Academic literature on the topic 'Non Markovian evolution'

We analyze two criteria of (non)Markovianity: one based on the mathematical concept of divisibility of the dynamical map and the other one based on distinguishability of quantum states. We illustrate these concepts from the geometric perspective using simple examples of qubit dynamics.

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.

The fully quantized model of double qubits coupled to a common bath is solved using the quantum state diffusion (QSD) approach in the non-Markovian regime. We have established the explicit time-local non-Markovian QSD equations for the two-qubit dissipative and dephasing models. Diffusive quantum trajectories are applied to the entanglement estimation of two-qubit systems in a non-Markovian regime. In both cases, non-Markovian features of entanglement evolution are revealed through quantum diffusive unravellings in the system state space.

This thesis will be oriented in the study of open quantum systems. The transition of processes that go between the Markovian and non-Markovian regime will be studied. The diagnose of non-Markovianity will be made in terms of the variation of the coherence of the state. Accordingly, an optical setup will be implemented that allows us to manipulate certain degrees of freedom, like the polarization and the optical path. Theoretically, we have found that the coherence of the system is transferred to the environment and it decreases as we move a parameter that we will take as time. This situation has been confirmed in the experiment. Then, due to the second part of the setup, which produces a non-Markovian evolution by also changing one of its parameters, we have accomplished the goal of returning the information back into the system and to measure the non-Markovianity of the process.
El trabajo de tesis estará orientado al estudio de sistemas cuánticos abiertos. Se estudiará la transición de procesos que van del régimen Markoviano al no Markoviano en forma controlada. El diagnóstico de no Markovianidad se hará en términos de la variación de la coherencia del estado. Para ello se implementará un arreglo óptico que permita manipular varios grados de libertad, tales como polarización y camino óptico. Teóricamente, encontramos que la coherencia del sistema se transfiere al entorno y disminuye al mover uno de estos parámetros que tomaremos como el tiempo, lo que se ha podido comprobar en el experimento. Posteriormente, utilizando otro arreglo que produce una evolución no- Markoviana cambiando uno de sus parámetros también como el tiempo, se ha logrado recuperar la coherencia del sistema. De esta manera se hace posible el retorno de la información y la medición de la no-Markovianidad de dicho proceso.
Tesis

Most bioinformatic analyses start by building sequence alignments by means of scoring matrices. An implicit approximation on which many scoring matrices are built is that protein sequence evolution is considered a sequence of Point Accepted Mutations (PAM) (Dayhoff et al., 1978), in which each substitution happens independently of the history of the sequence, namely with a probability that depends only on the initial and final amino acids. But different protein sites evolve at a different rate (Echave et al., 2016) and this feature, though included in many phylogenetic reconstruction algorithms, is generally neglected when building or using substitution matrices. Moreover, substitutions at different protein sites are known to be entangled by coevolution (de Juan et al., 2013). This thesis is devoted to the analysis of the consequences of neglecting these effects and to the development of models of protein sequence evolution capable of incorporating them. We introduce a simple procedure that allows including the among-site rate variability in PAM-like scoring matrices through a mean-field-like framework, and we show that rate variability leads to non trivial evolutions when considering whole protein sequences. We also propose a procedure for deriving a substitution rate matrix from Single Nucleotide Polymorphisms (SNPs): we first test the statistical compatibility of frequent genetic variants within a species and substitutions accumulated between species; moreover we show that the matrix built from SNPs faithfully describes substitution rates for short evolutionary times, if rate variability is taken into account. Finally, we present a simple model, inspired by coevolution, capable of predicting at the same time the along-chain correlation of substitutions and the time variability of substitution rates. This model is based on the idea that a mutation at a site enhances the probability of fixing mutations in the other protein sites in its spatial proximity, but only for a certain amount of time.

The formulation of quantum physics stands among the most revolutionary theories of the twentieth century. During the first decades of this century, many phenomena concerning the microscopic world were unexplained or had ad-hoc descriptions. The theory of quantum physics introduced a framework that allowed predicting these phenomena with unprecedented precision. While quantum mechanics offered counter-intuitive explanations for these experimental results, it predicted unexpected quantum phenomena which were considered symptoms of an ill-defined theory. Decades passed and more and more empirical evidences sustained the existence of purely quantum effects and therefore the validity of this theory. Hence, it became a solid branch of science and physicists started to engineer scenarios where quantum effects could provide improvements if compared with classical scenarios. This approach gave birth to quantum information science, where quantum particles are manipulated to perform information tasks. Several innovative protocols, e.g. concerning state teleportation, dense coding, cryptography and integer factorization algorithms, proved that quantum physics allowed performances unattainable in classical settings. The formulation of quantum protocols able to provide substantial speed-ups raised wide interest of the academic world and private companies. Nonetheless, the implementation of more and more complex quantum protocols became an increasingly harder task. Indeed, manipulating a large number of quantum particles with a level of noise that is small enough to obtain quantum advantages is, even nowadays, a demanding goal. The purely-quantum features essential for these speed-ups are fragile when noise influences experimental apparatus. Hence, in order to access the full potential of quantum theory, the ability to handle noisy environments is a fundamental goal. This thesis is devoted to the study of open quantum systems (OQS), namely those where the interaction between the target quantum system and its surrounding environment is taken under consideration during the evolution. Indeed, isolated systems cannot provide realistic descriptions of dynamics. Understanding how to exploit and manipulate environments in order to obtain dynamics that are less aggressive with the information stored in our OQS is therefore an essential goal to achieve quantum advantages. There are two possible dynamical regimes for the information encoded in an OQS. We call an evolution Markovian when there is a one-way flow of information from the OQS to the environment. Instead, the non-Markovian regime is distinguished by one or more time intervals when this flow is reversed. In this case, we say that we witness information backflows. A characterization based on the different types of information quantifiers that can be considered in this context is fundamental to exploit these phenomena in information processing scenarios. The main goal of this thesis is to examine the potential of correlation measures to show backflows when the OQS dynamics is non-Markovian. The first three works that we expose are devoted to this topic. First, we study how entanglement and quantum mutual information behave under non-Markovian evolutions. We follow with the formulation of a correlation measure that is able to witness almost-all non-Markovian evolutions. The last work along this topic provides the first one-to-one relation between correlation backflows and non-Markovian evolutions. The last work in this thesis adopts a different point of view under which we can characterize OQS evolutions. We quantify non-Markovianity through the minimal amount of Markovian noise that has to be added in order to make an evolution Markovian.
La formulación de la física cuántica se encuentra entre las teorías más revolucionadoras del siglo XX. Durante las primeras décadas de siglo, muchos fenómenos asociados al mundo microscópico yacían sin una descripción clara, o bien ésta era ad-hoc. La física cuántica introdujo un marco que permitió explicar estos fenómenos con una precisión sin precedentes. Si bien sus explicaciones eran contraintuitivas, los inesperados fenómenos cuánticos que predijo se consideraron síntomas de una teoría mal definida. Pasaron los años y cada vez más evidencias empíricas sostuvieron la existencia de efectos puramente cuánticos, validando esta teoría. La física cuántica se convirtió en una sólida rama de la ciencia, y los físicos comenzaron a diseñar escenarios en los que sus efectos pudieran proporcionar mejoras en comparación con sus alternativas clásicas. Este enfoque dio origen al campo de la información cuántica, donde las partículas cuánticas se manipulan para realizar tareas de información. Varios innovadores protocolos, como la teletransportación de estados cuánticos, la “codificación densa”, la criptografía y los algoritmos de factorización de enteros, demostraron el potencial de la física cuántica frente a estrategias clásicas. La formulación de protocolos cuánticos capaces de proporcionar considerables mejoras despertó un gran interés en el mundo académico y en las empresas privadas. No obstante, la implementación de protocolos cuánticos cada vez más complejos se convirtió en una tarea sustancialmente más difícil. De hecho, manipular una gran cantidad de partículas cuánticas con un nivel de ruido lo suficientemente pequeño como para obtener ventajas cuánticas es, incluso a día de hoy, un objetivo exigente. Las características puramente cuánticas vitales para obtener estas mejoras son frágiles al ruido que afecta los instrumentos experimentales. Por lo tanto, para acceder a todo el potencial subyacente a la teoría cuántica, la capacidad de manejar ambientes ruidosos resulta un objetivo fundamental. Esta tesis está dedicada al estudio de los sistemas cuánticos abiertos (SCA), es decir, aquellos en los que se tiene en cuenta la interacción entre el sis6 tema cuántico objeto y su ambiente circundante durante la evolución. De hecho, los sistemas aislados no pueden proporcionar descripciones realistas de la dinámica. Entender cómo explotar estos ambientes para obtener dinámicas menos agresivas con la información almacenada en nuestro SCA, es un objetivo primordial para conseguir ventajas cuánticas. Hay dos posibles regímenes dinámicos para la información codificada en un SCA. Decimos que una evolución es Markoviana cuando hay un flujo de información unidireccional desde el SCA al medio ambiente. Por contra, en el régimen no Markoviano se distinguen unos intervalos temporales en los que este flujo se invierte. En este caso, decimos que somos testigos de reflujos de información. Una caracterización basada en los diferentes tipos de cuantificadores de información que pueden considerarse en este contexto es fundamental para explotar estos fenómenos en escenarios de procesamiento de información. El objetivo principal de esta tesis es examinar el potencial de las medidas de correlación para mostrar reflujos cuando la dinámica es no Markoviana. Los tres primeros trabajos que exponemos están dedicados a este tema. En primer lugar, estudiamos los potenciales del entanglement entrelazamiento y la información mutua cuántica. Seguidamente presentamos la formulación de una medida de correlación capaz de presenciar casi todas las evoluciones no Markovianas. Por último, proponemos la primera relación de equivalencia entre los reflujos de correlación y la no Markovianidad. Concluimos proponiendo un punto de vista diferente bajo el cual podemos caracterizar las evoluciones de SCA. Cuantificamos la no Markovianidad a través de la mínima cantidad de ruido Markoviano que debe agregarse para tornar una evolución en Markoviana.
Fotònica

We discuss two central spin models coupled, respectively, to a quantum Heisenberg XY spin star environment [1] and to an antiferromagnetic environment [2]. In the first model [1], the exact quantum dynamics of the reduced density matrix of two coupled spin qubits in a quantum Heisenberg XY spin star environment in the thermodynamic limit at arbitrarily finite temperatures is obtained using a novel operator technique. In this approach, the transformed Hamiltonian becomes effectively Jaynes-Cumming like and thus the analysis is also relevant to cavity quantum electrodynamics. This special operator technique is mathematically simple and physically clear, and allows us to treat systems and environments that could all be strongly coupled mutually and internally. To study their entanglement evolution, the concurrence of the reduced density matrix of the two coupled central spins is also obtained exactly. It is shown that the dynamics of the entanglement depends on the initial state of the system and the coupling strength between the two coupled central spins, the thermal temperature of the spin environment and the interaction between the constituents of the spin environment. We also investigate the effect of detuning which in our model can be controlled by the strength of a locally applied external magnetic field. It is found that the detuning has a significant effect on the entanglement generation between the two spin qubits.

We study the non-equilibrium dynamics of a pair of qubits made of two-level atoms separated in space with distance r and interacting with one common electromagnetic field but not directly with each other. Our calculation makes a weak coupling assumption, but no Born or Markov approximation. We derived a non-Markovian master equation for the evolution of the reduced density matrix of the two-qubit system after integrating out the electromagnetic field modes. It contains a Markovian part with a Lindblad type operator and a nonMarkovian contribution, the physics of which is the main focus of this study. We use the concurrence function as a measure of quantum entanglement between the two qubits. Two classes of states are studied in detail: Class A is a one parameter family of states which are the superposition of the highest energy |I〉 ≡ |11〉 and lowest energy |O〉 ≡ |00〉 states, υiz, |A〉≡p|I〉+(1−p)|O〉, with 0 ≤ p ≤ 1; and Class B states |B〉 are linear combinations of the symmetric |+〉=12(|01〉+|10〉) and the antisymmetric |−〉=12(|01〉−|10〉) Bell states.

Many real-world domains are subject to a structured non-stationarity which affects the agent's goals and the environmental dynamics. Meta-reinforcement learning (RL) has been shown successful for training agents that quickly adapt to related tasks. However, most of the existing meta-RL algorithms for non-stationary domains either make strong assumptions on the task generation process or require sampling from it at training time. In this paper, we propose a novel algorithm (TRIO) that optimizes for the future by explicitly tracking the task evolution through time. At training time, TRIO learns a variational module to quickly identify latent parameters from experience samples. This module is learned jointly with an optimal exploration policy that takes task uncertainty into account. At test time, TRIO tracks the evolution of the latent parameters online, hence reducing the uncertainty over future tasks and obtaining fast adaptation through the meta-learned policy. Unlike most existing methods, TRIO does not assume Markovian task-evolution processes, it does not require information about the non-stationarity at training time, and it captures complex changes undergoing in the environment. We evaluate our algorithm on different simulated problems and show it outperforms competitive baselines.

A continuous-time, non-homogenous pure birth Markov chain serves to model external pitting corrosion in buried pipelines. The analytical solution of Kolmogorov’s forward equations for this type of Markov process gives the transition probability function in a discrete space of pit depths. The transition probability function can be completely identified by making a correlation between the stochastic pit depth mean and the deterministic mean obtained experimentally. Previously reported Monte Carlo simulations have been used for the prediction of the evolution of the pit depth distribution mean value with time for different soil types. The simulated pit depth distributions are used to develop a stochastic model based on Markov chains to predict the progression of pitting corrosion depth and rate distributions from the observed soil properties and pipeline coating characteristics. The proposed model can also be applied to pitting corrosion data from repeated in-line pipeline inspections. Real-life case studies presented in this work show how pipeline inspection and maintenance planning can be improved through the use of the proposed Markovian model for pitting corrosion.

Gears exhibit vibrations during operation which contain apparently random components. Due to time-varying stiffness and backlash nonlinearity, it is very hard, if not impossible, to get a closed form response of gears under combination of deterministic and random loads. This paper employs a numerical method termed as path integration to obtain the probability density of the response at discrete time instants. The random excitation is assumed to be White noise. The response of the gear is a Markovian processes under the random excitation. In order to capture the probability density evolution, discretization is applied to both space and time. The transition probability between adjacent time instants is assumed to be Gaussian and the calculation of the probability density is made on a reduced finite space. The mean and variance, which are used to construct the Gaussian distribution, are obtained through a direct numerical integration scheme with one stochastic Newmark method. Statistic linearization technique is utilized within each individual time-step to find a linear equivalent of the original system with backlash nonlinearity. Through this method the evolution of the probability distribution function of the response displacement and the velocity is calculated. Three representative cases with different levels of constant load are investigated.