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

TL;DR

This review discusses recent advances in understanding and characterizing genuine quantum non-Markovianity, emphasizing information-theoretic approaches and operational criteria to distinguish quantum from classical memory effects.

Contribution

It provides a comprehensive survey of frameworks and criteria for identifying genuine quantum non-Markovianity, clarifying their physical motivations and limitations.

Findings

Comparison of state-distinguishability and channel-based approaches

Criteria for distinguishing genuine quantum non-Markovianity

Analysis of strengths and limitations of different frameworks

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.