We study the relation between the sudden death and revival of the entanglement of two qubits in a common squeezed reservoir, and the normal decoherence, by getting closer to the Decoherence Free Subspace and calculating the effect on the death and revival times.

Quantum annealing is a promising technique which leverages quantum mechanics to solve hard optimization problems. Considerable progress has been made in the development of a physical quantum annealer, motivating the study of methods to enhance the efficiency of such a solver. In this work, we present a quantum annealing approach to measure similarity among molecular structures. Implementing real-world problems on a quantum annealer is challenging due to hardware limitations such as sparse connectivity, intrinsic control error, and limited precision. In order to overcome the limited connectivity, a problem must be reformulated using minor-embedding techniques. Using a real data set, we investigate the performance of a quantum annealer in solving the molecular similarity problem. We provide experimental evidence that common practices for embedding can be replaced by new alternatives which mitigate some of the hardware limitations and enhance its performance. Common practices for embedding include minimizing either the number of qubits or the chain length, and determining the strength of ferromagnetic couplers empirically. We show that current criteria for selecting an embedding do not improve the hardware's performance for the molecular similarity problem. Furthermore, we use a theoretical approach to determine the strength of ferromagnetic couplers. Such an approach removes the computational burden of the current empirical approaches, and also results in hardware solutions that can benefit from simple local classical improvement. Although our results are limited to the problems considered here, they can be generalized to guide future benchmarking studies.

Starting from the requirement of distinguishability of two atoms by their positions, it is shown that photon recoil has a strong influence on finite-time disentanglement and in some cases prevents its appearance. At near-field inter atomic distances well localized atoms -with maximally one atom being initially excitedmay suffer disentanglement at a single finite time or even at a series of equidistant finite times, depending on their mean inter atomic distance and their initial electronic preparation.

Quantum entanglement is a physical resource, associated with the peculiar nonclassical correlations that are possible between separated quantum systems. Entanglement can be measured, transformed, and purified. A pair of quantum systems in an entangled state can be used as a quantum information channel to perform computational and cryptographic tasks that are impossible for classical systems.The aim of this work is to study various aspects of quantum entanglement and coherence, illustrated by several examples. We relate the concepts of decoherence and disentanglement, via a model of two two-level atoms in different types of reservoir, including both cases of independent and common bath. Finally, we relate decoherence and disentanglement, by focussing on the sudden death of the entanglement and the dependence of the death time with the "distance" of our initial condition, from the decoherence free subspace. In particular, we study the sudden death of the entanglement, in a two-atom system with a common reservoir. lX ACKNOWLEDGEMENTS Foremost, I would like to thanks my God for being with me in every step that I take, for strengthening my heart, enlightening my mind and for having placed in my path those who have been my support and company throughout this study period.I would like to thank my advisor, Prof. Michael Orszag, who shared with me a lot of his expertise and research insight. He quickly became for me the role model of a successful researcher in the field. I am deeply grateful to the examining committee for their important comments and contributions made to this work. Thanks to the National Commission of Scientific Research and Technology-CONICYT for the trust and support that they gave me in order to study my Ph.D. I would also like to express my gratitude to Juan, Carolina, Giliana and Liliana, the department staff, who always had excellent disposition to help. To my friend Daniela for her help in the printing and distribution of this work, and for making the time in the university so pleasant.Wholehearted thanks to my parents Rector and Nenella, and my sister Karin, for their love, affection and understanding. For the company and support given forever.And in a special way I would like to thank to my husband Daniel for his support, understanding and love that allows me to feel able to achieve my goals. Thanks you for listening and for your advice (this is something you do very well). Thanks for being part of my life, you are the best thing that has happened to me.

In this paper we give a formal definition of the high-order Boltzmann machine (BM), and extend the well-known results on the convergence of the learning algorithm of the two-order BM. From the Bahadur-Lazarsfeld expansion we characterize the probability distribution learned by the high order BM. Likewise a criterion is given to establish the topology of the BM depending on the significant correlations of the particular probability distribution to be learned.