Concepts of quantum non-Markovianity: a hierarchy

Understand

Markovian approximation is a widely-employed idea in descriptions of the dynamics of open quantum systems (OQSs).

• Although it is usually claimed to be a concept inspired by classical Markovianity, the term quantum Markovianity is used inconsistently and often unrigorously in the literature.
• In this report we compare the descriptions of classical stochastic processes and quantum stochastic processes (as arising in OQSs), and show that there are inherent differences that lead to the non-trivial problem of characterizing quantum non-Markovianity.
• Rather than proposing a single definition of quantum Markovianity, we study a host of Markov-related concepts in the quantum regime.