Degree of Non-Markovianity of Quantum Evolution

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