Many quantum information tasks require measurements to distinguish between different quantum-mechanically entangled states (Bell states) of a particle pair. In practice, measurements are often limited to linear evolution and local measurement (LELM) of the particles. We investigate LELM distinguishability of the Bell states of two qubits (two-state particles) and qutrits (three-state particles), via standard projective measurement and via generalized measurement, which allows detection channels beyond the number of orthogonal single-particle states. Projective LELM can only distinguish 3 of 4 qubit Bell states; we show that generalized measurement does no better. We show that projective LELM can distinguish only 3 of 9 qutrit Bell states that generalized LELM allows at most 5 of 9. We have also made progress on distinguishing qubit $\times$ qutrit hyperentangled Bell states, which are made up of tensor products of the qubit Bell states and the qutrit Bell states, showing that the maximum number distinguishable with projective LELM measurements is between 9 and 11.

Many quantum information protocols rely on the ability to distinguish between entangled quantum states known as Bell states. However, theoretical limits exist on the maximal distinguishability of these entangled states using linear evolution and local measurement (LELM) devices. In the case of two particles entangled in multiple qubit variables, the maximum number of distinguishable Bell states is known. However, in the more general case of two particles entangled in multiple qudit variables, only an upper bound is known under additional assumptions. I have written software in Matlab and Mathematica to explore computationally the maximum number of Bell states that can be distinguished in the case of two particles entangled in a qutrit variable, and the case of two particles entangled in both a qutrit and qubit variable. Using code I have written in Mathematica, I have reduced the number of cases to check for sets of 9 qubit x qutrit Bell states from 94,143,280 to 10,365. Further work needs to be done to computationally check these cases for distinguishability by an LELM apparatus.

The idea to assimilate classical information theory with quantum mechanics resulted in the creation of a new field in physics known as quantum information. One of the first papers in this new field occurred in the early 1970's when Stephen Wiesner wrote the seminal manuscript titled: "Conjugate Coding". However, its importance wasn't imme- diately recognized and wasn't published until 1983. The 1980's and 1990's saw a number of important papers published in quantum information leading to the subfields of quantum cryptography, quantum teleportation, quantum entanglement, distinguishability of quantum states, and quantum cloning. It was also during the 1980's, that a new model of computing, known as quantum computation, was beginning to emerge. It offered the possibility of solving certain problems faster than a classical computer by exploiting various properties of quantum mechanics. Research in this field was undoubtedly stimulated by a well known talk given by Richard Feynman in 1981 at MIT on quantum simulations. Both quantum information and quantum computation were initially developed with quantum discrete variables in mind. However, over the course of the last decade, there has been a significant increase in using quantum continuous variables. This thesis will focus on the topic of quantum information and quantum computation using continuous variables. Specifically, we will theoretically consider the cloning of continuous-variable entanglement, the distinguishability of Gaussian states, new continuous-variable quantum cryptography protocols and finally, the universality of quantum computation using continuous-variable cluster states.

The idea to assimilate classical information theory with quantum mechanics resulted in the creation of a new field in physics known as quantum information. One of the first papers in this new field occurred in the early 1970's when Stephen Wiesner wrote the seminal manuscript titled: "Conjugate Coding". However, its importance wasn't imme- diately recognized and wasn't published until 1983. The 1980's and 1990's saw a number of important papers published in quantum information leading to the subfields of quantum cryptography, quantum teleportation, quantum entanglement, distinguishability of quantum states, and quantum cloning. It was also during the 1980's, that a new model of computing, known as quantum computation, was beginning to emerge. It offered the possibility of solving certain problems faster than a classical computer by exploiting various properties of quantum mechanics. Research in this field was undoubtedly stimulated by a well known talk given by Richard Feynman in 1981 at MIT on quantum simulations. Both quantum information and quantum computation were initially developed with quantum discrete variables in mind. However, over the course of the last decade, there has been a significant increase in using quantum continuous variables. This thesis will focus on the topic of quantum information and quantum computation using continuous variables. Specifically, we will theoretically consider the cloning of continuous-variable entanglement, the distinguishability of Gaussian states, new continuous-variable quantum cryptography protocols and finally, the universality of quantum computation using continuous-variable cluster states.

In this thesis, optimum current injection strategy for Magnetic Resonance Electrical Impedance Tomography (MREIT) is studied. Distinguishability measure based on magnetic flux density is defined for MREIT. Limit of distinguishability is analytically derived for an infinitely long cylinder with concentric and eccentric inhomogeneities. When distinguishability limits of MREIT and Electrical Impedance Tomography (EIT) are compared, it is found that MREIT is capable of detecting smaller perturbations than EIT. When conductivities of inhomogeneity and background object are equal to 0.8S and 1S respectively, MREIT provides improvement of %74 in detection capacity. Optimum current injection pattern is found based on the distinguishability definition. For 2-D cylindrical body with concentric and eccentric inhomogeneities, opposite drive provides best result. As for the 3-D case, a sphere with azimuthal symmetry is considered. Distinguishability limit expression is obtained and optimum current injection pattern is again opposite drive. Based these results, optimum current injection principles are provided and Regional Image Reconstruction (RIR) using optimum currents is proposed. It states that conductivity distribution should be reconstructed for a region rather than for the whole body. Applying current injection principles and RIR provides reasonable improvement in image quality when there is noise in the measurement data. For the square geometry, when SNR is 13dB, RIR provides decrement of nearly %50 in conductivity error rate of small inhomogeneity. Pulse sequence optimization is done for Gradient Echo (GE) and it is compared with Spin Echo (SE) in terms of their capabilities for MREIT.

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Beaucoup de services vitaux de la vie quotidienne dépendent de systèmes d'ingénierie hautement complexes et interconnectés; Ces systèmes sont constitués d'un grand nombre de capteurs interconnectés, d'actionneurs et de composants du système. L'étude des systèmes interconnectés joue un rôle important dans l'étude de la fiabilité des systèmes dynamiques; car elle permet d'étudier les propriétés d'un système interconnecté en analysant ses sous-composants moins complexes. Le diagnostic des pannes est essentiel pour assurer des opérations sûres et fiables des systèmes de contrôle interconnectés. Dans toutes les situations, le système global et / ou chaque sous-système peuvent être analysés à différents niveaux pour déterminer la fiabilité du système global. Dans certains cas, il est important de déterminer les informations anormales des variables internes du sous-système local, car ce sont les causes qui contribuent au fonctionnement anormal du processus global. Cette thèse porte sur les défis de l'application de la théorie inverse du système et des techniques FDD basées sur des modèles pour traiter le problème articulaire du diagnostic des fautes et de l'analyse des causes racines (FD et RCA). Nous étudions ensuite le problème de l'inversibilité de la gauche, de l'observabilité et de la diagnosticabilité des fauts du système interconnecté, formant un algorithme FD et RCA multi-niveaux basé sur un modèle. Ce système de diagnostic permet aux composants individuels de surveiller la dynamique interne localement afin d'améliorer l'efficacité du système et de diagnostiquer des ressources de fautes potentielles pour localiser un dysfonctionnement lorsque les performances du système global se dégradent. Par conséquent, un moyen d'une combinaison d'intelligence locale avec une capacité de diagnostic plus avancée pour effectuer des fonctions FDD à différents niveaux du système est fourni. En conséquence, on peut s'attendre à une amélioration de la localisation des fauts et à de meilleurs moyens de maintenance prédictive. La nouvelle structure du système, ainsi que l'algorithme de diagnostic des fautes, met l'accent sur l'importance de la RCA de défaut des dispositifs de terrain, ainsi que sur l'influence de la dynamique interne locale sur la dynamique globale. Les contributions de cette thèse sont les suivantes: Tout d'abord, nous proposons une structure de système non linéaire interconnecté inversible qui garantit le fauts dans le sous-système de périphérique de terrain affecte la sortie mesurée du système global de manière unique et distincte. Une condition nécessaire et suffisante est développée pour assurer l'inversibilité du système interconnecté qui nécessite l'inversibilité de sous-systèmes individuels. Deuxièmement, un observateur interconnecté à deux niveaux est développé; Il se compose de deux estimateurs d'état, vise à fournir des estimations précises des états de chaque sous-système, ainsi que l'interconnexion inconnue. En outre, il fournira également une condition initiale pour le reconstructeur de données et le filtre de fauts local une fois que la procédure FD et RCA est déclenchée par tout fauts. D'une part, la mesure utilisée dans l'estimateur de l'ancien sous-système est supposée non accessible; La solution est de la remplacer par l'estimation fournie par l'estimateur de ce dernier sous-système. / Many of the vital services of everyday life depend on highly complex and interconnected engineering systems; these systems consist of large number of interconnected sensors, actuators and system components. The study of interconnected systems plays a significant role in the study of reliability theory of dynamic systems, as it allows one to investigate the properties of an interconnected system by analyzing its less complicated subcomponents. Fault diagnosis is crucial in achieving safe and reliable operations of interconnected control systems. In all situations, the global system and/or each subsystem can be analyzed at different levels in investigating the reliability of the overall system; where different levels mean from system level down to the subcomponent level. In some cases, it is important to determine the abnormal information of the internal variables of local subsystem, in order to isolate the causes that contribute to the anomalous operation of the overall process. For example, if a certain fault appears in an actuator, the origin of that malfunction can have different causes: zero deviation, leakage, clogging etc. These origins can be represented as root cause of an actuator fault. This thesis concerns with the challenges of applying system inverse theory and model based FDD techniques to handle the joint problem of fault diagnosis & root cause analysis (FD & RCA) locally and performance monitoring globally. By considering actuator as individual dynamic subsystem connected with process dynamic subsystem in cascade, we propose an interconnected nonlinear system structure. We then investigate the problem of left invertibility, fault observability and fault diagnosability of the interconnected system, forming a novel model based multilevel FD & RCA algorithm. This diagnostic algorithm enables individual component to monitor internal dynamics locally to improve plant efficiency and diagnose potential fault resources to locate malfunction when operation performance of global system degrades. Hence, a means of acombination of local intelligence with a more advanceddiagnostic capability (combining fault monitoring anddiagnosis at both local and global levels) to performFDDfunctions on different levels of the plantis provided. As a result, improved fault localization and better predictive maintenance aids can be expected. The new system structure, together with the fault diagnosis algorithm, is the first to emphasize the importance of fault RCA of field devices, as well as the influences of local internal dynamics on the global dynamics. The developed model based multi-level FD & RCA algorithm is then a first effort to combine the strength of the system level model based fault diagnosis with the component level model based fault diagnosis. The contributions of this thesis include the following: Firstly, we propose a left invertible interconnected nonlinear system structure which guarantees that fault occurred in field device subsystem will affect the measured output of the global system uniquely and distinguishably. A necessary and sufficient condition is developed to ensure invertibility of the interconnected system which requires invertibility of individual subsystems. Second, a two level interconnected observer is developed which consists of two state estimators, aims at providing accurately estimates of states of each subsystem, as well as the unknown interconnection. In addition, it will also provide initial condition for the input reconstructor and local fault filter once FD & RCA procedure is triggered by any fault. Two underlyingissues are worth to be highlighted: for one hand, the measurement used in the estimator of the former subsystem is assumed not accessible; the solution is to replace it by the estimate provided by the estimator of the latter subsystem. In fact, this unknown output is the unknown interconnection of the interconnected system, and also the input of the latter subsystem.