Initial correlations in open system's dynamics: The Jaynes-Cummings model

Employing the trace distance as a measure for the distinguishability of quantum states, we study the influence of initial correlations on the dynamics of open systems. We concentrate on the Jaynes-Cummings model for which the knowledge of the exact joint dynamics of system and reservoir allows the treatment of initial states with arbitrary correlations. As a measure for the correlations in the initial state we consider the trace distance between the system-environment state and the product of its marginal states. In particular, we examine the correlations contained in the thermal equilibrium state for the total system, analyze their dependence on the temperature and on the coupling strength, and demonstrate their connection to the entanglement properties of the eigenstates of the Hamiltonian. A detailed study of the time dependence of the distinguishability of the open system states evolving from the thermal equilibrium state and its corresponding uncorrelated product state shows that the open system dynamically uncovers typical features of the initial correlations.Comment: 12 pages, 7 figure

Quantum probes to assess correlations in a composite system

We suggest and demonstrate experimentally a strategy to obtain relevant information about a composite system by only performing measurements on a small and easily accessible part of it, which we call quantum probe. We show in particular how quantitative information about the angular correlations of couples of entangled photons generated by spontaneous parametric down conversion is accessed through the study of the trace distance between two polarization states evolved from different initial conditions. After estimating the optimal polarization states to be used as quantum probe, we provide a detailed analysis of the connection between the increase of the trace distance above its initial value and the amount of angular correlations.Comment: 6 pages, 4 figure

NON-MARKOVIANITY AND INITIAL CORRELATIONS IN THE DYNAMICS OF OPEN QUANTUM SYSTEMS

In the present thesis we investigate two basic issues in the dynamics of open quantum systems, namely, the concept of non-Markovianity and the effects of initial system-environment correlations in the subsequent reduced dynamics. In recent research, a great effort has been put into the study and understanding of non-Markovian features within the dynamics of open quantum systems. At the same time, quantum non-Markovianity has been defined and quantified in terms of quantum dynamical maps, using either a divisibility property or the behavior of the trace distance between pairs of reduced states evolved from different initial states. We investigate these approaches by means of several examples, focusing in particular on their relation with the very definition of non-Markov process used in classical probability theory. Indeed, the notion of non-Markovian behavior in the dynamics of the state of a physical system and the notion of non-Markov process are quite different and it will appear how the former represents sufficient, but not necessary condition with respect to the latter. In particular, we explicitly show that the above-mentioned divisibility property in the classical case is not, in general, equivalent to the Chapman-Kolmogorov equation, proper to Markov stochastic processes. Furthermore, by taking into account a bipartite open system, we emphasize how the presence of non-Markovian effects strongly depends on where the border between open system and environment is set. A second relevant topic investigated in this thesis concerns the dynamics of open quantum system in the presence of initial system-environment correlations. By means of the approach based on trace distance, we go beyond the usual assumption that the open system and the environment are initially uncorrelated. The trace-distance analysis provides a characterization of open-system dynamics relying on measurements on the open system only, without the need for any extra information about the total system or system-environment interaction. After an introduction to the general theoretical scheme, we report an all-optical experimental realization, in which the total system under investigation consists of a couple of entangled photons generated by spontaneous parametric down conversion and initial correlations are introduced in a general fashion by means of a spatial light modulator. Finally, we take into account the Jaynes-Cummings model, showing how trace distance establishes general connections between correlation properties of initial total states and dynamical quantities that characterize the evolution of the open system

Dissipative Continuous Spontaneous Localization (CSL) model

Collapse models explain the absence of quantum superpositions at the macroscopic scale, while giving practically the same predictions as quantum mechanics for microscopic systems. The Continuous Spontaneous Localization (CSL) model is the most refined and studied among collapse models. A well-known problem of this model, and of similar ones, is the steady and unlimited increase of the energy induced by the collapse noise. Here we present the dissipative version of the CSL model, which guarantees a finite energy during the entire system's evolution, thus making a crucial step toward a realistic energy-conserving collapse model. This is achieved by introducing a non-linear stochastic modification of the Schr\uf6dinger equation, which represents the action of a dissipative finite-temperature collapse noise. The possibility to introduce dissipation within collapse models in a consistent way will have relevant impact on the experimental investigations of the CSL model, and therefore also on the testability of the quantum superposition principle

Critical assessment of two-qubit post-Markovian master equations

A post-Markovian master equation has been recently proposed as a tool to describe the evolution of a system coupled to a memory-keeping environment [A. Shabani and D. A. Lidar, Phys. Rev. A 71, 020101 (R) (2005)]. For a single qubit affected by appropriately chosen environmental conditions, the corresponding dynamics is always legitimate and physical. Here we extend such situation to the case of two qubits, only one of which experiences the environmental effects. We show how, despite the innocence of such an extension, the introduction of the second qubit should be done cum grano salis to avoid consequences such as the breaking of the positivity of the associated dynamical map. This hints at the necessity of using care when adopting phenomenologically derived models for evolutions occurring outside the Markovian framework.Comment: 7 pages, 1 figure, RevTeX4. Close to published versio

Sofosbuvir-based therapies in genotype 2 hepatitis C virus cirrhosis: A real-life experience with focus on ribavirin dose

This study aimed to investigate the efficacy and safety of sofosbuvir-based therapies for the treatment of cirrhosis from hepatitis C virus (HCV) genotype 2 infection. Data of all consecutive HCV genotype 2 cirrhotic patients who started sofosbuvir-based treatments between January 2015 and March 2017 in eight Italian tertiary hospitals were collected retrospectively. Overall, 273 patients (Child A: 94.5%) were enrolled. In the 194 subjects treated with sofosbuvir/ribavirin, median initial ribavirin dosage was 13.9 mg/kg/day, and therapy duration was 16 weeks. Sustained virological response (SVR) rates were 93.8% in intention-to-treat (ITT) and 95.3% in per-protocol (PP) analyses for the 129 treatment-naïve patients, and 96.9% (ITT) and 98.4% (PP) for the 65 treatment-experienced subjects. Adverse events were reported in 142 patients (73.2%), but only 1.5% discontinued treatment. Eighty-eight subjects with treatment-induced anemia (mild: 34.5%, moderate: 7.7%, severe: 3.1%) had to reduce ribavirin dosage, but SVR rates were comparable to the weight-based dose group, both in ITT (95.4% and 94.3%) and PP (97.7% and 95.2%) analyses, respectively. Moreover, ITT and PP SVR rates were similar between shorter (<20 weeks) (94.1% and 96.0%, respectively) and prolonged (≥20 weeks) regimens (95.7% and 96.7%, respectively). SVR rates in the 79 subjects treated with sofosbuvir/daclatasvir (without ribavirin) were similar (ITT: 96.2%; PP: 97.4%, respectively), without de novo/worsening anemia. In conclusion, in a real-life study centered on genotype 2 patients with well-compensated cirrhosis, sofosbuvir-based regimens were associated with good SVR and tolerability rates, regardless of previous antiviral treatments, without a significant impact of on treatment ribavirin dose reductions

Charging a quantum battery in a non-Markovian environment: a collisional model approach

We study the effect of non-Markovianity in the charging process of an open-system quantum battery. We employ a collisional model framework, where the environment is described by a discrete set of ancillary systems and memory effects in the dynamics can be introduced by allowing these ancillas to interact. We study in detail the behaviour of the steady-state ergotropy and the impact of the information backflow to the system on the different features characterizing the charging process. Remarkably, we find that there is a maximum value of the ergotropy achievable: this value can be obtained either in the presence of memoryless environment, but only in the large-loss limit, as derived in [D. Farina et al., Phys. Rev. B 99, 035421 (2019)], or in the presence of an environment with memory also beyond the large-loss limit. In general, we show that the presence of an environment with memory allows us to generate steady-state ergotropy near to its maximum value for a much larger region in the parameter space and thus potentially in a shorter time. Relying on the geometrical measure of non-Markovianity, we show that in both the cases of an environment with and without memory the ergotropy maximum is obtained when the non-Markovianity of the dynamics of the battery is zero, possibly as the result of a non-trivial interplay between the memory effects induced by, respectively, the environment and the charger connected to the battery

Non-perturbative treatment of open-system multi-time expectation values in Gaussian bosonic environments

We determine the conditions for the equivalence between the multi-time expectation values of a general finite-dimensional open quantum system when interacting with, respectively, an environment undergoing a free unitary evolution or a discrete environment under a free evolution fixed by a proper Gorini-Kossakowski-Lindblad-Sudarshan generator. We prove that the equivalence holds if both environments are bosonic and Gaussian and if the one- and two-time correlation functions of the corresponding interaction operators are the same at all times. This result leads to a non-perturbative evaluation of the multi-time expectation values of operators and maps of open quantum systems interacting with a continuous set of bosonic modes by means of a limited number of damped modes, thus setting the ground for the investigation of open-system multi-time quantities in fully general regimes.Comment: 16 pages, 1 figure. Submission to a special issue of 'Open Systems and Information Dynamics' devoted to the memory of Prof. Andrzej Kossakowsk

Improving the precision of frequency estimation via long-time coherences

In recent years, several estimation strategies have been formulated to determine the value of an unknown parameter in the most precise way, taking into account the presence of noise. These strategies typically rely on the use of quantum entanglement between the sensing probes and they have been shown to be optimal in the asymptotic limit in the number of probes, as long as one performs measurements on shorter and shorter time scales. Here, we present a different approach to frequency estimation, which exploits quantum coherence in the state of each sensing particle in the long time limit and is obtained by properly engineering the environment. By means of a commonly used master equation, we show that our strategy can overcome the precision achievable with entanglement-based strategies for a finite number of probes. We discuss a possible implementation of the scheme in a realistic setup that uses trapped ions as quantum sensors