random wavelet series based on a tree indexed markov chain we study the global and local regularity properties of random wavelet series whose coefficients exhibit correlations given by a tree indexed markov chain we determine the law of the spectrum of singularities of these series thereby performing their multifractal analysis we also show that almost every sample path displays an oscillating singularity at almost every point and that the points at which a sample path has at most a given holder exponent form a set with large intersection

second order resolvability intrinsic randomness and fixed length source coding for mixed sources information spectrum approach the second order achievable asymptotics in typical random number generation problems such as resolvability intrinsic randomness and fixed length source coding are considered in these problems several researchers have derived the first order and the second order achievability rates for general sources using the information spectrum methods although these formulas are general their computations are quite hard hence an attempt to address explicit computation problems of achievable rates is meaningful in particular for i i d sources the second order achievable rates have earlier been determined simply by using the asymptotic normality in this paper we consider mixed sources of two i i d sources the mixed source is a typical case of nonergodic sources and whose self information does not have the asymptotic normality nonetheless we can explicitly compute the second order achievable rates for these sources on the basis of two peak asymptotic normality in addition extensions of our results to more general mixed sources such as a mixture of countably infinite i i d sources or markov sources and a continuous mixture of i i d sources are considered

nonlocality asymmetry and distinguishing bipartite states entanglement is a useful resource because some global operations cannot be locally implemented using classical communication we prove a number of results about what is and what is not locally possible we focus on orthogonal states which can always be globally distinguished we establish the necessary and sufficient conditions for a general set of 2 ifmmode times else texttimes fi 2 quantum states to be locally distinguishable and for a general set of 2 ifmmode times else texttimes fi n quantum states to be distinguished given an initial measurement of the qubit these results reveal a fundamental asymmetry to nonlocality which is the origin of nonlocality without entanglement and we present a very simple proof of this phenomenon

exact closed form representations for the time domain surface impedances of a homogeneous lossy half space in this paper we derive exact closed form representations for the transverse electric and transverse magnetic time domain surface impedances associated with a plane wave that is obliquely incident on a homogeneous lossy half space the time domain surface impedances are expressed in terms of modified bessel functions and incomplete lipschitz hankel integrals the limitations on the validity of a previously published approximate expression are also discussed

the proper formula for relative entropy and its asymptotics in quantum probability umegaki s relative entropys trd logd logd of states and with density operatorsd andd respectively is shown to be an asymptotic exponent considered from the quantum hypothesis testing viewpoint it is also proved that some other versions of the relative entropy give rise to the same asymptotics as umegaki s one as a byproduct the inequality tra logab tra loga logb is obtained for positive definite matricesa andb

numerical computation of 2d sommerfeld integrals a novel asymptotic extraction technique abstract the accurate and efficient computation of the elements in the impedance matrix is a crucial step in the application of galerkin s method to the analysis of planar structures as was demonstrated in a previous paper it is possible to decompose the angular integral in the polar representation for the 2d sommerfeld integrals in terms of incomplete lipschitz hankel integrals ilhis when piecewise sinusoidal basis functions are employed since bessel series expansions can be used to compute these ilhis a numerical integration of the inner angular integral is not required this technique provides an efficient method for the computation of the inner angular integral however the outer semi infinite integral still converges very slowly when a real axis integration is applied therefore it is very difficult to compute the impedance elements accurately and efficiently in this paper it is shown that this problem can be overcome by using the ilhi representation for the angular integral to develop a novel asymptotic extraction technique for the outer semi infinite integral the usefulness of this asymptotic extraction technique is demonstrated by applying it to the analysis of a printed strip dipole antenna in a layered medium

numerical computation of 2d sommerfeld integrals decomposition of the angular integral abstract spectral domain techniques are frequently used in conjunction with galerkin s method to obtain the current distribution on planar structures when this technique is employed a large percentage of the computation time is spent filling the impedance matrix therefore it is important to develop accurate and efficient numerical techniques for the computation of the impedance elements which can be written as two dimensional 2d sommerfeld integrals once the current distribution has been found then the near zone electric field distribution can be obtained by computing another set of 2d sommerfeld integrals the computational efficiency of the 2d sommerfeld integrals can be improved in two ways the first method which is discussed in this paper involves finding a new way to compute the inner angular integral in the polar representation of these integrals it turns out that the angular integral can be decomposed into a finite number of incomplete lipschitz hankel integrals which in turn can be calculated using series expansions therefore the angular integral can be computed by summing a series instead of applying a standard numerical integration algorithm this new technique is found to be more accurate and efficient when piecewise sinusoidal basis functions are used to analyze a printed strip dipole antenna in a layered medium the incomplete lipschitz hankel integral representation for the angular integral is then used in another paper to develop a novel asymptotic extraction technique for the outer semi infinite integral

general formulas for capacity of classical quantum channels the capacity of a classical quantum channel or in other words the classical capacity of a quantum channel is considered in the most general setting where no structural assumptions such as the stationary memoryless property are made on a channel a capacity formula as well as a characterization of the strong converse property is given just in parallel with the corresponding classical results of verdu han 1994 which are based on the so called information spectrum method the general results are applied to the stationary memoryless case with or without cost constraint on inputs whereby a deep relation between the channel coding theory and the hypothesis testing for two quantum states is elucidated

multifractal analysis of infinite products we construct a family of measures called infinite products which generalize gibbs measures in the one dimensional lattice gas model the multifractal properties of these measures are studied under some regularity conditions in particular if the function is differentiable we prove a formula which gives the hausdorff dimension and packing dimension of the set of singularity points of a given order mathematical examples include riesz products g measures andg measures

a note on the radiation boundary conditions for the helmholtz equation the radiation boundary conditions in two dimensions are derived in the body fitted coordinate system using the method of successive approximations for the wave envelope function results are valid for a convex scatterer with continuous radius of curvature on the surface of the scatterer in the special case when the computational boundary is circular the boundary operators derived are identical to the bayliss operators the on surface radiation condition is examined it is shown that for a large conducting circular cylinder a boundary operator of infinite order should be used due to the breakdown of the asymptotic expansions of the boundary operators on the surface of the scatterer the leading order result based on the boundary operator of infinite order applied on the surface of the cylinder is the same as the result obtained by the method of physical optics

on multifractality and time subordination for continuous functions let be a continuous function this paper relates to the existence of a decomposition of z as z g f where is a monofractal function with exponent 0 h 1 and f 0 1 0 1 is a time subordinator i e the integral of a positive borel measure supported by 0 1 an equivalent question consists of searching for a multifractal parametrization of z which transforms z into a monofractal function we establish that such a decomposition can be found for a large class of functions which includes the usual examples of multifractal functions we find an interesting relationship between self similar functions and self similar measures as an application of our results our theorems yield new insights in the understanding of the multifractal behaviour of functions giving a significant role to the regularity analysis of borel measures

asymptotic state discrimination and a strict hierarchy in distinguishability norms in this paper we consider the problem of discriminating quantum states by local operations and classical communication locc when an arbitrarily small amount of error is permitted this paradigm is known as asymptotic state discrimination and we derive necessary conditions for when two multipartite states of any size can be discriminated perfectly by asymptotic locc we use this new criterion to prove a gap in the locc and separable distinguishability norms we then turn to the operational advantage of using two way classical communication over one way communication in locc processing with a simple two qubit product state ensemble we demonstrate a strict majorization of the two way locc norm over the one way norm

a hierarchy of information quantities for finite block length analysis of quantum tasks we consider two fundamental tasks in quantum information theory data compression with quantum side information as well as randomness extraction against quantum side information we characterize these tasks for general sources using so called one shot entropies these characterizations in contrast to earlier results enable us to derive tight second order asymptotics for these tasks in the i i d limit more generally our derivation establishes a hierarchy of information quantities that can be used to investigate information theoretic tasks in the quantum domain the one shot entropies most accurately describe an operational quantity yet they tend to be difficult to calculate for large systems we show that they asymptotically agree up to logarithmic terms with entropies related to the quantum and classical information spectrum which are easier to calculate in the i i d limit our technique also naturally yields bounds on operational quantities for finite block lengths

absorbing boundary conditions on arbitrary boundaries for the scalar and vector wave equations the solution of open region scattering problems involving inhomogeneous arbitrarily shaped objects may be performed through the use of partial differential equation techniques which require enclosing the scatterer by an outer boundary on which an absorbing boundary condition abc is applied in order to minimize the size of the domain to be meshed and consequently the number of unknowns if may be advisable to implement abc s devised for outer boundaries of arbitrary shapes such abc s are obtained for the 3d scalar and vector wave equations they incorporate most of existing boundary conditions when used in conjunction with a finite element technique the numerical results derived by using a simplified form of these abc s compare favourably to those obtained by using a rigorous hybrid finite element integral equation formulation these boundary conditions have been obtained in the frequency domain framework they may however be used in time domain calculations

a novel asymptotic extraction technique for the efficient evaluation of a class of double sommerfeld integrals when the galerkin method of moments mom is used in the numerical analysis of microwave microstrip networks elements of a network impedance matrix are required two dimensional 2d sommerfeld spectral integrals must be evaluated in such cases when semi infinite circuit feed lines are used certain specific types of sommerfeld integrals arise whose integrands oscillate rapidly and present serious numerical difficulties for their evaluation in this paper a novel accurate and much more efficient asymptotic extraction technique aet is developed that involves extracting an inner asymptotic angular integral which is then evaluated analytically before evaluating the outer integral numerically

tight asymptotic bounds on local hypothesis testing between a pure bipartite state and the white noise state we consider asymptotic hypothesis testing or state discrimination with asymmetric treatment of errors between an arbitrary fixed bipartite pure state psi rangle and the white noise state the completely mixed state under one way local operations and classical communications locc two way locc and separable positive operator valued measures povms as a result we derive the hoeffding bounds under two way locc povms and separable povms further we derive stein s lemma type of optimal error exponents under one way locc two way locc and separable povms up to the third order which clarifies the difference between one way and two way locc povm our results clarify the relationship between the entanglement of renyi entropy and the hypothesis testing under locc since the entanglement of renyi entropy appears in the formula of both the hoeffding bounds and stein s lemma type of error exponents this paper gives a very rare example in which the optimal performance under the infinite round two way locc is also equal to that under separable operations and can be attained with two round communication but not with the one way locc

local hypothesis testing between a pure bipartite state and the white noise state in this paper we treat a local discrimination problem in the framework of asymmetric hypothesis testing we choose a known bipartite pure state psi rangle as an alternative hypothesis and the completely mixed state as a null hypothesis as a result we analytically derive an optimal type 2 error and an optimal positive operator valued measure povm for one way local operations and classical communication locc povm and separable povm for two way locc povm we study a family of simple three step locc protocols and show that the best protocol in this family has strictly better performance than any one way locc protocol in low dimensional systems when there may exist differences between two way locc povm and one way locc povm

the multifractal nature of levy processes we show that the sample paths of most levy processes are multifractal functions and we determine their spectrum of singularities

fdtd model of electrically thick frequency dispersive coatings on metals and semiconductors based on surface impedance boundary conditions a new finite difference time domain fdtd model for conductors coated with electrically thick frequency dispersive coatings is developed the model is based on first order impedance boundary conditions as the most important original feature of the model the frequency dependence of the material parameters of the coating is very general dispersive coatings of lorentz debye or drude type with multiple pole pairs and a fixed electrical conductivity can be modeled with the proposed technique another new property of the model is the use of rational approximation in a way that enables accurate approximation of the impedance function in a wide range corresponding to several thickness resonances of the coating the conductor losses in the metal backing that are neglected in many earlier models are accounted for in the proposed model the model is formulated for planar interfaces in the general three dimensional situation for the yee algorithm and verified against analytical reference results with numerical examples in one dimensional and two dimensional problems

the singularity spectrum of levy processes in multifractal time abstract let x x t t 0 be a levy process and a positive borel measure on r suppose that the integral of defines a continuous increasing multifractal time f t 0 0 t under suitable assumptions on we compute the singularity spectrum of the sample paths of the process x in time defined as the process x f t t 0 a fundamental example consists in taking a measure equal to an independent random cascade and independently of a suitable stable levy process x then the associated process x in time is naturally related to the so called fixed points of the smoothing transformation in interacting particles systems our results rely on recent heterogeneous ubiquity theorems

hausdorff and packing spectra large deviations and free energy for branching random walks in mathbb r d consider an mathbb r d valued branching random walk brw on a supercritical galton watson tree without any assumption on the distribution of this brw we compute almost surely and simultaneously the hausdorff and packing dimensions of the level sets e k of infinite branches in the boundary of the tree endowed with its standard metric along which the averages of the brw have a given closed connected set of limit points k this goes beyond multifractal analysis which only considers those level sets when k ranges in the set of singletons alpha alpha in mathbb r d we also give a 0 law for the hausdorff and packing measures of the level sets e and compute the free energy of the associated logarithmically correlated random energy model in full generality moreover our results complete the previous works on multifractal analysis by including the levels which do not belong to the range of the gradient of the free energy this covers in particular a situation that was until now badly understood namely the case where a first order phase transition occurs as a consequence of our study we can also describe the whole singularity spectrum of mandelbrot measures as well as the associated free energy function or lq spectrum when a first order phase transition occurs

transmission of pulsed plane wave into dispersive half space prony s method approximation time domain impulse transmission functions of a dispersive half space due to an obliquely incident pulsed plane wave of either te or tm polarization are presented as inverse fourier transforms the frequency domain transmission functions are approximated by using prony s method as finite series of exponential decaying functions the inverse fourier transform of these exponential decaying functions are evaluated analytically in closed forms time domain response due to a specific pulse shape is obtained by convoluting the impulse transmission functions with the required pulse shape

higher order impedance and absorbing boundary conditions traditionally generalized impedance boundary conditions gibcs have been used to model dielectrics and coated surfaces and absorbing boundary conditions abcs have been used to simulate nonreflecting surfaces the two types have the same mathematical form and in most instances a higher order condition involving higher order field derivatives has a better accuracy we demonstrate that there is a close connection between the two and this enables us to use a systematic method which is available for generating gibcs of any desired order to derive new two and three dimensional abcs the method is applicable to curvilinear doubly curved surfaces and examples are given finally curves are presented that quantify the accuracy of two dimensional abcs up to the fourth order and show how higher order abcs can improve the efficiency of large scale partial differential equation pde solutions

asymptotic error rates in quantum hypothesis testing we consider the problem of discriminating between two different states of a finite quantum system in the setting of large numbers of copies and find a closed form expression for the asymptotic exponential rate at which the error probability tends to zero this leads to the identification of the quantum generalisation of the classical chernoff distance which is the corresponding quantity in classical symmetric hypothesis testing

optimal sequence of quantum measurements in the sense of stein s lemma in quantum hypothesis testing we derive a necessary and sufficient condition for a sequence of quantum measurements to achieve the optimal performance in quantum hypothesis testing we discuss what quantum measurement we should perform in order to attain the optimal exponent of the second error probability under the condition that the first error probability goes to 0 as an asymptotically optimal measurement we propose a projection measurement characterized by the irreducible representation theory of the special linear group sl especially in the spin 1 2 system it is realized by the simultaneous measurement of the total momentum and a momentum of a specified direction as a by product we obtain another proof of quantum stein s lemma in addition an asymptotically optimal measurement is constructed in the quantum gaussian case and it is physically meaningful

strong converse and stein s lemma in quantum hypothesis testing the hypothesis testing problem for two quantum states is treated we show a new inequality between the errors of the first kind and the second kind which complements the result of hiai and petz 1991 to establish the quantum version of stein s lemma the inequality is also used to show a bound on the probability of errors of the first kind when the power exponent for the probability of errors of the second kind exceeds the quantum relative entropy which yields the strong converse in quantum hypothesis testing finally we discuss the relation between the bound and the power exponent derived by han and kobayashi 1989 in classical hypothesis testing

a multifractal formalism let x be a metric space and a borel probability measure on x for q t r and e x write formula then hq t and pq t are borel measures hq t is a multifractal generalization of the centered hausdorff measure and pq t is a multifractal generalization of the packing measure the measures hq t and pq t define for a fixed q in the usual way a generalized hausdorff dimension dimq e and a generalized packing dimension dimq e of subsets e of x we study the functions b q dimq supp b q dimq supp and their relation to the so called multifractal spectra functions of formula we prove among other things that f f is bounded from above by the legendre transform of b b and that equality holds for graph directed self similar measures and cookie cutter measures finally we discuss the connection with generalized renyi dimensions

bounds on multipartite entangled orthogonal state discrimination using local operations and classical communication we show that entanglement guarantees difficulty in the discrimination of orthogonal multipartite states locally the number of pure states that can be discriminated by local operations and classical communication is bounded by the total dimension over the average entanglement a similar general condition is also shown for pure and mixed states these results offer a rare operational interpretation for three abstractly defined distancelike measures of multipartite entanglement

channel coding rate in the finite blocklength regime this paper investigates the maximal channel coding rate achievable at a given blocklength and error probability for general classes of channels new achievability and converse bounds are given which are tighter than existing bounds for wide ranges of parameters of interest and lead to tight approximations of the maximal achievable rate for blocklengths n as short as 100 it is also shown analytically that the maximal rate achievable with error probability isclosely approximated by c v n q 1 where c is the capacity v is a characteristic of the channel referred to as channel dispersion and q is the complementary gaussian cumulative distribution function

discriminating quantum states the multiple chernoff distance we consider the problem of testing multiple quantum hypotheses rho 1 otimes n ldots rho r otimes n where an arbitrary prior distribution is given and each of the r hypotheses is n copies of a quantum state it is known that the minimal average error probability p e decays exponentially to zero that is p e exp xi n o n however this error exponent xi is generally unknown except for the case that r 2 in this paper we solve the long standing open problem of identifying the above error exponent by proving nussbaum and szkola s conjecture that xi min i neq j c rho i rho j the right hand side of this equality is called the multiple quantum chernoff distance and c rho i rho j max 0 leq s leq1 log operatorname tr rho i s rho j 1 s has been previously identified as the optimal error exponent for testing two hypotheses rho i otimes n versus rho j otimes n the main ingredient of our proof is a new upper bound for the average error probability for testing an ensemble of finite dimensional but otherwise general quantum states this upper bound up to a states dependent factor matches the multiple state generalization of nussbaum and szkola s lower bound specialized to the case r 2 we give an alternative proof to the achievability of the binary hypothesis chernoff distance which was originally proved by audenaert et al

an efficient implementation of surface impedance boundary conditions for the finite difference time domain method an efficient way to implement the surface impedance boundary conditions sibc for the finite difference time domain fdtd method is presented in this paper surface impedance boundary conditions are first formulated for a lossy dielectric half space in the frequency domain the impedance function of a lossy medium is approximated with a series of first order rational functions then the resulting time domain convolution integrals are computed using recursive formulas which are obtained by assuming that the fields are piecewise linear in time thus the recursive formulas derived here are second order accurate unlike a previously published method 7 which requires preprocessing to compute the exponential approximation prior to the fdtd simulation the preprocessing time is eliminated by performing a rational approximation on the normalized frequency domain impedance this approximation is independent of material properties and the results are tabulated for reference the implementation of the sibc for a pec backed lossy dielectric shell is also introduced

scaling exponents and multifractal dimensions for independent random cascades this paper is concerned with mandelbrot s stochastic cascade measures the problems of i scaling exponents of structure functions of the measure q and ii multifractal dimensions are considered for cascades with a generator vector w1 wc of the general type these problems were previously studied for independent strongly bounded variableswi 0 a wi c consequently a broad class of models used in applications including kolmogorov s long normal model in turbulence long stable universal cascades in atmospheric dynamics has not been covered roughly speaking problems i ii are here solved under the condition that the scaling exists the function is calculated for all arguments previously this was done for positiveq and a new effect emerges the function can generally involve discontinuities in the first derivative as well as in the second

a localized jarnik besicovitch theorem abstract fundamental questions in diophantine approximation are related to the hausdorff dimension of sets of the form x r x where 1 and x is the diophantine approximation exponent of an irrational number x we go beyond the classical results by computing the hausdorff dimension of the sets x r x f x where f is a continuous function our theorem applies to the study of the approximation exponents by various approximation families it also applies to functions f which are continuous outside a set of prescribed hausdorff dimension

interpolatability distinguishes locc from separable von neumann measurements local operations with classical communication locc and separable operations are two classes of quantum operations that play key roles in the study of quantum entanglement separable operations are strictly more powerful than locc but no simple explanation of this phenomenon is known we show that in the case of von neumann measurements the ability to interpolate measurements is an operational principle that sets apart locc and separable operations

comparison of local radiation boundary conditions for the scalar helmholtz equation with general boundary shapes the relative accuracy of several local radiation boundary conditions based on the second order bayliss turkel 1980 condition are evaluated these boundary conditions permit the approximate solution of the scalar helmholtz equation in an infinite domain using traditional finite element and finite difference techniques unlike the standard bayliss turkel condition the generalizations considered here are applicable to noncircular solution domains the accuracy of these conditions are investigated for elliptical and linear circular boundaries

surface impedance boundary conditions in time domain for guided structures of arbitrary cross section with lossy dielectric walls this paper presents a procedure to implement the concept of surface impedance boundary condition sibc for lossy dielectrics in time domain the sibc formulation validation and results are obtained with a time domain numerical method namely the transmission line matrix tlm the formulation of surface impedance in frequency domain is converted to the time domain using a rational approximation followed by a bilinear transform with a canonical representation in the state space this surface impedance formulation has been implemented in tlm simulations show that the proposed model is valid for interfaces between air and a lossy dielectric and arbitrary conductivity sigma an application that concerns mode propagation in a rectangular tunnel with lossy dielectric walls is shown a comparison with an approximate method proposed by marcatilli is presented it confirms that the propagation in electrically large guided structures such as tunnels with lossy dielectric walls can be efficiently modeled by this approach

numerical computation of the incomplete lipschitz hankel integral je o a z abstract two factorial neumann series expansions are derived for the incomplete lipschitz hankel integral je 0 a z these expansions are used together with the neumann series expansion given by agrest in an algorithm which efficiently computes je 0 a z to a user defined number of significant digits other expansions for je 0 a z which are found in the literature are also discussed but these expansions are found to offer no significant computational advantages when compared with the expansions used in the algorithm

accurate computation of the radiation from simple antennas using the finite difference time domain method two antennas are considered a cylindrical monopole and a conical monopole both are driven through an image plane from a coaxial transmission line each of these antennas corresponds to a well posed theoretical electromagnetic boundary value problem and a realizable experimental model these antennas are analyzed by a straightforward application of the finite difference time domain fd td method the computed results for these antennas are shown to be in excellent agreement with accurate experimental measurements for both the time domain and the frequency domain the graphical displays presented for the transient near zone and far zone radiation from these antennas provide physical insight into the radiation process

approximating the surface impedance of a homogeneous lossy half space an example of dialable accuracy we present an approximation by exponentials of the time domain surface impedance of a lossy half space gauss chebyshev quadrature of order n 1 is employed to approximate an integral representation of the modified bessel functions comprising the time domain impedance kernel an explicit error estimate is obtained in terms of the physical parameters the computation time and the number of quadrature points n we show that our approximation is as accurate as other approaches which do not come with such an error estimate the paper investigates the conditions under which the derived error estimate also applies to the approximation of j a roden and s d gedney see trans microwave theory tech vol 47 p 1954 1999

conformal fdtd modeling of imperfect conductors at millimeter wave bands the dey mittra conformal finite difference time domain cfdtd algorithm for perfect electrical conductors is modified for the analysis of finite conductivity conductors at millimeter wave frequencies formulas are derived for cfdtd coefficients using voltage state variables and a constant surface impedance boundary condition sibc the approach permits a fast implementation suitable for cuda type gpu hardware accuracy and stability are investigated with respect to the stability constraints on intersection areas introduced by dey mittra and benkler as well as the distance stability constraints of zagorodnov that permits 100 courant temporal sampling a relaxation of the zagorodnov distance constraints permits increased accuracy with respect to all alternative area constraints analytic solutions are used to judge the performance of the proposed cfdtd modifications for millimeter wave band applications

network oriented dyadic time domain green s function for a sequentially excited infinite planar array of dipoles in free space during the past few years we have performed an effective wideband analysis for characterizing the electrodynamic behavior of phased array antennas infinite periodic structures frequency selective surfaces and related applications with emphasis on gaining physical insight into the phenomenology of short pulse radiation the present contribution shows the current status of our network oriented dyadic time domain green s function td gf for a planar array of sequentially excited dipoles that constitutes a prototype study of sequentially short pulsed radiation by infinite periodic arrays the dispersive effects of the td floquet waves fw and the consequences of a te and tm field decomposition are discussed in details in this network formulation the equivalent td transmission line tl voltages and currents excited by equivalent td current generators are determined an expression for the tm voltage tl gf is provided for the first time in terms of incomplete lipschitz hankel integrals and bessel functions together with some remarks for its evaluation as shown in previous publications for the scalar potentials real td physical observables are determined by pairing td floquet waves with positive and negative indices it is shown that the vectorial td radiated field is reconstructed at any time with the superposition of a few td fws

a study of locc detection of a maximally entangled state using hypothesis testing we study how well we can answer the question is the given quantum state equal to a certain maximally entangled state using locc in the context of hypothesis testing under several locality and invariance conditions optimal tests will be derived for several special cases by using basic theory of group representations some optimal tests are realized by performing quantum teleportation and checking whether the state is teleported we will also give a finite process for realizing some optimal tests the performance of the tests will be numerically compared

fdtd modeling of arrays and grids of lossy conductors based on impedance sheet conditions fast finite difference time domain fdtd modeling techniques for arrays of parallel wires and wire meshes are developed the analytical basis of the models lies in the use of impedance sheet conditions kontorovich conditions for dense wire arrays and grids connecting the tangential electric fields and the averaged currents in the plane of a wire array or grid the proposed methods allow us to avoid the direct discretization of the fields inside the wires greatly simplifying the modeling task the conductor losses in the wires are accounted for assuming a strong or weak skin effect the impedance sheet conditions are formulated in the time domain using the convolution integral which is evaluated recursively in fdtd numerical examples and comparisons with analytical results are provided to verify the proposed techniques

implementation of collocated surface impedance boundary conditions in fdtd surface impedance boundary conditions sibcs for finite difference time domain fdtd are implemented with collocated h and e components in which first order spatial finite difference have been used for the spatial derivatives transient error analysis is done for the reflected field for the whole possible range of modeled material conductivity magnitude and phase error analysis of the calculated reflection coefficients for wideband pulses is presented as well the resulting numerical errors are compared with the errors of traditional sibcs implementation when the tangential magnetic fields on the boundary are approximated with the neighboring fdtd magnetic field component located at half cell size distance in space and half time step behind in time it is shown that the collocated fields approach is considerably more accurate for both constant real resistive and dispersive complex lossy dielectric sibcs in both magnitude and especially phase unlike the traditional approach it is stable for all values of modeled material conductivity the collocated fields approach is also applied to sibcs with coating and the transient and reflection coefficient errors are studied it is shown that in contrast to the traditional implementation it is stable for arbitrarily thin coating and for any substrate conductivity and requires storage only half of the auxiliary coefficients when computing the convolution integrals

one shot classical quantum capacity and hypothesis testing the one shot classical capacity of a quantum channel quantifies the amount of classical information that can be transmitted through a single use of the channel such that the error probability is below a certain threshold in this work we show that this capacity is well approximated by a relative entropy type measure defined via hypothesis testing combined with a quantum version of stein s lemma our results give a conceptually simple proof of the well known holevo schumacher westmoreland theorem for the capacity of memoryless channels more generally we obtain tight capacity formulas for arbitrary not necessarily memoryless channels

an information spectrum approach to classical and quantum hypothesis testing for simple hypotheses the information spectrum analysis made by han for classical hypothesis testing for simple hypotheses is extended to a unifying framework including both classical and quantum hypothesis testing the results are also applied to fixed length source coding when loosening the normalizing condition for probability distributions and for quantum states we establish general formulas for several quantities relating to the asymptotic optimality of tests codes in terms of classical and quantum information spectra

second order asymptotics for quantum hypothesis testing in the asymptotic theory of quantum hypothesis testing the minimal error probability of the first kind jumps sharply from zero to one when the error exponent of the second kind passes by the point of the relative entropy of the two states in an increasing way this is well known as the direct part and strong converse of quantum stein s lemma here we look into the behavior of this sudden change and have make it clear how the error of first kind grows smoothly according to a lower order of the error exponent of the second kind and hence we obtain the second order asymptotics for quantum hypothesis testing this actually implies quantum stein s lemma as a special case meanwhile our analysis also yields tight bounds for the case of finite sample size these results have potential applications in quantum information theory our method is elementary based on basic linear algebra and probability theory it deals with the achievability part and the optimality part in a unified fashion

combining multifractal additive and multiplicative chaos the purpose of this article is the study of the new class of multifrac tal measures which combines additive and multiplicative chaos defined by x j 1 b j j 2 x

distinguishability of quantum states by separable operations in this paper we study the distinguishability of multipartite quantum states by separable operations we first present a necessary and sufficient condition for a finite set of orthogonal quantum states to be distinguishable by separable operations an analytical version of this condition is derived for the case of d 1 pure states where d is the total dimension of the state space under consideration a number of interesting consequences of this result are then carefully investigated remarkably we show there exists a large class of 2 otimes 2 separable operations not being realizable by local operations and classical communication before our work only a class of 3 otimes 3 nonlocal separable operations was known bennett phys rev a 59 1070 1999 we also show that any basis of the orthogonal complement of a multipartite pure state is indistinguishable by separable operations if and only if this state cannot be a superposition of one or two orthogonal product states i e has an orthogonal schmidt number not less than three thus generalize the recent work about indistinguishable bipartite subspaces watrous phys rev lett 95 080505 2005 notably we obtain an explicit construction of indistinguishable subspaces of dimension 7 or 6 by considering a composite quantum system consisting of two qutrits resp three qubits which is slightly better than the previously known indistinguishable bipartite subspace with dimension 8

inside singularity sets of random gibbs measures we evaluate the scale at which the multifractal structure of some random gibbs measures becomes discernible the value of this scale is obtained through what we call the growth speed in holder singularity sets of a borel measure this growth speed yields new information on the multifractal behavior of the rescaled copies involved in the structure of statistically self similar gibbs measures our results are useful to understand the multifractal nature of various heterogeneous jump processes

the use of surface impedance concepts in the finite difference time domain method surface impedance concepts are introduced into the finite difference time domain fdtd method lossy conductors are replaced by surface impedance boundary conditions sibc reducing the solution space and producing significant computational savings specifically a sibc is developed to replace a lossy dielectric half space an efficient implementation of this fdtd sibc based on the recursive properties of convolution with exponentials is presented finally three problems are studied to illustrate the accuracy of the fdtd sibc formulation a plane wave incident on a lossy dielectric half space a line current over a lossy dielectric half space and wave propagation in a parallel plate waveguide with lossy walls

distinguishability of bell states more than two multipartite orthogonal states cannot always be discriminated if only local operations and classical communication locc are allowed we show that four bell states cannot be discriminated by locc even probabilistically using the separability properties of a four party unlockable bound entangled state using an existing inequality among the measures of entanglement we show that any three bell states cannot be discriminated with certainty by locc exploiting the inequality we calculate the distillable entanglement of a certain class of 4 multiply sign in circle 4 mixed states

discrimination of two channels by adaptive methods and its application to quantum system the optimal exponential error rate for adaptive discrimination of two channels is discussed in this problem adaptive choice of input signal is allowed this problem is discussed in various settings it is proved that adaptive choice does not improve the exponential error rate in these settings these results are applied to quantum state discrimination

an accurate and efficient analysis for transient plane waves obliquely incident on a conductive half space te case we develop a method for the analytical evaluation of the inverse laplace transform representations for transient transverse magnetic tm plane wave obliquely incident on a conductive half space we assume that the permittivity and conductivity of the dispersive half space are independent of frequency the time domain expressions for the reflected and transmitted waves are first represented as inverse laplace transforms the transient fields are then shown to consist of two canonical integrals the canonical integrals in turn are solved analytically thereby yielding close form solutions involving incomplete lipschitz hankel integrals ilhis the ilhis are computed numerically using efficient convergent and asymptotic series expansions thus enabling the efficient computation of the transient fields the exact closed form expressions are verified by comparing with previously published results and with results obtained using standard numerical integration and fast fourier transform fft algorithms an asymptotic series representation for the ilhis is also employed to obtain a relatively simple late time approximation for the transient fields this approximate late time expression is shown to accurately model the fields over a large portion of its time history

on non scale invariant infinitely divisible cascades multiplicative processes multifractals and more recently also infinitely divisible cascades have seen increased popularity in a host of applications requiring versatile multiscale models ranging from hydrodynamic turbulence to computer network traffic from image processing to economics the methodologies prevalent as of today rely to a large extent on iterative schemes used to produce infinite detail and repetitive structure across scales while appealing due to their simplicity these constructions have limited applicability as they lead by default to power law progression of moments through scales to nonstationary increments and often to inherent log periodic scaling which favors an exponential set of scales this paper studies and develops a wide class of infinitely divisible cascades idc thereby establishing the first reported cases of controllable scaling of moments in non power law form embedded in the framework of idc these processes exhibit stationary increments and scaling over a continuous range of scales criteria for convergence further statistical properties as well as matlab routines are provided

nonlocal variables with product state eigenstates an alternative proof for existence of quantum nonlocality without entanglement i e existence of variables with product state eigenstates which cannot be measured locally is presented a simple nonlocal variable for the case of one way communication is given and the limit for its approximate measurability is found

the chernoff lower bound for symmetric quantum hypothesis testing we consider symmetric hypothesis testing in quantum statistics where the hypotheses are density operators on a finite dimensional complex hilbert space representing states of a finite quantum system we prove a lower bound on the asymptotic rate exponents of bayesian error probabilities the bound represents a quantum extension of the chernoff bound which gives the best asymptotically achievable error exponent in classical discrimination between two probability measures on a finite set in our framework the classical result is reproduced if the two hypothetic density operators commute recently it has been shown elsewhere phys rev lett 98 2007 160504 that the lower bound is achievable also in the generic quantum noncommutative case this implies that our result is one part of the definitive quantum chernoff bound

a general formula for channel capacity a formula for the capacity of arbitrary single user channels without feedback not necessarily information stable stationary etc is proved capacity is shown to equal the supremum over all input processes of the input output inf information rate defined as the liminf in probability of the normalized information density the key to this result is a new converse approach based on a simple new lower bound on the error probability of m ary hypothesis tests among equiprobable hypotheses a necessary and sufficient condition for the validity of the strong converse is given as well as general expressions for spl epsiv capacity

wide angle one way wave equations a one way wave equation also known as a paraxial or parabolic wave equation is a differential equation that permits wave propagation in certain directions only such equations are used regularly in underwater acoustics in geophysics and as energy absorbing numerical boundary conditions the design of a one way wave equation is connected with the approximation of 1 s2 1 2 on 1 1 by a rational function which has usually been carried out by pade approximation this article presents coefficients for l2 l and other alternative classes of approximants that have better wide angle behavior for theoretical results establishing the well posedness of these wide angle equations see the work of trefethen and halpern well posedness of one way wave equations and absorbing boundary conditions math comput 47 421 435 1986

the graph and range singularity spectra of b adic independent cascade functions abstract with the iso holder sets of a function we naturally associate subsets of the graph and the range of the function we compute the hausdorff dimension of these subsets for a class of statistically self similar multifractal functions namely the b adic independent cascade functions

application of the fast fourier transform to the computation of the sommerfeld integral for a vertical electric dipole above a half space the fast fourier transform fft is used in conjunction with analytical techniques to obtain an approximate expression for the sommerfeld integral associated with a vertical electric dipole above a half space the resulting expression which is an analytic function of the source and observation locations can be used in lieu of a numerical integration of the sommerfeld integral it can be used in either the near zone or the far zone and it can even be applied for observation angles close to grazing the accuracy of the expansion directly depends on the number of terms used in the fft results obtained using the expansion are compared with those obtained both from a direct numerical integration of the sommerfeld integral and the reflection coefficient method

testing for a pure state with local operations and classical communication we examine the problem of using local operations and classical communication locc to distinguish a known pure state from an unknown possibly mixed state bounding the error probability from above and below we study the asymptotic rate of detecting multiple copies of the pure state and show that if the overlap of the two states is great enough then they can be distinguished asymptotically as well with locc as with global measurements otherwise the maximal schmidt coefficient of the pure state is sufficient to determine the asymptotic error rate

absorbing boundary conditions for convex object conformable boundaries absorbing boundary conditions abcs are developed that can be applied on object conformable outer boundaries the new abcs are based on the local enforcement of the nth order bayliss turkel boundary conditions where a scattering center is defined for each outer boundary node a demonstration of the effectiveness of the new construction is provided by considering representative numerical experiments using the finite elements method results show that the new abcs provide accuracy that compares very favorably with the method of moments solution

adversarial hypothesis testing and a quantum stein s lemma for restricted measurements recall the classical hypothesis testing setting with two sets of probability distributions p and q one receives either n i i d samples from a distribution p in p or from a distribution q in q and wants to decide from which set the points were sampled it is known that the optimal exponential rate at which errors decrease can be achieved by a simple maximum likelihood ratio test which does not depend on p or q but only on the sets p and q we consider an adaptive generalization of this model where the choice of p in p and q in q can change in each sample in some way that depends arbitrarily on the previous samples in other words in the k th round an adversary having observed all the previous samples in rounds 1 ldots k 1 chooses p k in p and q k in q with the goal of confusing the hypothesis test we prove that even in this case the optimal exponential error rate can be achieved by a simple maximum likelihood test that depends only on p and q we then show that the adversarial model has applications in hypothesis testing for quantum states using restricted measurements for example it can be used to study the problem of distinguishing entangled states from the set of all separable states using only measurements that can be implemented with local operations and classical communication locc the basic idea is that in our setup the deleterious effects of entanglement can be simulated by an adaptive classical adversary we prove a quantum stein s lemma in this setting in many circumstances the optimal hypothesis testing rate is equal to an appropriate notion of quantum relative entropy between two states in particular our arguments yield an alternate proof of li and winter s recent strengthening of strong subadditivity for von neumann entropy

absorbing boundary conditions for acoustic and elastic waves in stratified media abstract absorbing boundary conditions are needed for computing numerical models of wave motions in unbounded spatial domains prior progress on this problem for acoustic and elastic waves has generally been concerned with waves propagating through uniform media the present paper is concerned with waves in stratified media which are of interest for example in geophysical problems suppose that the medium consists of homogeneous layers separated by parallel horizontal interfaces and suppose that absorbing boundary conditions are needed along a vertical computational boundary the boundary conditions that are described in this paper are based on a quantity known as the ray parameter according to snell s law this parameter remains the same when a plane wave propagates through a stratified medium and undergoes reflection refraction and in the case of elastic waves conversion once can therefore use the same absorbing boundary conditions in all layers for acoustic waves the absorption properties are the same in all layers for elastic waves the absorption properties vary somewhat from one layer to another however one still obtains good absorption in all layers even in the presence of strong contrasts between layers the boundary conditions are also effective in absorbing rayleigh waves which propagate along free surfaces of elastic media the boundary formulas developed here can be applied without modification to problems in both two and three dimensions

on the chernoff distance for asymptotic locc discrimination of bipartite quantum states motivated by the recent discovery of a quantum chernoff theorem for asymptotic state discrimination we investigate the distinguishability of two bipartite mixed states under the constraint of local operations and classical communication locc in the limit of many copies while for two pure states a result of walgate et al shows that locc is just as powerful as global measurements data hiding states divincenzo et al show that locality can impose severe restrictions on the distinguishability of even orthogonal states here we determine the optimal error probability and measurement to discriminate many copies of particular data hiding states extremal d d werner states by a linear programming approach surprisingly the single copy optimal measurement remains optimal for n copies in the sense that the best strategy is measuring each copy separately followed by a simple classical decision rule we also put a lower bound on the bias with which states can be distinguished by separable operations

hypothesis testing on invariant subspaces of the symmetric group part i quantum sanov s theorem and arbitrarily varying sources we report a proof of the quantum sanov theorem by the elementary application of basic facts about representations of the symmetric group together with a complete characterization of the optimal error exponent in a situation where the null hypothesis is given by an arbitrarily varying quantum source instead our approach differs from previous ones in two ways first it supports a reasoning inspired by the method of types second the measurement scheme we propose to distinguish the two alternatives not only does that job asymptotically perfectly but also yields additional information about the null hypothesis an example of that is given the measurement is composed of projections onto permutation invariant subspaces thus providing a direct link between one of the most basic tasks in quantum information on the one hand and fundamental objects in representation theory on the other we additionally connect to the representation theory by proving a relation between kostka numbers and quantum states and to state estimation via a generalization of a well known spectral estimation theorem to non i i d sequences

impedance boundary condition simulation in the fdtd fvtd hybrid the simulation of the impedance boundary condition ibc for the finite difference time domain fdtd and the finite volume time domain fvtd hybrid algorithm with overlapping grids is explained in detail this paper does not discuss the validity of the ibc model and our model assumes the surface impedance or surface admittance has a constant resistive part and a nonnegative imaginary part which is a linear function of frequency this model is restrictive but with this assumption the use of a convolution integral is avoided and for many applications this is sufficient comparisons of the calculations based on our time domain algorithm with the mie series solutions and the method of moment mom solutions are given the agreement between our solutions and the referenced solutions shows that our ibc simulation gives credible numerical results

everything you always wanted to know about locc but were afraid to ask in this paper we study the subset of generalized quantum measurements on finite dimensional systems known as local operations and classical communication locc while locc emerges as the natural class of operations in many important quantum information tasks its mathematical structure is complex and difficult to characterize here we provide a precise description of locc and related operational classes in terms of quantum instruments our formalism captures both finite round protocols as well as those that utilize an unbounded number of communication rounds while the set of locc is not topologically closed we show that finite round locc constitutes a compact subset of quantum operations additionally we show the existence of an open ball around the completely depolarizing map that consists entirely of locc implementable maps finally we demonstrate a two qubit map whose action can be approached arbitrarily close using locc but nevertheless cannot be implemented perfectly

vector one way wave absorbing boundary conditions for fem applications in the paper a derivation is presented which leads to a new and general class of vector absorbing boundary conditions abcs for use with the finite element method fem the derivation is based on a vector one way wave equation and a polynomial approximation of the vector radical it is shown that wide angle absorbing boundary conditions as proposed in halpern and trefethen 1988 for optimal absorption of out going waves can be obtained in vector form vector plane waves are used to evaluate the accuracy and the reflection performance of these boundary conditions in a wide range of incidence angles the implementation of the vector abcs in a fem formulation is also provided to show how up to the fifth order absorbing accuracy can be achieved with derivatives only up to the second order a possible formulation is described which not only yields a third order accuracy with first order derivatives but also retains the symmetry of the fem matrix

exact surface impedance admittance boundary conditions for complex geometries theory and applications a methodology useful to derive exact and higher order surface impedance admittance boundary conditions hoi abc s for complex geometries is presented it is shown that exact surface boundary conditions are always expressed through dyadic integral operators involving the tangential magnetic and electric fields all over the surface of the body quasi local surface boundary conditions that include curvature effects are shown to be computable through an asymptotic approximation of the integral operators finally an example of a surface admittance boundary condition useful to analyze a structure exhibiting discontinuities along its surface boundary is presented practical examples to demonstrate the feasibility of the proposed methodology as well as the accuracy of the resulting surface boundary conditions are also presented

a sufficient and necessary condition for 2n 1 orthogonal states to be locally distinguishable in a c2 cn system we investigate the local distinguishability of a set of orthogonal states on c2 cn by mathematical induction we prove that a set of 2n 1 orthogonal states on c2 cn can be locally discriminated by local operation and classical communication if and only if at most one of them is entangled that is the sum of schmidt rank of these states should be no greater than the total hilbert space dimension 2n furthermore we give some discussion about locally distinguishing any number of orthogonal states on c2 cn and explain why this schmidt rank criterion cannot be generalized to locally discriminate any number of orthogonal states

saddle point in the minimax converse for channel coding a minimax metaconverse has recently been proposed as a simultaneous generalization of a number of classical results and a tool for the nonasymptotic analysis in this paper it is shown that the order of optimizing the input and output distributions can be interchanged without affecting the bound in the course of the proof a number of auxiliary results of separate interest are obtained in particular it is shown that the optimization problem is convex and can be solved in many cases by the symmetry considerations as a consequence it is demonstrated that in the latter cases the multiletter input distribution in information spectrum verdu han converse bound can be taken to be a memoryless product of single letter ones a tight converse for the binary erasure channel is rederived by computing the optimal nonproduct output distribution for discrete memoryless channels a conjecture of poor and verdu regarding the tightness of the information spectrum bound on the error exponents is resolved in the negative concept of the channel symmetry group is established and relations with the definitions of symmetry by gallager and dobrushin are investigated