The degree of non-Markovianity of quantum processes has been characterized in several different ways in the recent literature. However, the relationship between the non-Markovian behavior and the flow of information between the system and the environment through an entropic measure has not been yet established. We propose an entanglement-based measure of non-Markovianity by employing the concept of assisted knowledge, where the environment E, acquires information about a system S, by means of its measurement apparatus A. The assisted knowledge, based on the accessible information in terms of von Neumann entropy, monotonically increases in time for all Markovian quantum processes. We demonstrate that the signatures of non-Markovianity can be captured by the nonmonotonic behavior of the assisted knowledge. We explore this scenario for a two-level system undergoing a relaxation process, through an experimental implementation using an optical approach that allows full access to the state of the environment. The inevitable interaction between a system and its environment typically results in the loss of quantum features, such as coherence [1,2]. One important aspect in the study of these so-called open quantum systems is the concept of non-Markovianity, which arises due to memory effects of the environment. Non-Markovian features might enable the system to recover part of the lost coherence and information back from the environment [1][2][3][4]. Although these memory effects have been investigated in the past, only recently an increase in the understanding of nonMarkovianity from a quantum information perspective has emerged [5][6][7][8][9][10][11].The non-Markovian nature of a dynamical quantum map can be characterized through a number of distinct methods [5][6][7][8][9][10]. To date, the measure defined by Breuer, Laine, and Piilo [6] based on trace distance, is the most significant quantifier of the degree of non-Markovianity, due to its interpretation: non-Markovianity manifests itself as a reverse flow of information from the environment back to the system. An alternative method to measure the degree of non-Markovianity relies on the fact that local, completely positive trace-preserving (CPTP) maps cannot increase the entanglement between an open quantum system and an isolated ancillary system [12]. Exploiting this property, Rivas, Huelga, and Plenio (RHP) have defined another measure for the degree of non-Markovianity [7]. According to the RHP measure, a dynamical process is said to be nonMarkovian if the entanglement between the open system and the isolated ancilla temporarily increases throughout the dynamics. Although the RHP measure provides a connection between the non-Markovian behavior of dynamical maps and entanglement, a meaning in terms of information flow is still lacking in this approach.Here, we propose an entanglement-based measure of non-Markovianity having a direct information based interpretation. Our method is based on the decoherence program [13], where a system S is coupled to a measurement ...

We use the classical correlation between a quantum system being measured and its measurement apparatus to analyze the amount of information being retrieved in a quantum measurement process. Accounting for decoherence of the apparatus, we show that these correlations may have a sudden transition from a decay regime to a constant level. This transition characterizes a nonasymptotic emergence of the pointer basis, while the system apparatus can still be quantum correlated. We provide a formalization of the concept of emergence of a pointer basis in an apparatus subject to decoherence. This contrast of the pointer basis emergence to the quantum to classical transition is demonstrated in an experiment with polarization entangled photon pairs.

The estimation of the entanglement of multipartite systems undergoing decoherence is important for assessing the robustness of quantum information processes. It usually requires access to the final state and its full reconstruction through quantum tomography. General dynamical laws may simplify this task. We found that when one of the parties of an initially entangled two-qubit system is subject to a noisy channel, a single universal curve describes the dynamics of entanglement for both pure and mixed states, including those for which entanglement suddenly disappears. Our result, which is experimentally demonstrated using a linear optics setup, leads to a direct and efficient determination of entanglement through the knowledge of the initial state and single-party process tomography alone, foregoing the need to reconstruct the final state.