The study of information revivals, witnessing the violation of certain data-processing inequalities, has provided an important paradigm in the study of non-Markovian quantum stochastic processes. Although often used interchangeably, we argue here that the notions of “revivals” and “backflows,” i.e., flows of information from the environment back into the system, are distinct: an information revival can occur without any backflow ever taking place. In this paper, we examine in detail the phenomenon of noncausal revivals and relate them to the theory of short Markov chains and squashed non-Markovianity. We also provide an operational condition, in terms of system-only degrees of freedom, to witness the presence of genuine backflow that cannot be explained by noncausal revivals. As a byproduct, we demonstrate that focusing on processes with genuine backflows, while excluding those with only noncausal revivals, resolves the issue of nonconvexity of Markovianity, thus enabling the construction of a convex resource theory of genuine quantum non-Markovianity.
The study of information revivals, witnessing the violation of certain data-processing inequalities, has provided an important paradigm in the study of non-Markovian quantum stochastic processes. Although often used interchangeably, we argue here that the notions of “revivals” and “backflows,” i.e., flows of information from the environment back into the system, are distinct: an information revival can occur without any backflow ever taking place. In this paper, we examine in detail the phenomenon of noncausal revivals and relate them to the theory of short Markov chains and squashed non-Markovianity. We also provide an operational condition, in terms of system-only degrees of freedom, to witness the presence of genuine backflow that cannot be explained by noncausal revivals. As a byproduct, we demonstrate that focusing on processes with genuine backflows, while excluding those with only noncausal revivals, resolves the issue of nonconvexity of Markovianity, thus enabling the construction of a convex resource theory of genuine quantum non-Markovianity.
The Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) equation, a cornerstone of open-system theory, describes Markovian semigroup dynamics in which information about the initial preparation cannot revive. Beyond this regime, information revivals are widely interpreted as backflow from a non-Markovian environment. However, a decrease followed by an increase in information retrievable from the system need not imply that information has returned from the environment [PRX Quantum 6, 020316 (2025)]. It may instead arise from noise correlations unrelated to the system's initial preparation, carried by inert degrees of freedom that never interact with the system and therefore cannot mediate backflow. Such revivals are called extrinsic; genuine backflow is reserved for revivals that cannot be explained this way. The framework developed in that work, however, assumes access to arbitrary initial system states, an assumption often incompatible with physical constraints or limited experimental control. This leaves open which properties of the available preparations are necessary for an information revival to certify genuine backflow. Here we extend the framework to allow the description of restricted families of initial states and show that genuine backflow is possible only if the family contains noncommuting states. If all available states commute, as in a classical stochastic process, every revival can be explained by a suitable inert extension and is therefore extrinsic. Noncommutativity of the available system states is thus necessary for information revivals to provide an operational signature of environmental memory.
A Markovian process of a system is defined classically as a process in which the future state of the system is fully determined by only its present state, not by its previous history. There have been several measures of non-Markovianity to quantify the degrees of non-Markovian effect in a process of an open quantum system based on information backflow from the environment to the system. However, the condition for the witness of the system information backflow does not coincide with the classical definition of a Markovian process. Recently, a new measure with a condition that coincides with the classical definition in the relevant limit has been proposed. Here, we focus on the new definition (measure) for quantum non-Markovian processes, and characterize the Markovian condition as a quantum process that has no information backflow through the reduced environment state (IBTRES) and no system-environment correlation effect (SECE). The action of IBTRES produces non-Markovian effects by flowing the information of quantum operations performed by an experimenter at earlier times back to the system through the environment, while the SECE can produce non-Markovian effect without carrying any earlier quantum operation information. We give the necessary and sufficient conditions for no IBTRES and no SECE, respectively, and show that a process is Markovian if and only if it has no IBTRES and no SECE. The quantitative measures and algorithms for calculating non-Markovianity, IBTRES, and solely SECE are explicitly presented.
In this PHD thesis, I address the study of the evolution of quantum correlations of continuous variable systems interacting with classical environments, portrayed by classical stochastic fields. In particular, the first goal is individuating the working regimes where a full quantum description of the system-environment interaction may be simulated with a stochastic approach. As a paradigmatic example, I consider quantum harmonic oscillators subject to phase diffusion and dissipation decoherence. My results show that the stochastic noise may take over the full quantum description of Markovian dephasing channels, while a stochastic approach to dissipation only works at a high temperature in the early stage of the dynamics. The second goal consists in better exploring the connection between the dynamics of correlations of the system, non-Markovianity and backflow of information. In many situations non-Markovianity cannot be proved but only revealed by means of appropriate witnesses, usually associated to backflow of information. My results show that stochastic phase diffusing and stochastic dissipative environments lead to non-Markovian dynamics, but their non-Markovianity stays unwitnessed unless revivals of correlations as nonclassicality, entanglement or discord are detected. This suggests that non-Markovianity sets the natural framework for revivals of correlations, but the true resource to obtain revivals is the backflow of information. The third goal consists in showing that effects of local or global noise on a bipartite system may easily be distinguished by means of standard laboratory techniques. Indeed, my results show that homodyne-detection-based schemes may discriminate the effects of a global stochastic noise affecting two probes from local perturbation, using as states of the probe ?lab-friendly? states.
We address the dynamics of quantum correlations for a bipartite continuous-variable quantum system interacting with its fluctuating environment. In particular, we consider two independent quantum oscillators initially prepared in a Gaussian state, e.g., a squeezed thermal state, and compare the dynamics resulting from local noise, i.e., oscillators coupled to two independent external fields, to that originating from common noise, i.e., oscillators interacting with a single common field. We prove non-Markovianity (nondivisibility) of the dynamics in both regimes and analyze the connections between nondivisibility, backflow of information, and revivals of quantum correlations. Our main results may be summarized as follows: (i) revivals of quantumness are present in both scenarios, however, the interaction with a common environment better preserves the quantum features of the system; (ii) the dynamics is always nondivisible but revivals of quantum correlations are present only when backflow of information is present as well. We conclude that nondivisibility in its own is not a resource to preserve quantum correlations in our system, i.e., it is not sufficient to observe recoherence phenomena. Rather, it represents a necessary prerequisite to obtain backflow of information, which is the true ingredient to obtain revivals of quantumness.
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.
Quantum memory effects can be qualitatively understood as a consequence of an environment-to-system backflow of information. Here, we analyze and compare how this concept is interpreted and implemented in different approaches to quantum non-Markovianity. We study a nonoperational approach, defined by the distinguishability between two system states characterized by different initial conditions, and an operational approach, which is defined by the correlation between different outcomes associated to successive measurement processes performed over the system of interest. The differences, limitations, and vantages of each approach are characterized in detail by considering diverse system-environment models and dynamics. As a specific example, we study a non-Markovian depolarizing map induced by the interaction of the system of interest with an environment characterized by incoherent and coherent self-dynamics.