being an analog of maximally entangled state. Our approach allows to classify
the non-Markovianity measures introduced so far in a unified rigorous
mathematical framework.
