The unavoidable interaction of a quantum system with its environment usually degrades its coherence and quantumness. The environment and the decoherence process may be described as the interaction with a classical or quantized bath. As a matter of fact, the classical description becomes progressively more reliable as far as the environment has many degrees of freedom, i.e. it becomes complex, or when the interaction between a quantum system and a classical fluctuating field is taken into account. In this thesis, I consider a qubit system coupled to a stochastic classical field and address�the decoherence and non-Markovianity induced by the external noise as well as the spectral characterization of the classical field by quantum-limited measurement on the qubit. I thus analyze the dynamics of quantum correlations between two non-interacting, initially entangled qubits subject to a classical noise generated by a stochastic process. Two relevant classes of noise are taken into account: Gaussian noise, such as the Ornstein-Uhlenbeck process, and non-Gaussian noise, such as the random telgraph noise and the colored noise with 1/f spectrum. I also discuss the evaluation of non-Markovianity of the induced dynamical map and link the presence of revivals of quantum correlations with the information backflow to the system. The precise characterization of the stochastic process generating the classical noise, possibly using minimal resources, is a crucial ingredient for the design of high-precision measurements and reliable communication protocols. To this purpose, I also address the characterization of the spectral parameters of classical noise by quantum probes, e.g. a qubit coupled to the stochastic process generating the noise. By using the tools of quantum estimation theory, I explore the performances of quantum measurements on the qubit and show that it is possible to effectively extract information about the noise.
The unavoidable interaction of a quantum system with its environment usually degrades its coherence and quantumness. The environment and the decoherence process may be described as the interaction with a classical or quantized bath. As a matter of fact, the classical description becomes progressively more reliable as far as the environment has many degrees of freedom, i.e. it becomes complex, or when the interaction between a quantum system and a classical fluctuating field is taken into account. In this thesis, I consider a qubit system coupled to a stochastic classical field and address�the decoherence and non-Markovianity induced by the external noise as well as the spectral characterization of the classical field by quantum-limited measurement on the qubit. I thus analyze the dynamics of quantum correlations between two non-interacting, initially entangled qubits subject to a classical noise generated by a stochastic process. Two relevant classes of noise are taken into account: Gaussian noise, such as the Ornstein-Uhlenbeck process, and non-Gaussian noise, such as the random telgraph noise and the colored noise with 1/f spectrum. I also discuss the evaluation of non-Markovianity of the induced dynamical map and link the presence of revivals of quantum correlations with the information backflow to the system. The precise characterization of the stochastic process generating the classical noise, possibly using minimal resources, is a crucial ingredient for the design of high-precision measurements and reliable communication protocols. To this purpose, I also address the characterization of the spectral parameters of classical noise by quantum probes, e.g. a qubit coupled to the stochastic process generating the noise. By using the tools of quantum estimation theory, I explore the performances of quantum measurements on the qubit and show that it is possible to effectively extract information about the noise.
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.
The goal of research in quantum information is to investigate how quantum systems can be used to store, transmit and elaborate information and how the non-classical nature of their correlations allows defining protocols that outperform their classical counterparts. Despite of the many progresses, both theoretical and experimental, made in this field in the latest decades, many challenges lie ahead for practical implementations of quantum technologies. One of the most important ones is caused by the unavoidable interaction of quantum systems with their surroundings: The coupling to the environment is generally detrimental to the quantum information contained in the system as the system undergoes decoherence. In the quest for quantum technologies, it is fundamental to overcome the problem of decoherence and loss of information. Different physical implementations of qubits, such as superconducting and solid-state devices, are affected by the interaction with the environment in a way that can be described in terms of classical stochastic noise. The classical noise model can also be used to give an approximate, sometimes equivalent, description of full quantum models of system-environment interaction. This thesis contains my personal contribution to the study of the dynamics of discrete-variable quantum systems affected by classical noise. It covers in particular single- and two-qubit systems affected by Gaussian and non-Gaussian noise. It also discusses the dynamics of a quantum walk affected by spatially correlated classical noise. Analytical solutions for particular forms of noise and interactions, and a general numerical method for simulation of the dynamics are presented. Moreover, the thesis presents the experimental implementation of a quantum optical simulator of noisy dynamics of single-qubit systems. Finally, the use of quantum systems as probes of the spectral properties of large classical environments is discussed, showing that entanglement is a resource for improvements in the precision of the estimation.
One of the main goals of the theory of open quantum systems is to devise methods which help preserve the quantum properties of a system interacting with its environment.One possible pathway to achieve this goal is to use non-Markovian reservoirs, characterized by information backflows and revivals of certain quantum properties.These reservoirs usually require advanced engineering techniques, which may turn their implementation impractical.In this dissertation we propose an alternative technique: the injection of a classical colored noise, which induces the desired quantum non-Markovianity.In order to do that, we investigate the dynamics of a quantum system interacting with its surrounding environment and under the injection of a classical stochastic colored noise.A time-local master equation for the system is derived by using the stochastic wave function formalism and functional calculus.Afterwards, the non-Markovianity of the evolution is detected by using the Andersson, Cresser, Hall and Li measure, which is based on the decay rates of the master equation in canonical Lindblad-like form.Finally, we evaluate the measure for three different colored noises and study the interplay between environment and noise pump necessary to induce quantum non-Markovianity, as well as the energy balance of the system.
We investigate qubit entanglement dynamics in a two-qubit cavity system with stochastically fluctuating coupling strength, comparing white noise (Markovian) and Ornstein-Uhlenbeck noise (non-Markovian) processes. We analytically solve the system dynamics for both Fock and coherent cavity states and systematically characterize how initial qubit configurations affect entanglement generation and preservation. Our results reveal distinct dynamical regimes: in the Fock-state cavity, initial states in the single-excitation subspace generate robust qubit entanglement in decoherence-free subspaces, while initially entangled states in the double-excitation subspace exhibit inevitable decay without protective symmetries. For coherent cavities, we identify a critical photon-number threshold in the intermediate coherent-state amplitude regime where dynamics transition from low-frequency to high-frequency entanglement oscillations, while universal entanglement loss occurs at large amplitudes. Remarkable resilience against entanglement sudden death emerges under strong non-Markovian noise with long correlation times, where repeated revivals occur. These findings establish cavity photon statistics and environmental memory time as key control parameters for engineering qubit entanglement dynamics in qubit-cavity systems, revealing how system-environment correlations govern quantum information preservation.
The non-Markovian nature of quantum systems recently turned to be a key subject for investigations on open quantum system dynamics. Many studies, from its theoretical grounding to its usefulness as a resource for quantum information processing and experimental demonstrations, have been reported in the literature. Typically, in these studies, a structured reservoir is required to make non-Markovian dynamics emerge. Here, we investigate the dynamics of a qubit interacting with a bosonic bath and under the injection of a classical stochastic colored noise. A canonical Lindblad-like master equation for the system is derived by using the stochastic wave function formalism. Then, the non-Markovianity of the evolution is witnessed by using the measure of Andersson, Cresser, Hall, and Li. We evaluate the measure for three different noises and study the interplay between environment and noise pump necessary to generate quantum non-Markovianity, as well as the energy balance of the system. Finally, we discuss the possibility to experimentally implement the proposed model.
We address the non-Markovian character of quantum maps describing the interaction of a qubit with a random classical field. In particular, we evaluate trace- and capacity-based non-Markovianity measures for two relevant classes of environments showing non-Gaussian fluctuations, described respectively by random telegraph noise and colored noise with spectra of the the form $1/{f}^{\ensuremath{\alpha}}$. We analyze the dynamics of both the trace distance and the quantum capacity, and show that the behavior of non-Markovianity based on both measures is qualitatively similar. Our results show that environments with a spectrum that contains a relevant low-frequency contribution are generally non-Markovian. We also find that the non-Markovianity of colored environments decreases when the number of fluctuators realizing the environment increases.