Genuine and Non-Genuine Quantum Non-Markovianity: A Unified Information-Theoretic Review

Abstract

Understanding whether the features of open quantum dynamics are genuinely quantum remains a central challenge in quantum dynamics. Even though the non-Markovian behavior of quantum dynamics has been widely investigated across different settings, there is still no consensus on which properties of a dynamics reflect genuine quantum features and which arise from classical or non-genuine quantum sources. In this review, we provide detailed information on recent developments in characterizing quantum non-Markovianity based on information backflow and the nature of its origin. We also present a survey on how various approaches separate classical and quantum contributions, as well as how they define operational tasks that reveal genuine quantum non-Markovianity. We analyze several frameworks, including state-distinguishability -based, channel-based (``CP-divisibility''), and process-tensor methods. For each framework, we outline the underlying physical motivation, the criteria proposed to distinguish genuine quantum non-Markovianity from practical or apparent memory effects. We further compare different approaches and their strengths and limitations. The review aims to clarify the conceptual and operational aspects of quantum non-Markovian processes based on their nature and to provide a foundation for future research on quantum non-Markovianity and its role in advancing quantum information science and technology.

Figures (4)

• Figure 1: Non-Markovian dynamics: A mental picture of a non-Markovian process can be a cup of hot tea kept inside a container having partially insulated walls - partially insulated to heat. The cup releases heat into the immediate environment (orange arrows), but because the walls are partially insulated, some of the heat flows back (blue lines) to the cup, creating a "backflow" and introducing memory into the process. Some heat still escapes through the insulation to the external, faraway environment (long orange arrows).
• Figure 2: Markov dynamics: We consider the same cup of hot tea as in Fig. \ref{['fig:example_non-Markov']}, but this time without the partially-insulated bounding walls. The cup releases heat to the environment (orange arrows). The environment does not store or return this heat (there are no blue arrows this time), and so cooling occurs in a one-way, memoryless manner, with no heat backflow. This type of dynamics is referred to as Markovian.
• Figure 3: Classification of non-Markovianity in quantum dynamics of physical systems.
• Figure 4: Trace distance between the evolved states $\rho_\pm=| \pm \rangle\langle \pm |$ for a qubit with Hamiltonians $H_i=\tfrac{\omega_i}{2}\sigma_z$ ($\omega_1=1$, $\omega_2=3$). The dashed line corresponds to each individual Markovian unitary evolution, for which the trace distance is constant, while the solid curve shows the classically mixed dynamics $\Phi_t=\tfrac{1}{2}(\Phi_t^{(1)}+\Phi_t^{(2)})$, exhibiting non-monotonic behavior.

Theorems & Definitions (10)

• Definition 1
• Definition 2: RHP non-Markovianity
• Definition 3: BLP non-Markovianity
• Remark 1
• Definition 4
• Definition 5
• Definition 6
• Definition 7: Process tensor
• Definition 8
• Definition 9