Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1711.03267 · Open Systems & Information Dynamics

Non-Markovian Evolution: a Quantum Walk Perspective

N. Pradeep Kumar, Subhashish Banerjee, R. Srikanth, Vinayak Jagadish, Francesco Petruccione

Published Sep 1, 2018• 71 citations
arXivHTMLPDF

Abstract

Quantum non-Markovianity of a quantum noisy channel is typically identified with information backflow or, more generally, with departure of the intermediate map from complete positivity. But here, we also indicate certain non-Markovian channels that cannot be witnessed by the CP-divisibility criterion. In complex systems, non-Markovianity becomes more involved on account of subsystem dynamics. Here we study various facets of non-Markovian evolution, in the context of coined quantum walks, with particular stress on disambiguating the internal vs. environmental contributions to non-Markovian backflow. For the above problem of disambiguation, we present a general power-spectral technique based on a distinguishability measure such as trace-distance or correlation measure such as mutual information. We also study various facets of quantum correlations in the transition from quantum to classical random walks, under the considered non-Markovian noise models. The potential for the application of this analysis to the quantum statistical dynamics of complex systems is indicated.

DOI
10.1142/s1230161218500142

Related papers

Witnessing non-Markovian dynamics through correlations

Dario De Santis, Markus Johansson, Bogna Bylicka +2 more

Non-Markovian effects in an open-system dynamics are usually associated to information backflows from the environment to the system. However, the way these backflows manifest and how to detect them is unclear. A natural approach is to study the backflow in terms of the correlations the evolving system displays with another unperturbed system during the dynamics. In this work, we study the power of this approach to witness non-Markovian dynamics using different correlation measures. We identify simple dynamics where the failure of completely positive divisibility is in one-to-one correspondence with a correlation backflow. We then focus on specific correlation measures, such as those based on entanglement and the mutual information, and identify their strengths and limitations. We conclude with a study of a recently introduced correlation measures based on state distinguishability and see how, for these measures, adding an extra auxiliary system enlarges the set of detectable non-Markovian dynamics.

arXiv:1903.12218•Physical Review A•Jul 13, 2020•16 citations

Exploring the non-Markovian dynamics in depolarizing maps

Ali Abu-Nada, Subhashish Banerjee, Vivek Balasaheb Sabale

The non-Markovian depolarizing channel is explored from the perspective of understanding its non-Markovian behavior as well as the occurrence of singularities. The study brings together the various ways to identify and quantify non-Markovianity. This includes dynamical techniques such as quantum information backflow witness, Breuer-Laine-Piilo, Rivas-Huelga-Plenio, and Hall-Cresser-Li-Andersson measures. In addition, geometrical visualization of non-Markovian effects is presented using the variation in the volume of accessible states during dynamical evolution. Further, a trajectory-based visualization of the dynamical map within the parameter space is presented. The trajectories traced during evolution demonstrate the loss of CP divisibility and the emergence of non-Markovianity under systematic variations of the system parameters. The effects of increasing system dimensions and qubit numbers on singularity and non-Markovianity are presented, with an extension of characterization techniques to higher-dimensional systems.

Physical Review A•Nov 8, 2024•5 citations

On a concept of quantum non-Markovianity weaker than CP-indivisibility

Shrikant Utagi, R. Srikanth, Subhashish Banerjee

The problem of defining quantum non-Markovianity has proven elusive, with various inequivalent criteria put forth to address it. We consider the question: what is the weakest notion of quantum non-Markovianity of system dynamics that would account for any aspect of memory? That is, a process indicated to be non-Markovian according to any existing criterion is also non-Markovian according to this criterion, but the converse may not be true. Correspondingly, we identify true memorylessness with the idea of the quantum dynamics being temporally self-similar, whereby the form of the intermediate map that propagates the state between two arbitrary time intervals is independent of the initial time $t_0$. 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.

•Nov 11, 2019•0 citations

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

Rajeev Gangwar, Ujjwal Sen

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.

quant-pharXiv:2603.28277•Mar 31, 2026•0 citations

Characterizing non-Markovianity via quantum interferometric power

Himadri Shekhar Dhar, Manabendra Nath Bera, Gerardo Adesso

Non-Markovian evolution in open quantum systems is often characterized in terms of the backflow of information from environment to system and is thus an important facet in investigating the performance and robustness of quantum information protocols. In this work, we explore non-Markovianity through the breakdown of monotonicity of a metrological figure of merit, called the quantum interferometric power, which is based on the minimal quantum Fisher information obtained by local unitary evolution of one part of the system, and can be interpreted as a quantifier of quantum correlations beyond entanglement. We investigate our proposed non-Markovianity indicator in two relevant examples. First, we consider the action of a single-party dephasing channel on a maximally entangled two-qubit state, by applying the Jamio\l{}kowski-Choi isomorphism. We observe that the proposed measure is consistent with established non-Markovianity quantifiers defined using other approaches based on dynamical divisibility, distinguishability, and breakdown of monotonicity for the quantum mutual information. Further, we consider the dynamics of two-qubit Werner states, under the action of a local, single-party amplitude damping channel, and observe that the nonmonotonic evolution of the quantum interferometric power is more robust than the corresponding one for entanglement in capturing the backflow of quantum information associated with the non-Markovian process. Implications for the role of non-Markovianity in quantum metrology and possible extensions to continuous variable systems are discussed.

arXiv:1501.02335•Physical Review A•Mar 18, 2015•94 citations

Exploring the Non-Markovian Dynamics in Depolarizing Maps

Ali Abu-Nada, Subhashish Banerjee, Vivek Balasaheb Sabale

The non-Markovian depolarizing channel is explored from the perspective of understanding its non-Markovian behaviour as well as the occurrence of singularities. The study brings together the various ways to identify and quantify non-Markovianity. This includes dynamical techniques such as quantum information backflow witness, BLP, RHP and HCLA measures. In addition, geometrical visualization of non-Markovian effects is presented using the variation in the volume of accessible states during dynamical evolution. Further, a trajectory-based visualization of the dynamical map, of the depolarizing channel, within the parameter space is presented. The trajectories traced during evolution, demonstrate the loss of CP-divisibility and the emergence of non-Markovianity under systematic variations of the system parameters.

arXiv:2403.04813•Mar 7, 2024•0 citations
Quantum non-Markovianity of a quantum noisy channel is typically identified with information backflow or, more generally, with departure of the intermediate map from complete positivity. But here, we also indicate certain non-Markovian channels that cannot be witnessed by the CP-divisibility criterion. In complex systems, non-Markovianity becomes more involved on account of subsystem dynamics. Here we study various facets of non-Markovian evolution, in the context of coined quantum walks, with particular stress on disambiguating the internal vs. environmental contributions to non-Markovian backflow. For the above problem of disambiguation, we present a general power-spectral technique based on a distinguishability measure such as trace-distance or correlation measure such as mutual information. We also study various facets of quantum correlations in the transition from quantum to classical random walks, under the considered non-Markovian noise models. The potential for the application of this analysis to the quantum statistical dynamics of complex systems is indicated.
Non-Markovian effects in an open-system dynamics are usually associated to information backflows from the environment to the system. However, the way these backflows manifest and how to detect them is unclear. A natural approach is to study the backflow in terms of the correlations the evolving system displays with another unperturbed system during the dynamics. In this work, we study the power of this approach to witness non-Markovian dynamics using different correlation measures. We identify simple dynamics where the failure of completely positive divisibility is in one-to-one correspondence with a correlation backflow. We then focus on specific correlation measures, such as those based on entanglement and the mutual information, and identify their strengths and limitations. We conclude with a study of a recently introduced correlation measures based on state distinguishability and see how, for these measures, adding an extra auxiliary system enlarges the set of detectable non-Markovian dynamics.
The non-Markovian depolarizing channel is explored from the perspective of understanding its non-Markovian behavior as well as the occurrence of singularities. The study brings together the various ways to identify and quantify non-Markovianity. This includes dynamical techniques such as quantum information backflow witness, Breuer-Laine-Piilo, Rivas-Huelga-Plenio, and Hall-Cresser-Li-Andersson measures. In addition, geometrical visualization of non-Markovian effects is presented using the variation in the volume of accessible states during dynamical evolution. Further, a trajectory-based visualization of the dynamical map within the parameter space is presented. The trajectories traced during evolution demonstrate the loss of CP divisibility and the emergence of non-Markovianity under systematic variations of the system parameters. The effects of increasing system dimensions and qubit numbers on singularity and non-Markovianity are presented, with an extension of characterization techniques to higher-dimensional systems.
The problem of defining quantum non-Markovianity has proven elusive, with various inequivalent criteria put forth to address it. We consider the question: what is the weakest notion of quantum non-Markovianity of system dynamics that would account for any aspect of memory? That is, a process indicated to be non-Markovian according to any existing criterion is also non-Markovian according to this criterion, but the converse may not be true. Correspondingly, we identify true memorylessness with the idea of the quantum dynamics being temporally self-similar, whereby the form of the intermediate map that propagates the state between two arbitrary time intervals is independent of the initial time t0t_0t0​. 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.
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.
Non-Markovian evolution in open quantum systems is often characterized in terms of the backflow of information from environment to system and is thus an important facet in investigating the performance and robustness of quantum information protocols. In this work, we explore non-Markovianity through the breakdown of monotonicity of a metrological figure of merit, called the quantum interferometric power, which is based on the minimal quantum Fisher information obtained by local unitary evolution of one part of the system, and can be interpreted as a quantifier of quantum correlations beyond entanglement. We investigate our proposed non-Markovianity indicator in two relevant examples. First, we consider the action of a single-party dephasing channel on a maximally entangled two-qubit state, by applying the Jamio\l{}kowski-Choi isomorphism. We observe that the proposed measure is consistent with established non-Markovianity quantifiers defined using other approaches based on dynamical divisibility, distinguishability, and breakdown of monotonicity for the quantum mutual information. Further, we consider the dynamics of two-qubit Werner states, under the action of a local, single-party amplitude damping channel, and observe that the nonmonotonic evolution of the quantum interferometric power is more robust than the corresponding one for entanglement in capturing the backflow of quantum information associated with the non-Markovian process. Implications for the role of non-Markovianity in quantum metrology and possible extensions to continuous variable systems are discussed.
The non-Markovian depolarizing channel is explored from the perspective of understanding its non-Markovian behaviour as well as the occurrence of singularities. The study brings together the various ways to identify and quantify non-Markovianity. This includes dynamical techniques such as quantum information backflow witness, BLP, RHP and HCLA measures. In addition, geometrical visualization of non-Markovian effects is presented using the variation in the volume of accessible states during dynamical evolution. Further, a trajectory-based visualization of the dynamical map, of the depolarizing channel, within the parameter space is presented. The trajectories traced during evolution, demonstrate the loss of CP-divisibility and the emergence of non-Markovianity under systematic variations of the system parameters.