Abstract The information encoded into an open quantum system that evolves under a Markovian dynamics is always monotonically non-increasing. Nonetheless, for a given quantifier of the information contained in the system, it is in general not clear if for all non-Markovian dynamics it is possible to observe a non-monotonic evolution of this quantity, namely a backflow. We address this problem by considering correlations of finite-dimensional bipartite systems. For this purpose, we consider a class of correlation measures and prove that if the dynamics is non-Markovian there exists at least one element from this class that provides a correlation backflow. Moreover, we provide a set of initial probe states that accomplish this witnessing task. This result provides the first one-to-one relation between non-Markovian quantum dynamics and correlation backflows. Finally, we introduce a measure of non-Markovianity.
Abstract The information encoded into an open quantum system that evolves under a Markovian dynamics is always monotonically non-increasing. Nonetheless, for a given quantifier of the information contained in the system, it is in general not clear if for all non-Markovian dynamics it is possible to observe a non-monotonic evolution of this quantity, namely a backflow. We address this problem by considering correlations of finite-dimensional bipartite systems. For this purpose, we consider a class of correlation measures and prove that if the dynamics is non-Markovian there exists at least one element from this class that provides a correlation backflow. Moreover, we provide a set of initial probe states that accomplish this witnessing task. This result provides the first one-to-one relation between non-Markovian quantum dynamics and correlation backflows. Finally, we introduce a measure of non-Markovianity.
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.
We investigate the ability of correlation measures to witness non-Markovian open-quantum-system dynamics. It is shown that the mutual information and any entanglement measure between the system and an ancilla do not witness all non-Markovian dynamics. A correlation measure is introduced, and it is proven that, in an enlarged setting with two ancillary systems, this measure detects almost all non-Markovian dynamics, except possibly a zero-measure set of dynamics that is nonbijective in finite time intervals. Our proof is constructive and provides different initial states detecting the non-Markovian evolutions. These states are all separable and some are arbitrarily close to a product state. A further advantage of the introduced correlation measure is that it can be efficiently computed through semidefinite programming.
In the dynamics of open quantum systems, information may propagate in time through either the system or the environment, giving rise to Markovian and non-Markovian temporal correlations, respectively. However, despite their notable coexistence in most physical situations, it is not yet clear how these two quantities may limit the existence of one another. Here, we address this issue by deriving several inequalities relating the temporal correlations of general multitime quantum processes. The dynamics are described by process tensors, and the correlations are quantified by the mutual information between subsystems of their Choi states. First, we prove a set of upper bounds to the non-Markovianity of a process given the degree of Markovianity in each of its steps. This immediately implies a nontrivial maximum value for the non-Markovianity of any process, independent of its Markovianity. Finally, we determine how the non-Markovianity limits the amount of total temporal correlations that could be present in a given process. These results show that, although any multitime process must pay a price in total correlations to have a given amount of non-Markovianity, this price vanishes exponentially with the number of steps of the process, while the maximum non-Markovianity grows only linearly. This implies that even a highly non-Markovian process might be arbitrarily close to having the maximum amount of total correlations if it has a sufficiently large number of steps.
Non-Markovian dynamics are characterized by information backflows, where the evolving open quantum system retrieves part of the information previously lost in the environment. Hence, the very definition of non-Markovianity implies an initial time interval when the evolution is noisy, otherwise no backflow could take place. We identify two types of initial noise, where the first has the only effect of degrading the information content of the system, while the latter is essential for the appearance of non-Markovian phenomena. Therefore, all non-Markovian evolutions can be divided into two classes: noisy non-Markovian (NNM), showing both types of noise, and pure non-Markovian (PNM), implementing solely essential noise. We make this distinction through a timing analysis of fundamental non-Markovian features. First, we prove that all NNM dynamics can be simulated through a Markovian pre-processing of a PNM core. We quantify the gains in terms of information backflows and non-Markovianity measures provided by PNM evolutions. Similarly, we study how the entanglement breaking property behaves in this framework and we discuss a technique to activate correlation backflows. Finally, we show the applicability of our results through the study of several well-know dynamical models.
We consider a two-level open quantum system undergoing pure dephasing, dissipative, or multiply decohering dynamics and show that whenever the dynamics is non-Markovian, the initial speed of evolution is a monotonic function of the relevant physical parameter driving the transition between the Markovian and non-Markovian behavior of the dynamics. In particular, within the considered models, a speed increase can only be observed in the presence of backflow of information from the environment to the system.
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.