radon nikodym derivatives of quantum instruments a convenient representation for radon nikodym derivatives of completely positive c p instruments on b h with respect to a scalar measure is suggested similar to the stinespring kraus representation for c p maps but involving possibly nonclosable unbounded operators the structure of covariant c p instruments is studied in detail in particular an exhaustive description is given to instruments covariant with respect to shifts or rotations corresponding to position or angle measurements

quantum instruments i extreme instruments the structure of completely positive quantum instruments is analyzed thoroughly we characterize the extreme points of the convex set of instruments the characterization holds also for nondiscrete instruments in infinite dimensions and is applied to quantum observables channels and preparations which are special cases of instruments we show that extreme instruments are discrete in finite dimensions

state reduction information and entropy in quantum measurement processes information obtained by a quantum measurement process performed on a physical system and the entropy change of the measured physical system are considered in detail it is shown that the condition for the amount of information obtained by the quantum measurement process to be represented by the shannon mutual entropy is that the intrinsic observable of the measured physical system commutes with the operational observable defined by the quantum measurement process when some measurement outcome is obtained the decrease of the shannon entropy of the measured system is compared with that of the von neumann entropy furthermore a condition is established under which the amount of information that can be established by the quantum measurement process becomes equal to the decrease of the shannon entropy of the measured physical system

path following for the pvtol aircraft this article presents a solution to the path following problem for the planar vertical take off and landing aircraft pvtol which is applicable to a class of smooth jordan curves our path following methodology enjoys the two properties of output invariance of the path i e if the pvtol s centre of mass is initialized on the path and its initial velocity is tangent to the path then the pvtol remains on the path at all future times and boundedness of the roll dynamics further our controller guarantees that after a finite time the time average of the roll angle is zero and the pvtol does not perform multiple revolutions about its longitudinal axis

tight bounds on accessible information and informational power the accessible information quantifies the amount of classical information that can be extracted from an ensemble of quantum states analogously the informational power quantifies the amount of classical information that can be extracted by a quantum measurement for both quantities we provide upper and lower bounds that depend only on the dimension of the system and we prove their tightness in the case of symmetric informationally complete sic ensembles and measurements stronger bounds are provided and their tightness proved for qubits and qutrits from our upper bounds we notice perhaps surprisingly that the statistics generated by sic ensembles or measurements in arbitrary dimension though optimal for tomographic purposes in fact never contain more than just one bit of information the rest being constituted by completely random bits on the other hand from our lower bounds we obtain an explicit strategy beating the so called pretty good one for the extraction of mutual information in the case of sic ensembles and measurements

a new approach to the cramer rao type bound of the pure state model this paper sheds light on non commutativity in quantum theory as regards theoretical estimation in it we calculate the quantum cramer rao type bound for many cases by use of a newly proposed powerful technique we also discuss the use of collective measurement in statistical estimation

covariant quantum instruments the structure of covariant instruments is studied and a general structure theorem is derived a detailed characterization is given to covariant instruments in the case of an irreducible representation of a locally compact group

optimum shape design for unsteady flows with time accurate continuous and discrete adjoint methods this paper presents an adjoint method for the optimal control of unsteady flows the goal is to develop the continuous and discrete unsteady adjoint equations and their corresponding boundary conditions for the time accurate method first this paper presents the complete formulation of the time dependent optimal design problem second we present the time accurate unsteady continuous and discrete adjoint equations third we present results that demonstrate the application of the theory to a two dimensional oscillating airfoil the results are compared with a multipoint approach to illustrate the added benefit of performing full unsteady optimization

minimal sufficient positive operator valued measure on a separable hilbert space we introduce a concept of a minimal sufficient positive operator valued measure povm which is the least redundant povm among the povms that have the equivalent information about the measured quantum system assuming the system hilbert space to be separable we show that for a given povm a sufficient statistic called a lehmann scheffe bahadur statistic induces a minimal sufficient povm we also show that every povm has an equivalent minimal sufficient povm and that such a minimal sufficient povm is unique up to relabeling neglecting null sets we apply these results to discrete povms and information conservation conditions proposed by the author

classical randomness in quantum measurements similarly to quantum states also quantum measurements can be mixed corresponding to a random choice within an ensemble of measuring apparatuses such mixing is equivalent to a sort of hidden variable which produces a noise of purely classical nature it is then natural to ask which apparatuses are indecomposable i e do not correspond to any random choice of apparatuses this problem is interesting not only for foundations but also for applications since most optimization strategies give optimal apparatuses that are indecomposable mathematically the problem is posed describing each measuring apparatus by a positive operator valued measure povm which gives the statistics of the outcomes for any input state the povms form a convex set and in this language the indecomposable apparatuses are represented by extremal points the analogous of pure states in the convex set of states differently from the case of states however indecomposable povms are not necessarily rank one e g von neumann measurements in this paper we give a complete classification of indecomposable apparatuses for discrete spectrum by providing different necessary and sufficient conditions for extremality of povms along with a simple general algorithm for the decomposition of a povm into extremals as an interesting application informationally complete measurements are analysed in this respect the convex set of povms is fully characterized by determining its border in terms of simple algebraic properties of the corresponding povms

time orthogonal unitary dilations and noncommutative feynman kac formulae an analysis of feynman kac formulae reveals that typically the unperturbed semigroup is expressed as the expectation of a random unitary evolution and the perturbed semigroup is the expectation of a perturbation of this evolution in which the latter perturbation is effected by a cocycle with certain covariance properties with respect to the group of translations and reflections of the line we consider generalisations of the classical commutative formalism in which the probabilistic properties are described in terms of non commutative probability theory based on von neumann algebras examples of this type are generated by means of second quantisation from a unitary dilation of a given self adjoint contraction semigroup called the time orthogonal unitary dilation whose key feature is that the dilation operators corresponding to disjoint time intervals act nontrivially only in mutually orthogonal supplementary hilbert spaces

a topological obstruction to continuous global stabilization of rotational motion and the unwinding phenomenon we show that a continuous dynamical system on a state space that has the structure of a vector bundle on a compact manifold possesses no globally asymptotically stable equilibrium this result is directly applicable to mechanical systems having rotational degrees of freedom in particular the result applies to the attitude motion of a rigid body in light of this result we explain how attitude stabilizing controllers obtained using local coordinates lead to unwinding instead of global asymptotic stability

some important classes of quantum measurements and their information gain the notions of ideal first kind and repeatable measurements are reformulated and their relations analyzed within a systematic theory of measurement in quantum mechanics this allows one to investigate new information theoretical characterizations of such measurements

robust output maneuvering for a class of nonlinear systems the output maneuvering problem involves two tasks the first called the geometric task is to force the system output to converge to a desired path parametrized by a continuous scalar variable q the second task called the dynamic task is to satisfy a desired dynamic behavior along the path this dynamic behavior is further specified via a time speed or acceleration assignment while the main concern is to satisfy the geometric task the dynamic task ensures that the system output follows the path with the desired speed a robust recursive design technique is developed for uncertain nonlinear plants in vectorial strict feedback form first the geometric part of the problem is solved then an update law is constructed that bridges the geometric design with the speed assignment the design procedure is illustrated through several examples

construction of the least informative observable conserved by a given quantum instrument for a quantum measurement process described by a quantum instrument i and a system observable corresponding to a positive operator valued measure povm e i is said to conserve the information of e if the joint successive measurement of i followed by e is equivalent to a single measurement of e we show that for any quantum instrument i we can construct a povm conserved by i intuitively the construction gives the infinite joint successive measurement of i we also show that the constructed povm is the least informative observable among povms conserved by i i e the constructed povm can be realized by a classical post processing of any povm conserved by i as typical examples of quantum instruments we explicitly evaluate povms of infinite successive measurements for photon counting and quantum counter instruments

application of the godunov method and its second order extension to cascade flow modeling the godunov method and a new second order accurate extension of the method are used for the solution of two dimensional euler equations both numerical schemes are described in detail their performances in the subsonic transonic and supersonic flow regimes are first tested on the problem of flow in a channel with a circular arc bump the niethods are then applied to calculate the transonic flow through a supercritical com pressor cascade designed by j sanzo for this case the solution with the second order extension of the godunov method gives verygood agreement with the design distribution of parameters given by sanzo

weak values with decoherence the weak value of an observable is experimentally accessible by weak measurements as theoretically analyzed by aharonov et al and recently experimentally demonstrated we introduce a w operator associated with the weak values and give a general framework of quantum operations to the w operator in parallel with the kraus representation of the completely positive map for the density operator the decoherence effect is also investigated in terms of the weak measurement by a shift of a probe wavefunction of continuous variable as an application we demonstrate how the geometric phase is affected by the bit flip noise

on local transverse feedback linearization given a control affine system and a controlled invariant submanifold we present necessary and sufficient conditions for local feedback equivalence to a system whose dynamics transversal to the submanifold are linear and controllable a key ingredient used in the analysis is the new notion of transverse controllability indices of a control system with respect to a set

a model for an objective description of macroscopic state variables in quantum mechanics abstract a generalised stochastic process is obtained for the boltzmann distribution function in quantum mechanics this is an example of an objective state space description of a quantum system

sequences of projective measurements in generalized probabilistic models we define a simple rule that allows us to describe sequences of projective measurements for a broad class of generalized probabilistic models this class embraces quantum mechanics and classical probability theory but for example also the hypothetical popescu rohrlich box for quantum mechanics the definition yields the established luders rule which is the standard rule for updating the quantum state after a measurement for the general case it can be seen as being the least disturbing or most coherent way of performing sequential measurements we show as an example that the spekkens toy model spekkens 2007 phys rev a 75 032110 provides an instance of our definition we also demonstrate the possibility of strong postquantum correlations as well as the existence of triple slit correlations for certain nonquantum toy models

comparison of quantum statistical models equivalent conditions for sufficiency a family of probability distributions i e a statistical model is said to be sufficient for another if there exists a transition matrix transforming the probability distributions in the former to the probability distributions in the latter the blackwell sherman stein bss theorem provides necessary and sufficient conditions for one statistical model to be sufficient for another by comparing their information values in statistical decision problems in this paper we extend the bss theorem to quantum statistical decision theory where statistical models are replaced by families of density matrices defined on finite dimensional hilbert spaces and transition matrices are replaced by completely positive trace preserving maps i e coarse grainings the framework we propose is suitable for unifying results that previously were independent like the bss theorem for classical statistical models and its analogue for pairs of bipartite quantum states recently proved by shmaya an important role in this paper is played by statistical morphisms namely affine maps whose definition generalizes that of coarse grainings given by petz and induces a corresponding criterion for statistical sufficiency that is weaker and hence easier to be characterized than petz s

switching through singularities asymptotic tracking is studied for systems which are not regular that is the relative degree is not well defined for these systems the input output linearizing control law has singularities we propose a tracking control law which switches between an approximate tracking law hauser et al ieee trans automat control 37 3 1992 392 398 close to the singularities and an exact tracking law away from the singularities and we study the applicability of this law based on the behavior of the system s zero dynamics at the switching boundary as in hauser et al ieee trans automat control 37 3 1992 392 398 the ball and beam example is used to motivate the study

on information gain by quantum measurements of continuous observables a generalization of shannon s amount of information into quantum measurements of continuous observables is introduced a necessary and sufficient condition for measuring processes to have a non negative amount of information is obtained this resolves groenewold s conjecture completely including the case of measurements of continuous observables as an application the approximate position measuring process considered by von neumann and later by davies is shown to have a non negative amount of information

on the entropic formulation of uncertainty for quantum measurements the formulation of the uncertainty principle based on entropy is given with the noncommuting observables described via positive operator valued measures

quantum discord discord between the whole and its constituent quantum discord a measure of quantum correlation beyond entanglement is initially defined as the discord between two classically equivalent while quantum discordant definitions of mutual information in this paper we report some new interpretations of discord which rely on the differences between measurement induced effects on the local measured system and the whole system specifically with proper quantitative definitions introduced in buscemi et al 2008 phys rev lett 100 210504 we find that quantum discord can be interpreted as the differences of measurement induced disturbance or information gain on the local measured system and on the whole system combined with previous similar results based on measurement induced entanglement and decoherence our results provide a unified view on quantum discord

quantum stochastic calculus operation valued stochastic processes and continual measurements in quantum mechanics the physical idea of a continual observation on a quantum system has been recently formalized by means of the concept of operation valued stochastic process ovsp in this article it is shown how the formalism of quantum stochastic calculus of hudson and parthasarathy allows in a simple way for constructing a large class of ovsp s that in particular contains the quantum counting processes of davies and srinivas and continual gaussian measurements this result is obtained by means of a stochastic dilation of the ovsp s at the level of the enlarged system probabilities turn out to be expressed in terms of projection valued measures associated with certain time dependent commuting self adjoint operators

quantum chaos an entropy approach a new definition of the entropy of a given dynamical system and of an instrument describing the measurement process is proposed within the operational approach to quantum mechanics it generalizes other definitions of entropy in both the classical and quantum cases the kolmogorov sinai ks entropy is obtained for a classical system and the sharp measurement instrument for a quantum system and a coherent states instrument a new quantity coherent states entropy is defined it may be used to measure chaos in quantum mechanics the following correspondence principle is proved the upper limit of the coherent states entropy of a quantum map as 0 is less than or equal to the ks entropy of the corresponding classical map chaos umpire sits and by decision more imbroils the fray by which he reigns next him high arbiter chance governs all john milton paradise lost book ii

the phase operator in quantum information processing it is shown that unitary depolarizers which play an important role in quantum information processing can be constructed in terms of the pegg barnett phase operator by using the result the classical information capacity of quantum dense coding with unitary encoding in a finite dimensional hilbert space is derived furthermore the relation between the capacity of quantum dense coding and the coherent information of a noisy quantum channel is obtained

optimal pointers for joint measurement of σx and σz via homodyne detection we study a model of a qubit in interaction with the electromagnetic field by means of homodyne detection the field quadrature at a t is observed continuously in time due to the interaction information about the initial state of the qubit is transferred to the field thus influencing the homodyne measurement results we construct random variables pointers on the probability space of homodyne measurement outcomes having distributions close to the initial distributions of x and z using variational calculus we find the pointers that are optimal these optimal pointers are very close to hitting the bound imposed by heisenberg s uncertainty relation on joint measurement of two non commuting observables we close the paper by giving the probability densities of the pointers

radon nikodým type theorem for α completely positive maps we introduce a new notion of completely positive map on a c algebra as a generalization of the notion of completely positive map then we study a theorem of the radon nikod m type that there is a one to one correspondence between completely positive maps and positive operators and as an application of the radon nikod m type theorem we give a characterization of pure completely positive maps finally we study a covariant version of the stinespring s theorem for a covariant completely positive map see theorem 4 3

reduction principles and the stabilization of closed sets for passive systems in this technical note we explore the stabilization of closed invariant sets for passive systems and present conditions under which a passivity based feedback asymptotically stabilizes the goal set our results rely on novel reduction principles allowing one to extrapolate the properties of stability attractivity and asymptotic stability of a dynamical system from analogous properties of the system on an invariant subset of the state space

non markovian quantum trajectories instruments and time continuous measurements the linear and nonlinear non markovian quantum state diffusion nmqsd equations are well known tools for the description of certain non markovian open quantum systems in this work we systematically investigate whether the normalized linear nmqsd or the nonlinear nmqsd solutions can be generated by means of a time continuous measurement by considering any conceivable measurement scheme we derive a necessary criterion for the measurement interpretation of both equations concrete examples show that the normalized linear nmqsd solutions are realizable only in the markovian limit in general the application of the presented criterion to the nonlinear nmqsd remains an open issue furthermore this criterion is a necessary one not only in the context of the nmqsds but also for a much broader class of stochastic schrodinger equations

coordinated path following for unicycles we formulate a coordinated path following problem for n unicycle mobile robots as an instance of a nested set stabilization problem stabilization of the first set corresponds to driving the unicycles to their assigned paths stabilization of the second set a subset of the first corresponds to meeting the coordination specification the first set is stabilized for initial conditions sufficiently close to the set in a decentralized manner using feedback linearization for general coordination tasks we utilize feedback linearization to stabilize the nested set in a centralized manner again for initial conditions sufficiently close to the second set in the special case in which coordination entails making the unicycles maintain a formation along their paths we employ a semi distributed control law under less restrictive communication assumptions experimental results are provided

an adjoint method for shape optimization in unsteady viscous flows a new method for shape optimization for unsteady viscous flows is presented it is based on the continuous adjoint approach using a time accurate method and is capable of handling both inverse and direct objective functions the objective function is minimized or maximized subject to the satisfaction of flow equations the shape of the body is parametrized via a non uniform rational b splines nurbs curve and is updated by using the gradients obtained from solving the flow and adjoint equations a finite element method based on streamline upwind petrov galerkin supg and pressure stabilized petrov galerkin pspg stabilization techniques is used to solve both the flow and adjoint equations the method has been implemented and tested for the design of airfoils based on enhancing its time averaged aerodynamic coefficients interesting shapes are obtained especially when the objective is to produce high performance airfoils the effect of the extent of the window of time integration of flow and adjoint equations on the design process is studied it is found that when the window of time integration is insufficient the gradients are most likely to be erroneous

a multiphase godunov method for compressible multifluid and multiphase flows we propose a new model and a solution method for two phase compressible flows the model involves six equations obtained from conservation principles applied to each phase completed by a seventh equation for the evolution of the volume fraction this equation is necessary to close the overall system the model is valid for fluid mixtures as well as for pure fluids the system of partial differential equations is hyperbolic hyperbolicity is obtained because each phase is considered to be compressible two difficulties arise for the solution one of the equations is written in non conservative form non conservative terms exist in the momentum and energy equations we propose robust and accurate discretisation of these terms the method solves the same system at each mesh point with the same algorithm it allows the simulation of interface problems between pure fluids as well as multiphase mixtures several test cases where fluids have compressible behavior are shown as well as some other test problems where one of the phases is incompressible the method provides reliable results is able to compute strong shock waves and deals with complex equations of state

concepts of conditional expectations in quantum theory a concept of conditional expectations in quantum theory is established with interrelations to previously introduced concepts of the cycon hellwig conditional expectations and a posteriori states which are analogous to the existing interrelations in the classical probability theory among conditional expectations related to random variables those related to subalgebras and conditional probability distributions these three concepts are shown to have satisfactory statistical interpretation in the quantum measuring processes for the above purpose we introduce an integration with respect to functions with values in the states of operator algebras and positive operator valued measures such that the resulting indefinite integrals are completely positive map valued measures eventually it is proved that in the von neumann algebraic formulation the cycon hellwig conditional expectations always exist as completely positive map valued measures

quantum incompatibility of channels with general outcome operator algebras a pair of quantum channels is said to be incompatible if they cannot be realized as marginals of a single channel this paper addresses the general structure of the incompatibility of completely positive channels with a fixed quantum input space and with general outcome operator algebras we define a compatibility relation for such channels by identifying the composite outcome space as the maximal projective c tensor product of outcome algebras we show theorems that characterize this compatibility relation in terms of the concatenation and conjugation of channels generalizing the recent result for channels with quantum outcome spaces these results are applied to the positive operator valued measures povms by identifying each of them with the corresponding quantum classical qc channel we also give a characterization of the maximality of a povm with respect to the post processing preorder in terms of the conjugate channel of the qc channel we consider another definition of compatibility of norma

a quantum analogue of hunt s representation theorem for the generator of convolution semigroups on lie groups in quantum mechanics certain operator valued measures are introduced called instruments which are an analogue of the probability measures of classical probability theory as in the classical case it is interesting to study convolution semigroups of instruments on groups and the associated semigroups of probability operators in this paper the case is considered of a finite dimensional hilbert space n level quantum system and of instruments defined on a finite dimensional lie group then the generator of a continuous semigroup of quantum probability operators is characterized in this way a quantum analogue of hunt s representation theorem for the generator of convolution semigroups on lie groups is obtained

distributed circular formation stabilization for dynamic unicycles this paper investigates the problem of designing distributed control laws making a group of dynamic unicycles converge to a common circle of prespecified radius whose center is stationary but dependent on the initial conditions and travel around the circle in a desired direction the vehicles are required to converge to a formation on the circle expressed by desired separations and ordering of the unicycles the information exchange between unicycles is modelled by a directed graph which is assumed to have a spanning tree a hierarchical approach is proposed which simplifies the control design by decoupling the problem of making the unicycles converge to a common circle from the problem of stabilizing the formation

method for optimally controlling unsteady shock strength in one dimension this paper presents a new formulation and computational solution of an optimal control problem concerning unsteady shock wave attenuation the adjoint system of equations for the unsteady euler system in one dimension is derived and used in an adjoint based solution procedure for the optimal control a novel algorithm is used to satisfy all necessary first order optimality conditions while locally minimizing an appropriate cost functional distributed control solutions with certain physical constraints are calculated for attenuating blast waves similar to those generated by ignition overpressure from the shuttle s solid rocket booster during launch results are presented for attenuating shocks traveling at mach 1 5 and 3 5 down to 85 80 and 75 of the uncontrolled wave s driving pressure the control solutions give insight into the magnitude and location of energy dissipation necessary to decrease a given blast wave s overpressure to a set target level over a given spatial domain while using only as m

measurement theory in local quantum physics in this paper we aim to establish foundations of measurement theory in local quantum physics for this purpose we discuss a representation theory of completely positive cp instruments on arbitrary von neumann algebras we introduce a condition called the normal extension property nep and establish a one to one correspondence between cp instruments with the nep and statistical equivalence classes of measuring processes we show that every cp instrument on an atomic von neumann algebra has the nep extending the well known result for type i factors moreover we show that every cp instrument on an injective von neumann algebra is approximated by cp instruments with the nep the concept of posterior states is also discussed to show that the nep is equivalent to the existence of a strongly measurable family of posterior states for every normal state two examples of cp instruments without the nep are obtained from this result it is thus concluded that in local quantum physics not every cp instrument represents a measuring process but in most of physically relevant cases every cp instrument can be realized by a measuring process within arbitrary error limits as every approximately finite dimensional von neumann algebra on a separable hilbert space is injective to conclude the paper the concept of local measurement in algebraic quantum field theory is examined in our framework in the setting of the doplicher haag roberts and doplicher roberts theory describing local excitations we show that an instrument on a local algebra can be extended to a local instrument on the global algebra if and only if it is a cp instrument with the nep provided that the split property holds for the net of local algebras

entropy reduction of quantum measurements it is shown that the entropy reduction the information gain in the initial terminology of an efficient ideal or pure quantum measurement coincides with the generalized quantum mutual information of a quantum classical channel mapping an a priori state to the corresponding posteriori probability distribution of the outcomes of the measurement as a result the entropy reduction is defined for arbitrary a priori states not only for states with finite von neumann entropy and its analytical properties is studied in detail by using general properties of the quantum mutual information by using this approach it is shown that the entropy reduction of an efficient quantum measurement is a nonnegative lower semicontinuous concave function on the set of all a priori states having continuous restrictions to subsets on which the von neumann entropy is continuous monotonicity and subadditivity of the entropy reduction are also easily proved by this method a simple continuity condition for the entropy reduction

quantum measuring processes of continuous observables the purpose of this paper is to provide a basis of theory of measurements of continuous observables we generalize von neumann s description of measuring processes of discrete quantum observables in terms of interaction between the measured system and the apparatus to continuous observables and show how every such measuring process determines the state change caused by the measurement we establish a one to one correspondence between completely positive instruments in the sense of davies and lewis and the state changes determined by the measuring processes we also prove that there are no weakly repeatable completely positive instruments of nondiscrete observables in the standard formulation of quantum mechanics so that there are no measuring processes of nondiscrete observables whose state changes satisfy the repeatability hypothesis a proof of the wigner araki yanase theorem on the nonexistence of repeatable measurements of observables not commuting conserved quantities is given in our framework we also discuss the implication of these results for the recent results due to srinivas and due to mercer on measurements of continuous observables

distilling entanglement from arbitrary resources we obtain the general formula for the optimal rate at which singlets can be distilled from any given noisy and arbitrarily correlated entanglement resource by means of local operations and classical communication locc our formula obtained by employing the quantum information spectrum method reduces to that derived by devetak and winter proc r soc london ser a 461 207 2005 in the special case of an independent and identically distributed resource the proofs rely on a one shot version of the so called hashing bound which in turn provides bounds on the one shot distillable entanglement under general locc

quantum stochastic approach to the description of quantum measurements in the present paper we consider the problem of the description of an arbitrary generalized quantum measurement with outcomes in a measurable space analysing the unitary invariants of a separable statistical realization of a quantum instrument we present the most general form of a possible integral representation of an instrument we introduce the notion of a stochastic realization of an instrument and establish a one to one correspondence between the class of unitarily and phase equivalent separable statistical realizations and the equivalence class of stochastic realizations of an instrument we further single out the invariant class of unitarily and phase equivalent separable statistical realizations for which the integral representation of an instrument is the same for all statistical realizations from this class and is wholly determined by the invariants of this class we call the special form of this integral representation the quantum stochastic representation of an instrument we show that the description of a generalized direct quantum measurement can be considered in the frame of a new general approach based on the notion of a family of quantum stochastic evolution operators satisfying the orthonormality relation this approach gives not only the complete statistical description of any generalized direct quantum measurement but the complete description in a hilbert space of the stochastic behaviour of a quantum system under a generalized direct measurement in the sense of specifying the probabilistic transition law governing the change from the initial state to a final one under a single measurement under this approach a unitary evolution of an isolated quantum system is included as a special case in the frame of the proposed approach which we call quantum stochastic approach all possible schemes of measurements upon a quantum system can be considered in the case of repeated or continuous in time measurements the quantum stochastic approach allows to define in the most general case the notion of the family of posterior pure state trajectories quantum trajectories in discrete or continuous time in the hilbert space of a quantum system and to give their probabilistic treatment

entanglement assisted capacity of quantum multiple access channels we find a regularized formula for the entanglement assisted ea capacity region for quantum multiple access channels qmac we illustrate the capacity region calculation with the example of the collective phase flip channel which admits a single letter characterization on the way we provide a first principles proof of the ea coding theorem based on a packing argument we observe that the holevo schumacher westmoreland theorem may be obtained from a modification of our ea protocol we remark on the existence of a family hierarchy of protocols for multiparty scenarios with a single receiver in analogy to the two party case in this way we relate several previous results regarding qmacs

adjoint based derivative computations for the optimal control of discontinuous solutions of hyperbolic conservation laws we propose a rigorous procedure to obtain the adjoint based gradient representation of cost functionals for the optimal control of discontinuous solutions of conservation laws hereby it is not necessary to introduce adjoint variables for the shock positions our approach is based on stability properties of the adjoint equation we give a complete analysis for the case of convex scalar conservation laws the adjoint equation is a transport equation with discontinuous coefficients and special reversible solutions must be considered to obtain the correct adjoint based gradient formula reversible solutions of the adjoint transport equation and the required stability properties are analyzed in detail

radon nikodym derivatives of quantum operations given a completely positive cp map t there is a theorem of the radon nikodym type w b arveson acta math 123 141 1969 v p belavkin and p staszewski rep math phys 24 49 1986 that completely characterizes all cp maps s such that t s is also a cp map this theorem is reviewed and several alternative formulations are given along the way we then use the radon nikodym formalism to study the structure of order intervals of quantum operations as well as a certain one to one correspondence between cp maps and positive operators already fruitfully exploited in many quantum information theoretic treatments we also comment on how the radon nikodym theorem can be used to derive norm estimates for differences of cp maps in general and of quantum operations in particular

probability operators and convolution semigroups of instruments in quantum probability in quantum measurement theory a central notion is that of instrument which is a certain kind of operator valued measure in this paper instruments on locally compact groups are studied and as in classical probability theory probability operators associated with instruments are introduced then the generator of a norm continuous semigroup of probability operators is characterized

asymptotic and non asymptotic analysis for a hidden markovian process with a quantum hidden system we focus on a data sequence produced by repetitive quantum measurement on an internal hidden quantum system and call it a hidden markovian process using a quantum version of the perron frobenius theorem we derive novel upper and lower bounds for the cumulant generating function of the sample mean of the data using these bounds we derive the central limit theorem and large and moderate deviations for the tail probability then we give the asymptotic variance by using the second derivative of the cumulant generating function we also derive another expression for the asymptotic variance by considering the quantum version of the fundamental matrix further we explain how to extend our results to a general probabilistic system

unitary measurements of discrete quantities in quantum mechanics the pure measurements of discrete physical quantities are characterized within quantum theory of measurement and their unitary representations are given probabilistic aspects of measurements related to the so called strong correlation conditions and a probabilistic characterization of the first kind measurements are examined the problem of the objectification of the measurement result is analyzed in terms of a classical behavior of the measuring apparatus as a by product a generalization of the wigner araki yanase theorem is given

remote preparation of arbitrary ensembles and quantum bit commitment the hughston jozsa wootters theorem shows that any finite ensemble of quantum states can be prepared at a distance and it has been used to demonstrate the insecurity of all bit commitment protocols based on finite quantum systems without superselection rules in this paper we prove a generalized hjw theorem for arbitrary ensembles of states on a c algebra we then use this result to demonstrate the insecurity of bit commitment protocols based on infinite quantum systems and quantum systems with abelian superselection rules

markovian limit for a reduced operation valued stochastic process operation valued stochastic processes give a formalization of the concept of continuous in time measurements in quantum mechanics in this article a first stage m of a measuring apparatus coupled to the system s is explicitly introduced and continuous measurement of some observables of m is considered one can speak of an indirect continuous measurement on s when the degrees of freedom of the measuring apparatus m are eliminated and the weak coupling limit is taken it is shown that an operation valued stochastic process describing a direct continuous observation of the system s is obtained

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

probabilistically reversible measurements probabilistically reversible quantum measurements are considered from the information theoretical point of view it is found that an upper bound on the probability of a reversing quantum measurement is given by the generalized bhattacharyya overlap of conditional probabilities of the measurement outcomes the relation between the upper bound of the probability and the information obtained by the quantum measurement is also discussed

realization schemes for quantum instruments in finite dimensions we present a general dilation scheme for quantum instruments with continuous outcome space in finite dimensions in terms of a measurement on a finite dimensional ancilla described by a positive operator valued measure povm the general result is then applied to a large class of instruments generated by operator frames which contains group covariant instruments as a particular case and allows one to construct dilation schemes based on a measurement on the ancilla followed by a conditional feed forward operation on the output in the case of tight operator frames our construction generalizes quantum teleportation and telecloning producing a whole family of generalized teleportation schemes in which the instrument is realized via a joint povm at the sender combined with a conditional feed forward operation at the receiver

synchronization and balancing on the n torus in this paper we study the behavior of a network of n agents each evolving on the circle we propose a novel algorithm that achieves synchronization or balancing in phase models under mild connectedness assumptions on the possibly time varying and unidirectional communication graphs the global convergence analysis on the n torus is a distinctive feature of the present work with respect to previous results that have focused on convergence in the euclidean space

a curve extension design for coordinated path following control of unicycles along given convex loops this article utilises a dynamic model of unicycles to address the convergence of vehicle formation about closed convex curves a novel curve extension method extending the target loop along the vector from the loop centre to the point on the loop is proposed to construct a family of level curves and the existence of a loop function on a tubular like neighbourhood is proved by referring to the tubular neighbourhood theorem path following control is derived based on the loop function which incorporated into the arc length function to propose the solution to coordinated formation control we show how backstepping technique lyapunov based theory and graph theory can be combined together to construct the coordinated path following controller under the bidirectional commutation topology it is proved that the designed cooperative control system is asymptotically stable if the graph is connected the proposed method is effective for a skewed superellipse which is a type of curve that includes circles ellip

saturation of repeated quantum measurements we study sequential measurement scenarios where the system is repeatedly subjected to the same measurement process we first provide examples of such repeated measurements where further repetitions of the measurement do not increase our knowledge on the system after some finite number of measurement steps we also prove however that repeating the luders measurement of an unsharp two outcome observable never saturates in this sense and we characterize the observable measured in the limit of infinitely many repetitions our result implies that a repeated measurement can be used to correct the inherent noise of an unsharp observable

on informational completeness of covariant localization observables and wigner coefficients an orthogonality theorem is obtained for square integrable representations on homogeneous spaces of a locally compact group from this a series of lemmas is derived showing the informational completeness of natural covariant localization operators as well as of the generalized wigner distributions matrix elements of the group some of these results give explicit reconstruction formulas for the quantum state from its expectation values against these families of operators the results are applied to special phase space representations of the heisenberg affine and galilei groups

generalized stochastic processes and continual observations in quantum mechanics we give here a mathematically rigorous form to an earlier work by barchielli lanz and prosperi in which it was found that a generalized stochastic process describes the results of continual observations of the position of a quantum particle with the help of albeverio and ho egh krohn s theory of feynman path integrals we define the characteristic functional of this process and demonstrate that it possesses the necessary properties of normalization continuity and positive definiteness an explicit calculation of the feynman path integral which defines the functional allows an analysis of the process to be made

barycentric decomposition of quantum measurements in finite dimensions we analyze the convex structure of the set of positive operator valued measures povms representing quantum measurements on a given finite dimensional quantum system with outcomes in a given locally compact hausdorff space the extreme points of the convex set are operator valued measures concentrated on a finite set of k d2 points of the outcome space d being the dimension of the hilbert space we prove that for second countable outcome spaces any povm admits a choquet representation as the barycenter of the set of extreme points with respect to a suitable probability measure in the general case krein milman theorem is invoked to represent povms as barycenters of a certain set of povms concentrated on k d2 points of the outcome space

path following for nonlinear systems with unstable zero dynamics in the path following problem formulated in this note it is required that the error between the system output and the desired geometric path eventually be less than any prespecified constant if in a nonlinear multiple input multiple output mimo system the output derivatives do not enter into its zero dynamics a condition relating path geometry and stabilizability of the zero dynamics is given under which a solution to this problem exists the solution is obtained by combining input to state stability and hybrid system methodologies

canonical approximate quantum measurements in order to generalize the wigner formula for the joint probability distribution of successive canonical measurements of discrete observables to continuous observables a mathematical model is investigated of a canonical approximate measurement of an arbitrary observable which generalizes von neumann s model of measuring interaction and davies s covariant instrument for approximate position measurement calculations of two types of root mean square errors show that this model clears certain requirements for good approximate measurements a modified wigner formula for successive canonical approximate measurements of arbitrary observables is established it is also shown that the canonical approximate measurement of a discrete observable is reduced to the conventional measurement satisfying the von neumann luders collapse postulate by a minor modification in the process of measurement