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In developing sensitive optical sensors, issues associated with optical crosstalk, dark count, and dark current persist. While designs have been created to mitigate the effects of these optical noises on the performance of the sensors, they are never fully addressed. This is mainly due to the highly probabilistic nature of the interaction of light and matter. This paper theoretically explores possible solutions that could lead to the significant reduction of these optical noises by presenting the problem in both the Markovian and Bayesian quantum feedback schemes and identifying the parameters that can be controlled and/or regulated. This paper then attempts to translate the quantum processes into realizable materials and/or systems suitable for fabrication or integration to existing system.

Using Gardiner and Collet's input-output model and the concept of cascade system, we determine the filtering equation for a quantum system driven by chosen non-classical states of light. The quantum system and electromagnetic field are described by making use of quantum stochastic unitary evolution. We consider two examples of the non-classical states of the field: a combination of vacuum and single photon states and a mixture of two coherent states. We describe the stochastic evolution conditioned on the results of the photon counting and quadrature measurements., Comment: 4 figures, 21 pages, updated 17.05.2018

We exploit the separation of the filtering and control aspects of quantum feedback control to consider the optimal control as a classical stochastic problem on the space of quantum states. We derive the corresponding Hamilton-Jacobi-Bellman equations using the elementary arguments of classical control theory and show that this is equivalent, in the Stratonovich calculus, to a stochastic Hamilton-Pontryagin setup. We show that, for cost functionals that are linear in the state, the theory yields the traditional Bellman equations treated so far in quantum feedback.

We introduce a new method to enhance the orthohydrogen-parahydrogen (o-p H2) conversion yield /rate of a H2 interacting with a solid surface. This method consists of two steps. The first step involves the dynamical quantum filtering (DQF) process, and the second step relies on the steric effect on o-p H2 conversion. The purpose of the DQF process is to align the rotation of free rotating o-H2 such that we have only H2 in helicopter-like rotational states or H2 in cartwheel-like rotational states. In the second process, we bring these aligned o-H2 close to a catalyst surface (e.g., metal oxide surface). Based on the steric effect, o-H2 that has a cartwheel-like rotation will be converted to p-H2 with high rate.

Estimates of growth of the standard d-dimensional Brownian motion W(t) and its integral V(t) = ∫t 0 W (s) ds are obtained, as t → ∞, and an application is discussed to the long time asymptotics of the solutions of the nonlinear stochastic equation of the quantum filtering theory.

In this thesis, we study measurement-based feedbacks stabilizing discrete-time quantum systems subject to quantum non-demolition (QND) measurements and stability of continuous-time quantum filters. This thesis contains two parts. In the first part, we generalize the mathematical methods underlying a discrete-time quantum feedback experimentally tested in Laboratoire Kastler Brossel (LKB) at Ecole Normale Supérieure (ENS) de Paris. In fact, we contribute to a control algorithm which has been used in this recent quantum feedback experiment. This experiment prepares and stabilizes on demand photon-number states (Fock states) of a microwave field in a superconducting cavity. We design real-time filters allowing estimation of the state despite measurement imperfections and delays, and we propose a feedback law which ensures the stabilization of a predetermined target state. This stabilizing feedback is obtained by stochastic Lyapunov techniques and depends on a filter estimating the quantum state. We prove that such control strategy extends to other discrete-time quantum systems under QND measurements. The second part considers an extension, to continuous-time, of a stability result for discrete-time quantum filters. Indeed, we prove the stability of a quantum filter associated to usual stochastic master equation driven by a Wiener process. This stability means that a “distance” between the physical state and its associated quantum filter decreases in average. Another subject that we study in this part is related to the design of a continuous-time optimal filter, in the presence of measurement imperfections. To this aim, we extend a construction method for discrete-time quantum filters with measurement imperfections. Finally, we obtain heuristically generalized continuous-time optimal filters whose dynamics are given by stochastic master equations driven by both Poisson and Wiener processes. We conjecture the stability of such optimal filters.; Dans cette thèse, nous étudions des rétroactions visant à stabiliser des systèmes quantiques en temps discret soumis à des mesures quantiques non-destructives (QND), ainsi que la stabilité des filtres quantiques à temps continu. Cette thèse comporte deux parties. Dans une première partie, nous généralisons les méthodes mathématiques sous-jacentes à une rétroaction quantique en temps discret testée expérimentalement au Laboratoire Kastler Brossel (LKB) de l'École Normale Supérieure (ENS) de Paris. Plus précisément,nous contribuons à un algorithme de contrôle qui a été utilisé lors de cette expérience récente de rétroaction quantique. L'expérience consiste en la préparation et la stabilisation à la demande d'états nombres de photons (états de Fock) d'un champ de micro-ondes au sein d'une cavité supraconductrice. Pour cela, nous concevons des filtres à temps-réel permettant d'estimer les états quantiques malgré des imperfections et des retards de mesure, et nous proposons une loi de rétroaction assurant la stabilisation d'un état cible prédéterminé. Cette rétroaction de stabilisation est obtenue grâce à des méthodes Lyapunov stochastique et elle repose sur un filtre estimant l'état quantique. Nous prouvons qu'une telle stratégie de contrôle se généralise à d'autres systèmes quantiques en temps discret soumis à des mesures QND. Dans une seconde partie, nous considérons une extension du résultat obtenu pour des filtres quantiques en temps discret au cas des filtres en temps continu. Dans ce but, nous démontrons la stabilité d'un filtre quantique associé à l'équation maîtresse stochastique usuelle découlant par un processus de Wiener. La stabilité signifie ici que la “distance”entre l'état physique et le filtre quantique associé décroit en moyenne. Cette partie étudie également la conception d'un filtre optimal en temps continu en présence d'imperfections de mesure. Pour ce faire, nous étendons la méthode utilisée précédemment pour construire les filtres quantiques en temps discret tolérants aux imperfections de mesure. Enfin,nous obtenons heuristiquement des filtres optimaux généraux en temps continu, dont la dynamique est décrite par des équations maîtresses stochastiques découlant à la fois par processus de Poisson et Wiener. Nous conjecturons que ces filtres optimaux sont stables.

In this thesis, we study measurement-based feedbacks stabilizing discrete-time quantum systems subject to quantum non-demolition (QND) measurements and stability of continuous-time quantum filters. This thesis contains two parts. In the first part, we generalize the mathematical methods underlying a discrete-time quantum feedback experimentally tested in Laboratoire Kastler Brossel (LKB) at Ecole Normale Supérieure (ENS) de Paris. In fact, we contribute to a control algorithm which has been used in this recent quantum feedback experiment. This experiment prepares and stabilizes on demand photon-number states (Fock states) of a microwave field in a superconducting cavity. We design real-time filters allowing estimation of the state despite measurement imperfections and delays, and we propose a feedback law which ensures the stabilization of a predetermined target state. This stabilizing feedback is obtained by stochastic Lyapunov techniques and depends on a filter estimating the quantum state. We prove that such control strategy extends to other discrete-time quantum systems under QND measurements. The second part considers an extension, to continuous-time, of a stability result for discrete-time quantum filters. Indeed, we prove the stability of a quantum filter associated to usual stochastic master equation driven by a Wiener process. This stability means that a “distance” between the physical state and its associated quantum filter decreases in average. Another subject that we study in this part is related to the design of a continuous-time optimal filter, in the presence of measurement imperfections. To this aim, we extend a construction method for discrete-time quantum filters with measurement imperfections. Finally, we obtain heuristically generalized continuous-time optimal filters whose dynamics are given by stochastic master equations driven by both Poisson and Wiener processes. We conjecture the stability of such optimal filters.; Dans cette thèse, nous étudions des rétroactions visant à stabiliser des systèmes quantiques en temps discret soumis à des mesures quantiques non-destructives (QND), ainsi que la stabilité des filtres quantiques à temps continu. Cette thèse comporte deux parties. Dans une première partie, nous généralisons les méthodes mathématiques sous-jacentes à une rétroaction quantique en temps discret testée expérimentalement au Laboratoire Kastler Brossel (LKB) de l'École Normale Supérieure (ENS) de Paris. Plus précisément,nous contribuons à un algorithme de contrôle qui a été utilisé lors de cette expérience récente de rétroaction quantique. L'expérience consiste en la préparation et la stabilisation à la demande d'états nombres de photons (états de Fock) d'un champ de micro-ondes au sein d'une cavité supraconductrice. Pour cela, nous concevons des filtres à temps-réel permettant d'estimer les états quantiques malgré des imperfections et des retards de mesure, et nous proposons une loi de rétroaction assurant la stabilisation d'un état cible prédéterminé. Cette rétroaction de stabilisation est obtenue grâce à des méthodes Lyapunov stochastique et elle repose sur un filtre estimant l'état quantique. Nous prouvons qu'une telle stratégie de contrôle se généralise à d'autres systèmes quantiques en temps discret soumis à des mesures QND. Dans une seconde partie, nous considérons une extension du résultat obtenu pour des filtres quantiques en temps discret au cas des filtres en temps continu. Dans ce but, nous démontrons la stabilité d'un filtre quantique associé à l'équation maîtresse stochastique usuelle découlant par un processus de Wiener. La stabilité signifie ici que la “distance”entre l'état physique et le filtre quantique associé décroit en moyenne. Cette partie étudie également la conception d'un filtre optimal en temps continu en présence d'imperfections de mesure. Pour ce faire, nous étendons la méthode utilisée précédemment pour construire les filtres quantiques en temps discret tolérants aux imperfections de mesure. Enfin,nous obtenons heuristiquement des filtres optimaux généraux en temps continu, dont la dynamique est décrite par des équations maîtresses stochastiques découlant à la fois par processus de Poisson et Wiener. Nous conjecturons que ces filtres optimaux sont stables.

In this paper we consider the purification of a quantum state using the information obtained from a continuous measurement record, where the classical measurement record is digitized to a single bit per measurement after the measurements have been made. Analysis indicates that efficient and reliable state purification is achievable for one- and two-qubit systems. We also consider quantum feedback control based on the discrete one-bit measurement sequences., 5 pages, 3 figures

We derive the form of the Belavkin-Kushner-Stratonovich equation describing the filtering of a continuous observed quantum system via non-demolition measurements when the statistics of the input field used for the indirect measurement are in a general coherent state. Dedicated to Robin Hudson on the occasion his 70th birthday.

This article provides a short personal account of my involvement in NMR spectroscopy, highlighting my main areas of research and interests from postgraduate study to the present day. Keywords: resolution enhancement; perfusion; titration; inositol triphosphate; vaccines; maximum quantum filtering; MRI; atherosclerosis; biofluids; metabonomics; systems biology

I study the rate at which information can be extracted from a finite-dimensional open quantum system using the quantum trajectory description of a continuous measurement. I derive the rate at which information is extracted for a measurement without any control; this sets the benchmark to which the subsequent control protocols are compared. Next I consider control protocols that increase the rate of information extraction. The first such protocol applies feedback so the state and the measurement basis are unbiased at all times. The use of unbiased bases means that this protocol is essentially quantum mechanical in nature. For observables with equally spaced eigenvalues, the “speed-up” in the information extraction afforded by unbiased basis feedback, is proportional to the square of the observed system’s Hilbert space. The second protocol considered optimally permutes the eigenvalues of the quantum state in the logical basis. As the measured observable and state commute at all times this protocol is essentially classical in nature. The speed-up provided by this protocol is also quadratic. The final protocol I consider is a new type of control. It merges open-loop quantum control and quantum filtering. This method also affords an improvement in the rate of information extraction.

A ∗-algebraic indefinite structure of quantum stochastic (QS) calculus is introduced and a continuity property of generalized nonadapted QS integrals is proved under the natural integrability conditions in an infinitely dimensional nuclear space. The class of nondemolition output QS processes in quantum open systems is characterized in terms of the QS calculus, and the problem of QS nonlinear filtering with respect to nondemolition, continuous measurements is investigated. The stochastic calculus of a posteriori conditional expectations in quantum observed systems is developed and a general quantum filtering stochastic equation for 2 QS process is derived. An application to the description of the spontaneous collapse of the quantum spin under continuous observation is given.

Feedback control protocols can stabilize and enhance the operation of quantum devices, however, unavoidable delays in the feedback loop adversely affect their performance. We introduce a quantum control methodology, combining open-loop control with quantum filtering, which is not constrained by feedback delays. For the problems studied (rapid purification and rapid measurement) we analytically derive lower bounds on the control performance that are comparable with the best corresponding bounds for feedback protocols., 5 pages, revtex4, 3 eps figures. Comments welcome. V2 minor corrections, published version.

The theory of nonlinear filtering concerns the optimal estimation of a Markov signal in noisy observations. Such estimates necessarily depend on the model that is chosen for the signal and observations processes. This thesis studies the sensitivity of the filter to the choice of underlying model over long periods of time, within the framework of continuous time filtering with white noise type observations. The first topic of this thesis is the asymptotic stability of the filter, which is studied using the theory of conditional diffusions. This leads to improvements on pathwise stability bounds, and to new insight into existing stability results in a fully probabilistic setting. Furthermore, I develop in detail the theory of conditional diffusions for finite-state Markov signals and clarify the duality between estimation and stochastic control in this context. The second topic of this thesis is the sensitivity of the nonlinear filter to the model parameters of the signal and observations processes. This section concentrates on the finite state case, where the corresponding model parameters are the jump rates of the signal, the observation function, and the initial measure. The main result is that the expected difference between the filters with the true and modified model parameters is bounded uniformly on the infinite time interval, provided that the signal process satisfies a mixing property. The proof uses properties of the stochastic flow generated by the filter on the simplex, as well as the Malliavin calculus and anticipative stochastic calculus. The third and final topic of this thesis is the asymptotic stability of quantum filters. I begin by developing quantum filtering theory using reference probability methods. The stability of the resulting filters is not easily studied using the preceding methods, as smoothing violates the nondemolition requirement. Fortunately, progress can be made by randomizing the initial state of the filter. Using this technique, I prove that the filtered estimate of the measurement observable is stable regardless of the underlying model, provided that the initial states are absolutely continuous in a suitable sense.

The problem of quantum state filtering consists of determining whether an unknown quantum state, which is chosen from a known set of states, is either a particular, specified state, or not. We consider this problem for the case that the filtering procedure is required to be unambiguous, which necessitates admitting inconclusive answers when the given states are not orthogonal. As an application, we propose an efficient, probabilistic procedure for distinguishing between sets of Boolean functions, which is an extension of the Deutsch-Jozsa algorithm., 4 pages, 1 figure, replaced with published version

We theoretically investigate magnetoresistance (MR) effects in connection with spin filtering in quantum-coherent transport through tunnel junctions based on non-magnetic/semimagnetic heterostructures. We find that spin filtering in conjunction with the suppression/enhancement of the spin-dependent Fermi seas in semimagnetic contacts gives rise to (i) spin-split kinks in the MR of single barriers and (ii) a robust beating pattern in the MR of double barriers with a semimagnetic well. We believe these are unique signatures for quantum filtering., Comment: Added references + corrected typos

Quantum filtering of the ejectile wave packet from hard $ep$ scattering on bound nucleons puts stringent constraints on the onset of color transparency in $(e,e'p)$ reactions in nuclei at moderate energies. Based on multiple-scattering theory, we derive a novel formula for nuclear transparency and discuss its energy dependence in terms of a color transparency sum rule., Comment: 14 pages (LATEX), 3 figures (not included, available from the authors), KFA-IKP(TH)-1992-16

A class of linear stochastic differential equations in Hilbert spaces is studied, which allows to construct probability densities and to generate changes in the probability measure one started with. Related linear equations for trace-class operators are discussed. Moreover, some analogue of filtering theory gives rise to related non-linear stochastic differential equations in Hilbert spaces and in the space of trace-class operators. Finally, it is shown how all these equations represent a new formulation and a generalization of the theory of measurements continuous in time in quantum mechanics.