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Updated: May 1, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
Published on: May 30, 2014
Degree of non-Markovianity of quantum evolution
Dariusz Chruściński1, Sabrina Maniscalco2
1Institute of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University, Grudzia¸dzka 5/7, 87-100 Toruń, Poland.
Abstract:
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.
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