Quantum system tend to have information lost from transmission through the correlations generated among degrees of freedom. For situations where we have a non-Markovian environment, the information contained in it may return to the system, and non-Markovian witnesses can capture such effect. In the present work, we sought how the environment structure affects the system information reachability since its finite size induces a quasiperiodic behavior in the decoherence and enables a highly non-Markovian behavior in the dynamics. To do that, we use a central qubit coupled to a spin chain with Ising interactions subject to a magnetic field, i.e., a central spin model, and solve the exact dynamics of the system. Moreover, we use two witnesses to analyze the presence of non-Markovianity: the Breuer-Laine-Piilo (BLP) trace distance-based measure and the conditional past-future correlator (CPF). On the other hand, we see how such behavior suppresses the classic plateau in Partial Information Plot (PIP) from the paradigm of quantum Darwinism and objective information from Spectrum Broadcast Structure (SBS). In addition to the system point of view, we show that the environmental structure avoids encoding accessible and distinguishable information for measurement in the environment for any model limit. Finally, he orthogonality between the density operators decodes the distinguishability between SBS states in the environment.
Quantum system tend to have information lost from transmission through the correlations generated among degrees of freedom. For situations where we have a non-Markovian environment, the information contained in it may return to the system, and non-Markovian witnesses can capture such effect. In the present work, we sought how the environment structure affects the system information reachability since its finite size induces a quasiperiodic behavior in the decoherence and enables a highly non-Markovian behavior in the dynamics. To do that, we use a central qubit coupled to a spin chain with Ising interactions subject to a magnetic field, i.e., a central spin model, and solve the exact dynamics of the system. Moreover, we use two witnesses to analyze the presence of non-Markovianity: the Breuer-Laine-Piilo (BLP) trace distance-based measure and the conditional past-future correlator (CPF). On the other hand, we see how such behavior suppresses the classic plateau in Partial Information Plot (PIP) from the paradigm of quantum Darwinism and objective information from Spectrum Broadcast Structure (SBS). In addition to the system point of view, we show that the environmental structure avoids encoding accessible and distinguishable information for measurement in the environment for any model limit. Finally, he orthogonality between the density operators decodes the distinguishability between SBS states in the environment.
Quantum systems interacting with environments tend to have their information lost from transmission through the correlations generated with the degrees of freedom of the environment. For situations where we have non- Markovian environments, the information contained in the environment may return to the system and such effect can be captured by non-Markovian witnesses. In the present work, we use a central qubit coupled to a spin chain with Ising interactions subject to a magnetic field, i.e., a central spin model, and solve the exact dynamics of a system subject to dephasing dynamics via Kraus operators. For such we use two witnesses to analyze the presence of non-Markovianity: the BLP trace-based measure and the conditional past-future correlator (CPF). Furthermore, we see how such behavior suppresses the classic plateau in Partial Information Plot (PIP) from the paradigm of quantum Darwinism, as well as objective information from Spectrum Broadcast Structure (SBS). In addition to the system point of view, we show the impossibility of encoding accessible information for measurement in the environment for any model limit.
Abstract Non-Markovian dynamics is central to quantum information processing, as memory effects strongly influence coherence preservation, metrology, and communication. In this work, we investigate the role of stochastic system–bath couplings in shaping non-Markovian behavior of open quantum systems, using the central spin model within a time-convolutionless master equation framework. We show that the character of the reduced dynamics depends jointly on the intrinsic memory of the environment and on the structure of the system–environment interaction. In certain regimes, the dynamics simplify to pure dephasing, while in general both amplitude damping and dephasing contribute to the evolution. By employing two complementary measures: the Quantum Fisher Information (QFI) flow and the Breuer–Laine–Piilo (BLP) measure, we demonstrate that QFI flow may fail to witness memory effects in weak-coupling and near-resonant regimes, whereas the BLP measure still detects information backflow. Furthermore, external modulation of the interaction kernel produces qualitatively richer behavior, including irregular and frequency-dependent revivals of non-Markovianity. These results clarify the physical origin of memory effects, highlight the limitations of single-witness approaches, and suggest that stochasticity and modulation can be harnessed to engineer robust, noise-resilient quantum technologies.
We have introduced PT-symmetry to a central spin model by adding a PT-symmetric interaction with a tunable hermiticity parameter γ. Using the pseudo-Hermitian formalism, we applied a Dyson map to transform the non-Hermitian Hamiltonian to its Hermitian representation. We have found that the decoherence slows down as γ increases, eventually ceasing at γ=1. We define a pseudo-Hermitian observable that commutes with the metric operator to add as the self-Hamiltonian. Einselection gradually forced the system to select the eigenstates of the self-Hamiltonian as γ→1. The steady-state purity of the central spin states in the strong environment regime exhibits a paradoxical decrease as γ increases. However, a turning point (minimum) corresponding to a maximum information dissipation to the spin bath is found. Finally, the Breuer-Laine-Piilo (BLP) measure, which is used to quantify the non-Markovianity of a quantum system, was evaluated for a finite time. The BLP measure in the strong environment regime exhibited similar turning point behavior, which means that the information backflow reaches a saturation point before declining. This decline signifies the point where PT-symmetry starts shielding the central spin from the environment.
In the first part of this thesis, we investigate the dynamics of open quantum systems coupled in a purely dephasing way to their environment, which is a paradigmatic example of decoherent dynamics. We focus more specifically on the emergence of non-Markovian effects in the dynamics of such open systems. After reviewing different measures of non-Markovianity, we obtain an analytical expression for the reduced density operator of a finite-dimensional open system coupled with its environment through time-dependent purely dephasing interactions. When the system is initially uncorrelated with its environment, we obtain the time-local master equation that describes its dynamics. In this case, we also derive an exact expression for the witness of non-Markovianity based on the volume of accessible states of the open system. These results are then applied to spin systems coupled to either a spin or a bosonic environment. For spin environments, we study non-Markovianity for different ranges of interaction and in different thermodynamical limits. Moreover, the generation of entanglement between the open system and its environment as well as between spins within the open system is investigated. For bosonic environments, we study the effect of the initial state of the environment on non-Markovianity. We also show that time-dependent modulations of the system-environment coupling can dramatically alter the non-Markovian behavior of the open system. Finally, we consider the case of an open quantum system simultaneously coupled to spin and bosonic baths. In that case, we study how the coupling between the different baths and of the presence of initial correlations in the environment affect the non-Markovianity displayed by the open quantum system. The second part of this thesis is a contribution to the investigation of how quantum systems can be used to process information. More precisely, we focus on the implementation of gate-based quantum computing using neutral atoms trapped in optical or magnetic lattices and interacting through dipole-dipole interactions when excited to Rydberg states. In this context, we present protocols implementing two-qubit quantum gates between atoms far apart in the lattice. To this end, we propose to use a chain of non-coding ancilla atoms to transfer the state of the control qubit to an atom near the target qubit. Before discussing entangling gates between distant qubits, we present two protocols that implement state transfer along a chain of two-level atoms relying respectively on single- and two-atom laser pulses combined with dipole blockade. After reviewing protocols implementing CZ and CNOT gates between nearby qubits using dipole-dipole interactions, we show how the state-transfer protocols previously presented can be used to perform entangling gates between distant qubits. The performance of the state-transfer and gate protocols are assessed using the process fidelity. Moreover, we provide a theoretical explanation for the behavior of the process fidelity with respect to dissipation and imperfect blockade.
In this doctoral thesis we will investigate how one can quantify the information flow in quantum and classical phase space models based on the Breuer-Laine-Piilo measure of quantum non-Markovianity, quantifying memory effects of some open quantum dynamics by the information flow between the open system and its environment. While this mea- sure is defined using the trace distance between density operators on the Hilbert space, in case of continuous variable quantum systems it would be desirable to quantify the infor- mation flow by means of the differently ordered quasi-probability distributions over their quantum phase space. We will show how one can approximate the trace distance by the Kolmogorov distance between Glauber P-functions and Husimi Q-functions and we will prove the existence of some optimal ordering such that the Kolmogorov distance between the respectively ordered quasi-distributions equals the trace distance. The Kolmogorov dis- tance represents in this context a classical analogue to the trace distance and can be used in the spirit of the Breuer-Laine-Piilo measure to quantify information flow in classical phase space models. We hence define the limit of classical uncertainty which presents a quantum- to-classical transition in which the approximation of the trace distance by the Kolmogorov distances of the quasi-probability distributions becomes exact. Employing the example of the Calderia-Leggett model of quantum Brownian motion we present some numerical data which shows that the Kolmogorov distance between the Wigner functions converges espe- cially fast against the trace distance, strongly suggesting that the Wigner function in fact is the optimal ordered quasi-distribution in the limit of classical uncertainty. Additionally, or method can be used to compare the information flow through quantum systems and their classical counterparts. We do so exemplarily for classical and quantum anharmonic chains as used in the Fermi-Pasta-Ulam-Tsingou (FPUT) model. We can show, that the infor- mation flow through the quantum and the classical chain is equivalent in case of harmonic coupling between the sites of the chain while significant differences emerge for anharmonic coupling. We can relate this differences to the resolution of the phase space distributions, limited by the Heisenberg uncertainty relation in the quantum case and arbitrary small for the classical chain, and the role of entanglement as genuine quantum correlation type.
In this work, we investigate the non-Markovian features of the Adapted Caldeira-Leggett model, a computationally efficient framework recently proposed to capture the essential physics of the standard Caldeira-Leggett model. While this effective model has been previously validated for decoherence and einselection, its ability to reproduce memory effects remains to be explored. By exploiting the model's capability to explicitly track both system and environment degrees of freedom, we provide a detailed characterization of non-Markovianity through the lens of information backflow. We evaluate the buildup of system-environment correlations and the corresponding modifications of the environmental state, assessing a quantitative upper bound for the revival of distinguishability in the reduced dynamics. Our results, obtained by comparing different distinguishability quantifiers such as trace distance and the square root of the Jensen-Shannon divergence, show that while correlations are primarily sensitive to coupling strength, environmental state changes are more heavily influenced by temperature. Our analysis substantiates the physical interpretation of the distinguishability-based approach to non-Markovianity, and confirms this variant of the Caldeira-Leggett model as a reliable tool for exploring the microscopic origins of different fundamental phenomena in quantum mechanics.