Degree of non-Markovianity of quantum evolution.
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 the non-Markovian one is further characterized by its degree. It enables one to introduce a non-Markovianity 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 the maximally entangled state. Our approach allows us to classify the non-Markovianity measures introduced so far in a unified rigorous mathematical framework.
Institute of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University, Grudzia¸dzka 5/7, 87-100 Toruń, Poland.
Dariusz
D
Chruściński
SUPA, EPS/Physics, Heriot-Watt University, Edinburgh, EH14 4AS, United Kingdom and Department of Physics and Astronomy, University of Turku, 20014 Turku, Finland.
Sabrina
S
Maniscalco