the structure of the singular solution table of the m pade approximation problem abstract a general interpolation problem is defined which contains as special cases the m pade approximation problem as well as classical interpolation problems e g newton pade approximation to study the structure of the solution table a new concept the minimal solution is introduced statements on the local and global structure of the solution table are obtained as a special case the well known block structure of the pade table is derived finally a characterization of the solution set is given

on the theory and computation of nonperfect pade hermite approximants abstract for a vector of k 1 power series we introduce two new types of rational approximations the weak pade hermite form and the weak pade hermite fraction a recurrence relation is then presented which computes pade hermite forms along with their weak counterparts along a sequence of perfect points in the pade hermite table the recurrence relation results in a fast algorithm for calculating a pade hermite approximant of any given type when the vector of power series is perfect the algorithm is shown to calculate a pade hermite form of type n0 nk in o kn 2 operations where n n0 nk this complexity is the same as that of other fast algorithms the new algorithm also succeeds in the nonperfect case usually with only a moderate increase in cost

coherent quantum lqg control based on a recently developed notion of physical realizability for quantum linear stochastic systems we formulate a quantum lqg optimal control problem for quantum linear stochastic systems where the controller itself may also be a quantum system and the plant output signal can be fully quantum such a control scheme is often referred to in the quantum control literature as coherent feedback control it distinguishes the present work from previous works on the quantum lqg problem where measurement is performed on the plant and the measurement signals are used as the input to a fully classical controller with no quantum degrees of freedom the difference in our formulation is the presence of additional non linear and linear constraints on the coefficients of the sought after controller rendering the problem as a type of constrained controller design problem due to the presence of these constraints our problem is inherently computationally hard and this also distinguishes it in an important way from the standard lqg problem we propose a numerical procedure for solving this problem based on an alternating projections algorithm and as an initial demonstration of the feasibility of this approach we provide fully quantum controller design examples in which numerical solutions to the problem were successfully obtained for comparison we also consider the case of classical linear controllers that use direct or indirect measurements and show that there exists a fully quantum linear controller which offers an improvement in performance over the classical ones

linear quantum systems with diagonal passive hamiltonian and a single dissipative channel abstract given any covariance matrix corresponding to a so called pure gaussian state a linear quantum system can be designed to achieve the assigned covariance matrix in most cases however one might obtain a system that is difficult to realize in practice in this paper we restrict our attention to a special class of linear quantum systems i e systems with diagonal passive hamiltonian and a single dissipative channel the practical implementation of such a system would be relatively simple we then parametrize the class of pure gaussian state covariance matrices that can be achieved by this particular type of linear quantum system

cascade and locally dissipative realizations of linear quantum systems for pure gaussian state covariance assignment this paper presents two realizations of linear quantum systems for covariance assignment corresponding to pure gaussian states the first one is called a cascade realization given any covariance matrix corresponding to a pure gaussian state we can construct a cascaded quantum system generating that state the second one is called a locally dissipative realization given a covariance matrix corresponding to a pure gaussian state if it satisfies certain conditions we can construct a linear quantum system that has only local interactions with its environment and achieves the assigned covariance matrix both realizations are illustrated by examples from quantum optics

vector orthogonal polynomials abstract the following well known framework will be applied to hermite pade approximants first the hermite pade type approximants will be defined from the error of approximation some supplementary conditions will be fixed in order to obtain hermite pade forms vector orthogonal polynomials will be deduced from these conditions their existence and uniqueness are studied in the normal case these results are ensured then some properties of vector orthogonal polynomials will be proved

approximants de pade hermite 2eme partie programmation in this second paper we propose an algorithm for the construction of the tables and of the pade hermite tables 3 then we present some numerical applications

approximation and limit theorems for quantum stochastic models with unbounded coefficients abstract we prove a limit theorem for quantum stochastic differential equations with unbounded coefficients which extends the trotter kato theorem for contraction semigroups from this theorem general results on the convergence of approximations and singular perturbations are obtained the results are illustrated in several examples of physical interest

approximants de pade hermite 1ere partie theorie we present in this first paper a generalization of pade approximants which gives us as particular cases shafer s and baker sd log approximants first we define these approximants following an old idea of hermite then we prove some fundamental properties for their constructions

hermite pade approximation basic notions and theorems abstract our purpose is to give a brief exposition of basic notions and facts on hermite pade approximation theory a hermite pade form hpf is defined here in the same way as a pade approximant is as a consequence in some cases hpf does not exist even in the modified version hpf need not be unique therefore it was worthwhile to choose some hpf as the optimal one all criteria of existence unicity etc are phrased in a unified manner they base on few quantities depending on the power series under consideration and are usable in the theory rather than in the numerical practice

vector orthogonal polynomials we give the relation between hermite pade approximants and vector orthogonal polynomials an algorithm for calculating vector orthogonal polynomials near the diagonal is described an exact multiple integral formula for vector orthogonal polynomials is proved an example is given showing how the recurrence relations of pade may be used to calculate hermite pade approximants of degrees m mu mu with mu increasing

low frequency approximation for a class of linear quantum systems using cascade cavity realization abstract this paper presents a method for approximating a class of complex transfer function matrices corresponding to physically realizable complex linear quantum systems the class of linear quantum systems under consideration includes interconnections of passive optical components such as cavities beam splitters phase shifters and interferometers this approximation method builds on a previous result for cascade realization and gives good approximations at low frequencies

singular perturbation approximations for a class of linear quantum systems this technical note considers the use of singular perturbation approximations for a class of linear quantum systems arising in the area of linear quantum optics the technical note presents results on the physical realizability properties of the approximate system arising from singular perturbation model reduction

quantum ito s formula and stochastic evolutions using only the boson canonical commutation relations and the riemann lebesgue integral we construct a simple theory of stochastic integrals and differentials with respect to the basic field operator processes this leads to a noncommutative ito product formula a realisation of the classical poisson process in fock space which gives a noncommutative central limit theorem the construction of solutions of certain noncommutative stochastic differential equations and finally to the integration of certain irreversible equations of motion governed by semigroups of completely positive maps the classical ito product formula for stochastic differentials with respect to brownian motion and the poisson process is a special case

h infty control of linear quantum stochastic systems the purpose of this paper is to formulate and solve a h infin controller synthesis problem for a class of noncommutative linear stochastic systems which includes many examples of interest in quantum technology the paper includes results on the class of such systems for which the quantum commutation relations are preserved such a requirement must be satisfied in a physical quantum system a quantum version of standard classical dissipativity results are presented and from this a quantum version of the strict bounded real lemma is derived this enables a quantum version of the two riccati solution to the h infin control problem to be presented this result leads to controllers which may be realized using purely quantum purely classical or a mixture of quantum and classical elements this issue of physical realizability of the controller is examined in detail and necessary and sufficient conditions are given our results are constructive in the sense that we provide explicit formulas for the hamiltonian function and coupling operator corresponding to the controller

application of the newton iteration algorithm to the parameter estimation for dynamical systems this paper uses the newton iteration to study new identification methods for determining the parameters of dynamical systems from step responses on the basis of the step response analysis we present the newton iterative algorithms moreover in order to test the accuracy of the estimated parameters the frequency and step response experiment are applied to the dynamical systems between the estimated and true models the simulation results show that the obtained models can capture the dynamics of the systems i e the estimated model s outputs are close to the outputs of the actual systems this confirms the effectiveness of the proposed newton iterative identification methods

on the quasi balanceable class of linear quantum stochastic systems abstract this paper is concerned with the characterization of the quasi balanceable class of linear quantum stochastic systems i e systems that can be approximated via the recently proposed quasi balanced truncation method it has previously been shown that the quasi balanceable class of systems includes the class of completely passive systems in this work we refine the previously established characterization of quasi balanceable systems and show that the class of quasi balanceable systems is strictly larger than the class of completely passive systems we derive a novel characterization of completely passive linear quantum stochastic systems solely in terms of the controllability gramian of such systems exploiting this result we prove that all linear quantum stochastic systems with a pure gaussian steady state active systems included are all quasi balanceable and establish a new complete parameterization for this important class of systems examples are provided to illustrate our results

an introduction to quantum filtering this paper provides an introduction to quantum filtering theory an introduction to quantum probability theory is given focusing on the spectral theorem and the conditional expectation as a least squares estimate and culminating in the construction of wiener and poisson processes on the fock space we describe the quantum ito calculus and its use in the modeling of physical systems we use both reference probability and innovations methods to obtain quantum filtering equations for system probe models from quantum optics

b splines and hermite pade approximants to the exponential function this paper is the continuation of a work initiated in p sablonniere an algorithm for the computation of hermite pade approximations to the exponential function divided differences and hermite pade forms numer algorithms 33 2003 443 452 about the computation of hermite pade forms hpf and associated hermite pade approximants hpa to the exponential function we present an alternative algorithm for their computation based on the representation of hpf in terms of integral remainders with b splines as peano kernels using the good properties of discrete b splines this algorithm gives rise to a great variety of representations of hpf of higher orders in terms of hpf of lower orders and in particular of classical pade forms we give some examples illustrating this algorithm in particular another way of constructing quadratic hpf already described by different authors finally we briefly study a family of cubic hpf

analysis of quantum linear systems response to multi photon states the purpose of this paper is to present a mathematical framework for analyzing the response of quantum linear systems driven by multi photon states both the factorizable namely no correlation among the photons in the channel and unfactorizable multi photon states are treated pulse information of a multi photon input state is represented in terms of tensor and the response of quantum linear systems to multi photon input states is characterized by tensor operations analytic forms of output correlation functions and output states are derived the proposed framework is applicable no matter whether the underlying quantum dynamic system is passive or active examples from the physics literature are used to illustrate the results presented