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arXiv:2603.28277

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

Rajeev Gangwar, Ujjwal Sen

quant-phcond-mat.stat-mechhep-thSubmitted Mar 30, 2026• Announced Mar 31, 2026• 0 citations• Revised Apr 8, 2026 (v3)

v1 · Mar 30, 2026 v2 · Mar 31, 2026 v3 · Apr 8, 2026

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.

Comments: A new section has been added; comments are welcome

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. This is identified with the quantum dynamical semigroup (QDS), renewing advocacy for a familiar candidate. Of practical importance is that our weaker criterion is useful for indicating the non-Markovianity of CP-divisible channels that manifest an effect of counteracting decoherence. This is illustrated with the examples of power-law noise (PLN) and Ornstein-Uhlenbeck Noise (OUN). For physically well motivated channels, we propose a geometric quantification of non-Markovianity according to our definition, which is shown to be applicable to stronger manifestations of quantum non-Markovianity, demonstrated here by application to various channels, including those that are CP-indivisible, P-indivisible and eternally non-Markovian. Finally, we indicate a few open questions that come up as natural consequences of this work.

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Currently, there is no systematic way to describe a quantum process with memory solely in terms of experimentally accessible quantities. However, recent technological advances mean we have control over systems at scales where memory effects are non-negligible. The lack of such an operational description has hindered advances in understanding physical, chemical, and biological processes, where often unjustified theoretical assumptions are made to render a dynamical description tractable. This has led to theories plagued with unphysical results and no consensus on what a quantum Markov (memoryless) process is. Here, we develop a universal framework to characterize arbitrary non-Markovian quantum processes. We show how a multitime non-Markovian process can be reconstructed experimentally, and that it has a natural representation as a many-body quantum state, where temporal correlations are mapped to spatial ones. Moreover, this state is expected to have an efficient matrix-product-operator form in many cases. Our framework constitutes a systematic tool for the effective description of memory-bearing open-system evolutions.