In this thesis I consider the general problem of how to make the best possible phase measurements using feedback. Both the optimum input state and optimum feedback are considered for both single-mode dyne measurements and two-mode interferometric measurements. I derive the optimum input states under general dyne measurements when the mean photon number is fixed, both for general states and squeezed states. I propose a new feedback scheme that introduces far less phase uncertainty than mark II feedback, and is very close to the theoretical limit. I also derive results for the phase variance when there is a time delay in the feedback loop, showing that there is a lower limit to the introduced phase variance, and this is approached quite accurately under some conditions. I derive the optimum input states for interferometry, showing that the phase uncertainty scales as 1/N for all the common measures of uncertainty. This is contrasted with the |j0> state, which does not scale as 1/N for all measures of phase uncertainty. I introduce an adaptive feedback scheme that is very close to optimum, and can give scaling very close to 1/N for the uncertainty. Lastly I consider the case of continuous measurements, for both the dyne and interferometric cases.

In this thesis I consider the general problem of how to make the best possible phase measurements using feedback. Both the optimum input state and optimum feedback are considered for both single-mode dyne measurements and two-mode interferometric measurements. I derive the optimum input states under general dyne measurements when the mean photon number is fixed, both for general states and squeezed states. I propose a new feedback scheme that introduces far less phase uncertainty than mark II feedback, and is very close to the theoretical limit. I also derive results for the phase variance when there is a time delay in the feedback loop, showing that there is a lower limit to the introduced phase variance, and this is approached quite accurately under some conditions. I derive the optimum input states for interferometry, showing that the phase uncertainty scales as 1/N for all the common measures of uncertainty. This is contrasted with the |j0> state, which does not scale as 1/N for all measures of phase uncertainty. I introduce an adaptive feedback scheme that is very close to optimum, and can give scaling very close to 1/N for the uncertainty. Lastly I consider the case of continuous measurements, for both the dyne and interferometric cases.

In this work our aim is to study several aspects related to quantum coherence as understood to correspond with the non-classical behaviour that can be observed for certain particular states of a physical system. In particular we are interested in the possible mechanisms that result in dynamically induced transitions between quantum and classical regimes. The thesis is organized as follows: The first chapter dubs as an introduction and serves to set out the basic philosophy underlying the questions addressed in this thesis. It also presents some elementary properties of states and state spaces in Quantum Theory including what we have chosen to define as classical and quantum behaviour. In chapter 2 we study some of the aspects related to observing quantum behaviour and of the properties of our main definition of classicality (and quantumness). Here we also study some of the restrictions imposed on measurements by the existence of globally conserved quantities (Wigner-Araki-Yanase theorem) and their relationship to weak measurements coupled to postselection. In the following chapter we review some of the basic tools used in the description of open quantum system dynamics that will be applied in other chapters. In chapter 4 we review the basics of decoherence and analyse the importance of the choice of initial conditions when trying to study the dynamical emergence of classical behaviour within Quantum Theory. Next we study the other direction of the transition and focus on how to obtain pure quantum states from states that originally were classically mixed. Along the same lines, in chapter 6 we cover some topics related to the production of pure quantum states from measurements. We pay special attention to a model of the non-selective continuous monitoring of a system coupled to another unmonitored system. Lastly we explore some of the possible similarities between the theory of phase transitions and the quantum-classical transition. We must emphasize that all the work done in this thesis assumes that Quantum Theory is generally valid (at least within a broad enough range of energies). Thus, when we say that a state is "classical" we will mainly be referring to one of all the possible states contained in Quantum Theory, but that is susceptible to being interpreted as corresponding to "classical" behaviour. Similarly when we speak of creating a "quantum", or "quantum coherent", state we mean that the system has evolved to this state from one of the "classical" ones, but all of these still correspond to valid states within Quantum Theory. In the opinion of the author the main original contributions that can be found in this thesis are the following: - The recognition of the relationship between the Wigner-Araki-Yanase theorem and weak measurements coupled to postselection (sections 2.2 and 2.4); - A mathematical proof of the possible ambiguities arising when two observers try to decide if a state corresponds to quantum or classical behaviour (section 2.6); - The implications of initial correlations in decoherence models. In particular how the choice of certain (correlated) initial conditions can result in residual coherence and the production of pure quantum states in a model that otherwise results in ideal decoherence when (locally equivalent) uncorrelated initial conditions are used (section 4.2); - Various results related to the production of quantum states from initially classical states (sections 5.2 to 5.4); - The analysis of the inverse of a generalized depolarizing channel (section 5.7); - The study of a model of the non-selective continuous monitoring, in the quantum Zeno limit, of a subsystem A interacting with an unmonitored subsystem B. In particular the absence of the purification of B, which has been previously predicted in the selective case, but the possibility of coherent dynamics for B (section 6.4); - The identification of the loose equivalent of a broken symmetry and order parameter in the quantum-classical transition (section 7.2).

yes / A time-dependent finite-state Markov chain that uses doubly stochastic transition matrices, is considered. Entropic quantities that describe the randomness of the probability vectors, and also the randomness of the discrete paths, are studied. Universal convex polytopes are introduced which contain all future probability vectors, and which are based on the Birkhoff–von Neumann expansion for doubly stochastic matrices. They are universal in the sense that they depend only on the present probability vector, and are independent of the doubly stochastic transition matrices that describe time evolution in the future. It is shown that as the discrete time increases these convex polytopes shrink, and the minimum entropy of the probability vectors in them increases. These ideas are applied to a sequence of non-selective measurements (with different projectors in each step) on a quantum system with -dimensional Hilbert space. The unitary time evolution in the intervals between the measurements, is taken into account. The non-selective measurements destroy stroboscopically the non-diagonal elements in the density matrix. This ‘hermaphrodite’ system is an interesting combination of a classical probabilistic system (immediately after the measurements) and a quantum system (in the intervals between the measurements). Various examples are discussed. In the ergodic example, the system follows asymptotically all discrete paths with the same probability. In the example of rapidly repeated non-selective measurements, we get the well known quantum Zeno effect with ‘frozen discrete paths’ (presented here as a biproduct of our general methodology based on Markov chains with doubly stochastic transition matrices).

In this thesis various subjects at the crossroads of quantummechanics and device physics are treated, spanning from afundamental study on quantum measurements to fabricationtechniques of controlling gates for nanoelectroniccomponents. Electron waveguide components, i.e. electronic componentswith a size such that the wave nature of the electron dominatesthe device characteristics, are treated both experimentally andtheoretically. On the experimental side, evidence of partialballistic transport at room-temperature has been found anddevices controlled by in-plane Pt/GaAs gates have beenfabricated exhibiting an order of magnitude improvedgate-efficiency as compared to an earlier gate-technology. Onthe theoretical side, a novel numerical method forself-consistent simulations of electron waveguide devices hasbeen developed. The method is unique as it incorporates anenergy resolved charge density calculation allowing for e.g.calculations of electron waveguide devices to which a finitebias is applied. The method has then been used in discussionson the influence of space-charge on gate-control of electronwaveguide Y-branch switches. Electron waveguides were also used in a proposal for a novelscheme of carrierinjection in low-dimensional semiconductorlasers, a scheme which altogether by- passes the problem ofslow carrier relaxation in suchstructures. By studying aquantum mechanical two-level system serving as a model forelectroabsorption modulators, the ultimate limits of possiblemodulation rates of such modulators have been assessed andfound to largely be determined by the adiabatic response of thesystem. The possibility of using a microwave field to controlRabi oscillations in two-level systems such that a large numberof states can be engineered has also been explored. A more fundamental study on quantum mechanical measurementshas been done, in which the transition from a classical to aquantum "interaction free" measurement was studied, making aconnection with quantum non-demolition measurements.

<p>In this thesis various subjects at the crossroads of quantummechanics and device physics are treated, spanning from afundamental study on quantum measurements to fabricationtechniques of controlling gates for nanoelectroniccomponents.</p><p>Electron waveguide components, i.e. electronic componentswith a size such that the wave nature of the electron dominatesthe device characteristics, are treated both experimentally andtheoretically. On the experimental side, evidence of partialballistic transport at room-temperature has been found anddevices controlled by in-plane Pt/GaAs gates have beenfabricated exhibiting an order of magnitude improvedgate-efficiency as compared to an earlier gate-technology. Onthe theoretical side, a novel numerical method forself-consistent simulations of electron waveguide devices hasbeen developed. The method is unique as it incorporates anenergy resolved charge density calculation allowing for e.g.calculations of electron waveguide devices to which a finitebias is applied. The method has then been used in discussionson the influence of space-charge on gate-control of electronwaveguide Y-branch switches.</p><p>Electron waveguides were also used in a proposal for a novelscheme of carrierinjection in low-dimensional semiconductorlasers, a scheme which altogether by- passes the problem ofslow carrier relaxation in suchstructures. By studying aquantum mechanical two-level system serving as a model forelectroabsorption modulators, the ultimate limits of possiblemodulation rates of such modulators have been assessed andfound to largely be determined by the adiabatic response of thesystem. The possibility of using a microwave field to controlRabi oscillations in two-level systems such that a large numberof states can be engineered has also been explored.</p><p>A more fundamental study on quantum mechanical measurementshas been done, in which the transition from a classical to aquantum "interaction free" measurement was studied, making aconnection with quantum non-demolition measurements.</p>

O processamento de informação quântica requer medidas, muitas vezes precedidas devoluções unitárias. Uma descrição realista de um computador quântico também deve levar em conta que o sistema interage com um ambiente externo - distinto do observador - que o remove de sua evolução ideal, gerando erros. Neste trabalho, fazemos um estudo da dinâmica de sistemas quânticos observados múltiplas vezes ou continuamente, enquanto interagem com ambientes externos. Para tanto, empregamos uma equação mestra híbrida, que permite modelar uma interação contínua e markoviana do sistema com o medidor, enquanto o ruído do ambiente apresenta características não markovianas. O estudo da dinâmica de uma medida contínua ruidosa revela que o sistema melhor preserva suas populações iniciais quando é realizada a medida de uma observável que não comuta com os operadores do ruído produzido pelo ambiente. Estes resultados, já conhecidos para o caso simples de um qubit de memória interagindo com o vácuo, são generalizados para uma temperatura inicial superior a zero e para um qubit submetido a uma porta quântica. A universalidade destes fenômenos de preservação da população inicial permite fazer analogia com o efeito Zenão quântico. Mantendo o mesmo formalismo, mas adaptando a interação com o ambiente para descrever um decaimento verificamos que o efeito Zenão quântico é observado para acoplamentos fracos com o ambiente. Tratamos também de como tal conhecimento sobre a preservação das populações pela medida auxilia na elaboração de melhores formas de preservar a informação em códigos quânticos. Com o auxílio da teoria das medidas fracas, propomos um possível método experimental simples para o teste da validade dos modelos de descrição de medidas contínuas. Com este estudo da dinâmica de uma medida quântica, esperamos elucidar questões de ordem prática no processamento de informação quântica, assim como ajudar no melhor entendimento de questões fundamentais, como o postulado da medida. / The processing of quantum information requires measurements, often preceded by unitary evolutions. A faithful description of a quantum computer should also take into account that the system interacts with an external environment - other than the observer - that removes it from its ideal evolution, causing errors. Here, we study the dynamics of quantum systems observed multiple times or continuously, while they interact with external environments. To do this, we employ a hybrid master equation, which allows us to model a continuous, Markovian interaction between the system and the measurement apparatus, while the environmental noise presents non-Markovian features. This study of the dynamics of the noisy continuous measurement reveals that the system better preserves its initial populations when the observable measured does not commute with the environmental noise operators. These results, already known for the simpler case of a memory qubit interacting with vacuum, are generalized for an initial temperature above zero and a qubit undergoing a quantum gate. The universality of these phenomena of preservation of the initial populations allows an analogy with the Quantum Zeno Effect. Keeping the same formalism, but adapting the environmental interaction to describe a decay, we verify that the quantum Zeno effect is observed for weak coupling with the environment. We also deal with how the knowledge about the preservation of the populations by the measurement helps in creating better ways to preserve the information in quantum codes. With the help of the weak measurement theory, we propose a simple experimental method to test the validity of models that describe a continuous measurement. With this study of the dynamics of a quantum measurement, we hope to help solve practical issues in quantum information processing, as well as provide greater insight into fundamental questions, such as the measurement postulate.

O processamento de informação quântica requer medidas, muitas vezes precedidas devoluções unitárias. Uma descrição realista de um computador quântico também deve levar em conta que o sistema interage com um ambiente externo - distinto do observador - que o remove de sua evolução ideal, gerando erros. Neste trabalho, fazemos um estudo da dinâmica de sistemas quânticos observados múltiplas vezes ou continuamente, enquanto interagem com ambientes externos. Para tanto, empregamos uma equação mestra híbrida, que permite modelar uma interação contínua e markoviana do sistema com o medidor, enquanto o ruído do ambiente apresenta características não markovianas. O estudo da dinâmica de uma medida contínua ruidosa revela que o sistema melhor preserva suas populações iniciais quando é realizada a medida de uma observável que não comuta com os operadores do ruído produzido pelo ambiente. Estes resultados, já conhecidos para o caso simples de um qubit de memória interagindo com o vácuo, são generalizados para uma temperatura inicial superior a zero e para um qubit submetido a uma porta quântica. A universalidade destes fenômenos de preservação da população inicial permite fazer analogia com o efeito Zenão quântico. Mantendo o mesmo formalismo, mas adaptando a interação com o ambiente para descrever um decaimento verificamos que o efeito Zenão quântico é observado para acoplamentos fracos com o ambiente. Tratamos também de como tal conhecimento sobre a preservação das populações pela medida auxilia na elaboração de melhores formas de preservar a informação em códigos quânticos. Com o auxílio da teoria das medidas fracas, propomos um possível método experimental simples para o teste da validade dos modelos de descrição de medidas contínuas. Com este estudo da dinâmica de uma medida quântica, esperamos elucidar questões de ordem prática no processamento de informação quântica, assim como ajudar no melhor entendimento de questões fundamentais, como o postulado da medida. / The processing of quantum information requires measurements, often preceded by unitary evolutions. A faithful description of a quantum computer should also take into account that the system interacts with an external environment - other than the observer - that removes it from its ideal evolution, causing errors. Here, we study the dynamics of quantum systems observed multiple times or continuously, while they interact with external environments. To do this, we employ a hybrid master equation, which allows us to model a continuous, Markovian interaction between the system and the measurement apparatus, while the environmental noise presents non-Markovian features. This study of the dynamics of the noisy continuous measurement reveals that the system better preserves its initial populations when the observable measured does not commute with the environmental noise operators. These results, already known for the simpler case of a memory qubit interacting with vacuum, are generalized for an initial temperature above zero and a qubit undergoing a quantum gate. The universality of these phenomena of preservation of the initial populations allows an analogy with the Quantum Zeno Effect. Keeping the same formalism, but adapting the environmental interaction to describe a decay, we verify that the quantum Zeno effect is observed for weak coupling with the environment. We also deal with how the knowledge about the preservation of the populations by the measurement helps in creating better ways to preserve the information in quantum codes. With the help of the weak measurement theory, we propose a simple experimental method to test the validity of models that describe a continuous measurement. With this study of the dynamics of a quantum measurement, we hope to help solve practical issues in quantum information processing, as well as provide greater insight into fundamental questions, such as the measurement postulate.

En circuit-QED, la technique la plus usuelle pour lire l'état d'un qubit est d'utiliser le couplage transverse entre le qubit et une cavité micro-onde dans la limite dispersive. Cependant, malgré d'importants progrès au cours de cette décennie, obtenir une lecture rapide, en un seul coup et hautement fidèle d'un qubit reste un défi majeur. En effet, la distinction de l'état d'un qubit est limitée par le compromis entre vitesse d'acquisition et précision. Cette limite a pour origine le couplage transverse qui impose deux importantes contraintes expérimentales : premièrement, augmenter les interactions pour lire plus rapidement restreint la durée de vie du qubit via l'effet Purcell. La seconde contrainte est sur la force du signal, qui est limitée pour éviter des transitions non voulues et induites par la mesure. Par conséquent, le défi expérimental à relever avec le couplage transverse est d'acquérir un signal faible en un temps court...Pour surmonter ces limitations, nous voulons changer de paradigme en introduisant un nouveau schéma de lecture qui se base sur un couplage cross-Kerr direct. Ce schéma est obtenu grâce à une molécule artificielle supraconductrice couplée à une cavité micro-onde 3D. La molécule est construite en couplant inductivement deux atomes transmons supraconducteurs. Elle manifeste alors deux modes propres : le mode symétrique qubit transmon et le mode antisymétrique ancilla. En insérant cette molécule dans la cavité de manière optimale, une hybridation transverse entre l'ancilla et la cavité conduit à deux résonateurs faiblement anharmoniques, appelés polaritons. Ces derniers possèdent un couplage cross-Kerr direct et large avec le qubit transmon. En mesurant le signal micro-onde transmis par un polariton, l'état du qubit peut être résolu.Théoriquement, dans ce nouveau paradigme, le qubit est immunisé contre les limitations du couplage transverse tel que l'effet Purcell. Cependant, pour les deux échantillons étudiés, un couplage transverse résiduel existe à cause d'imperfections expérimentales. Même faible, il limite pour l'instant la durée de vie du qubit et nos performances de lecture. Malgré cela, nous avons obtenu une lecture du qubit en un seul coup avec une fidélité allant jusqu'à 97.2 % en 500 ns par une mesure dite de verrouillage grâce à la non-linéarité du polariton. Dans une limite linéaire à faible nombre de photons, nous démontrons une fidélité atteignant 94.7 % en seulement 50 ns de lecture grâce à l'ajout d'un amplificateur paramétrique Josephson. Dans ce régime, les sauts quantiques sont résolus et le qubit est lu de manière non-destructive 99.2 % du temps. / Using the transverse coupling between a qubit and a microwave cavity in the dispersive limit is the most common technique in circuit-QED to readout a qubit state. However, despite important progress in the last decade, implementing a fast single shot high fidelity readout remains a major challenge. Indeed, inferring the qubit state is limited by the trade-off between speed and accuracy. The transverse coupling imposes two significant experimental limitations: firstly, increasing the interaction for faster readout leads to limited qubit lifetime via the Purcell effect. Secondly, the strength of the signal is limited to avoid unwanted measurement-induced transitions. Therefore, the experimental challenge with transverse coupling is to acquire a weak signal in a short time...To overcome these limitations, we want to change this coupling paradigm by introducing a new readout scheme relying on a direct cross-Kerr coupling. This scheme is obtained thanks to a superconducting artificial molecule coupled to a microwave 3D cavity. The molecule is built by inductively coupling two transmon artificial atoms, resulting in two eigenmodes: a symmetric mode, the transmon qubit and an antisymmetric mode, the ancilla. By optimal positioning of the molecule in the cavity, a transverse hybridization between ancilla and cavity leads to two weakly anharmonic resonators, called polaritons. The latter possess a large and direct cross-Kerr coupling with the transmon qubit. By driving one of the polariton, the qubit states can be resolved.Theoretically, in such a coupling scheme, the qubit is immune to the limitation of the transverse coupling such as the Purcell effect. However, for the two studied samples, a residual transverse coupling remains due to experimental imperfections. Even if it is weak, it limits for now the qubit lifetime and the readout performances. Despite this, we observe single shot qubit readout performance with fidelity as high as 97.2 % in a 500 ns latching measurement using the non-linearity of the polariton. In a low photons number linear regime, we report fidelity as high as 94.7 % in only 50 ns thanks to the addition of a Josephson parametric amplifier. In this regime, quantum jumps are resolved and the qubit is measured non-destructively 99.2 % of the time.