analysis of one dimensional helmholtz equation with pml boundary in this paper the linear conforming finite element method for the one dimensional berenger s pml boundary is investigated and well posedness of the given equation is discussed furthermore optimal error estimates and stability in the l 2 or h 1 norm are derived under the assumption that h h email protected 2 and h email protected 3 are sufficiently small where h is the mesh size and w denotes a fixed frequency numerical examples are presented to validate the theoretical error bounds

the adaptive computation of far field patterns by a posteriori error estimation of linear functionals this paper is concerned with the derivation of a priori and a posteriori error bounds for a class of linear functionals arising in electromagnetics which represent the far field pattern of the scattered electromagnetic field the a posteriori error bound is implemented into an adaptive finite element algorithm and a series of numerical experiments is presented

a tensor product finite element method for the diffraction grating problem with transparent boundary conditions abstract we consider the diffraction grating problem in optics which has been modeled by a boundary value problem governed by a helmholtz equation with transparent boundary conditions a tensor product finite element method is proposed to numerically solve the problem an fft based matrix decomposition algorithm is developed to solve the linear system arising in the vertically layered medium case which can be used as a preconditioning technique for the general case numerical examples are presented to illustrate the accuracy and efficiency of the method

a posteriori error analysis for the conical diffraction problem abstract maxwell s equations for conical diffraction can be reduced to a system of two helmholtz equations in r 2 coupled via quasi periodic transmission conditions on a set of piecewise smooth interfaces a finite element formulation of the conical diffraction problem is presented in a bounded domain by introducing the nonlocal boundary operators an a posteriori error estimate is established when the truncation of the nonlocal boundary operators takes place as our work in wang et al 2015 a duality argument is applied to overcome the difficulty caused by the fact that the truncated pseudo differential mapping does not converge to the original pseudo differential mapping in its operator norm the a posteriori error estimate consists of two parts finite element discretization error and the truncation error of the nonlocal boundary operators in particular the truncation error is exponentially decaying with respect to the truncation parameter

an adaptive finite element method with perfectly matched absorbing layers for the wave scattering by periodic structures we develop a finite element adaptive strategy with error control for the wave scattering by periodic structures the unbounded computational domain is truncated to a bounded one by an extension of the perfectly matched layer pml technique which attenuates both the outgoing and evanescent waves in the pml region pml parameters such as the thickness of the layer and the medium property are determined through sharp a posteriori error estimates numerical experiments are included to illustrate the competitive behavior of the proposed adaptive method

an adaptive multilevel method for time harmonic maxwell equations with singularities we develop an adaptive edge finite element method based on reliable and efficient residual based a posteriori error estimates for low frequency time harmonic maxwell equations with singularities the resulting discrete problem is solved by the multigrid preconditioned minres minimum residual iteration algorithm we demonstrate the efficiency and robustness of the proposed method by extensive numerical experiments for cavity problems with singular solutions which include in particular scattering over screens

adaptive galerkin methods with error control for a dynamical ginzburg landau model in superconductivity the time dependent ginzburg landau model which describes the phase transitions taking place in superconductors is a coupled system of nonlinear parabolic equations it is discretized semi implicitly in time and in space via continuous piecewise linear finite elements a posteriori error estimates are derived for the l infty l 2 norm by studying a dual problem of the linearization of the original system other than the dual of error equations numerical simulations are included which illustrate the reliability of the estimators and the flexibility of the proposed adaptive method

a least squares non polynomial finite element method for solving the polygonal line grating problem abstract this paper is concerned with the diffraction by a polygonal line grating using the fourier bessel functions that capture the singularities at corners and representing the diffraction field towards infinity by a truncation of the rayleigh expansion we propose a least squares finite element method for solving the problem we analyze the convergence and give an error estimate for the method numerical experiments are also presented to show the effectiveness of our method

an adaptive finite element method for the h ψ formulation of time dependent eddy current problems in this paper we develop an adaptive finite element method based on reliable and efficient a posteriori error estimates for the h formulation of eddy current problems with multiply connected conductors multiply connected domains are considered by making cuts the competitive performance of the method is demonstrated by an engineering benchmark problem team workshop problem 7 and a singular problem with analytic solution

a semidefinite program for distillable entanglement we show that the maximum fidelity obtained by a positive partial transpose p p t distillation protocol is given by the solution to a certain semidefinite program this gives a number of new lower and upper bounds on p p t distillable entanglement and thus new upper bounds on 2 locally distillable entanglement in the presence of symmetry the semidefinite program simplifies considerably becoming a linear program in the case of isotropic and werner states using these techniques we determine the p p t distillable entanglement of asymmetric werner states and maximally correlated states we conclude with a discussion of possible applications of semidefinite programming to quantum codes and 1 local distillation

numerical analysis of a pml model for time dependent maxwell s equations in this paper we study a perfectly matched layer model for the three dimensional time dependent maxwell s equations we develop both semi and fully discrete finite element methods for solving the truncated pml problem by nedelec edge elements optimal convergence rates are proved for both semi and fully discrete schemes to our knowledge this is the first error analysis obtained for time domain finite element method for pml models

perfectly matched layers for diffraction gratings in inhomogeneous media stability and error estimates we study the scattering of acoustic or electromagnetic waves at diffraction gratings in inhomogeneous media the refractive index stabilizes to 1 as the distance to the grating increases outgoing solutions are characterized by means of the limiting absorption principle we prove the unique solvability of the problem with perfectly matched layer of finite length further we show that solutions of the latter problem approximate outgoing solutions of the original problem with an error that exponentially tends to zero as the length of perfectly matched layer tends to infinity contribution of eigenvalues and resonances to the error of approximation is clarified

discontinuous galerkin methods for the helmholtz equation with large wave number this paper develops and analyzes some interior penalty discontinuous galerkin ipdg methods using piecewise linear polynomials for the helmholtz equation with the first order absorbing boundary condition in two and three dimensions it is proved that the proposed discontinuous galerkin methods are stable hence well posed without any mesh constraint for each fixed wave number k optimal order with respect to h error estimate in the broken h 1 norm and suboptimal order estimate in the l 2 norm are derived without any mesh constraint the latter estimate improves to optimal order when the mesh size h is restricted to the preasymptotic regime i e k 2 h gtrsim 1 numerical experiments are also presented to gauge the theoretical result and to numerically examine the pollution effect with respect to k in the error bounds the novelties of the proposed ipdg methods include the following first the methods penalize not only the jumps of the function values across the element edges but also the jumps of the normal and tangential derivatives second the penalty parameters are taken as complex numbers of positive imaginary parts so essentially and practically no constraint is imposed on the penalty parameters since the helmholtz problem is a non hermitian and indefinite linear problem as expected the crucial and the most difficult part of the whole analysis is to establish the stability estimates i e a priori estimates for the numerical solutions to this end the cruxes of our analysis are to establish and to make use of a local version of the rellich identity for the laplacian and to mimic the stability analysis for the pde solutions given in p cummings analysis of finite element based numerical methods for acoustic waves elastic waves and fluid solid interactions in the frequency domain ph d thesis the university of tennessee knoxville tn 2001 p cummings and x feng math models methods appl sci 16 2006 pp 139 160 u hetmaniuk commun math sci 5 2007 pp 665 678

game theoretic characterization of antidegradable channels we introduce a guessing game involving a quantum channel three parties the sender the receiver and an eavesdropper eve and a quantum public side channel we prove that a necessary and sufficient condition for the quantum channel to be antidegradable is that eve wins the game we thus obtain a complete operational characterization of antidegradable channels in a game theoretic framework

additivity for unital qubit channels additivity of the holevo capacity is proved for product channels under the condition that one of the channels is a unital qubit channel with the other completely arbitrary as a byproduct this proves that the holevo bound is the classical information capacity of such qubit channels and provides an explicit formula for this classical capacity additivity of minimal entropy and multiplicativity of p norms are also proved under the same assumptions the proof relies on a new bound for the p norm of an output state from the half noisy phase damping channel

adaptive finite element frequency domain method for eddy current problems in the present paper adaptive finite element methods are studied for time harmonic eddy current problems in the case of three dimensional isotropic and linear materials we adopt the formulation based on the magnetic field and a magnetic scalar potential in this paper since it needs the least number of unknowns reliable and efficient a posteriori error estimates are obtained and the efficiency of the adaptive algorithm is demonstrated by numerical and engineering experiments

on the logic foundation of fuzzy reasoning abstract fuzzy reasoning and fuzzy formal deduction theory are two closely related subjects and each of them has been investigated by many researchers unfortunately it seems that the two branches have not been successfully connected the aim of this paper is to establish a so called quasi propositional deductive system syntactically as well as semantically and then set a logic foundation for developing the theory of fuzzy reasoning therefrom

private capacity of quantum channels is not additive recently there has been considerable activity on the subject of the additivity of various quantum channel capacities here we construct a family of channels with a sharply bounded classical and hence private capacity on the other hand their quantum capacity when combined with a zero private and zero quantum capacity erasure channel becomes larger than the previous classical capacity as a consequence we can conclude for the first time that the classical private capacity is nonadditive in fact in our construction even the quantum capacity of the tensor product of two channels can be greater than the sum of their individual classical private capacities we show that this violation occurs quite generically every channel can be embedded into our construction and a violation occurs whenever the given channel has a larger entanglement assisted quantum capacity than unassisted classical capacity

randomizing quantum states constructions and applications the construction of a perfectly secure private quantum channel in dimension d is known to require 2 log d shared random key bits between the sender and receiver we show that if only near perfect security is required the size of the key can be reduced by a factor of two more specifically we show that there exists a set of roughly d log d unitary operators whose average effect on every input pure state is almost perfectly randomizing as compared to the d2 operators required to randomize perfectly aside from the private quantum channel variations of this construction can be applied to many other tasks in quantum information processing we show for instance that it can be used to construct locc data hiding schemes for bits and qubits that are much more efficient than any others known allowing roughly log d qubits to be hidden in 2 log d qubits the method can also be used to exhibit the existence of quantum states with locked classical correlations an arbitrarily large amplification of the correlation being accomplished by sending a negligibly small classical key our construction also provides the basic building block for a method of remotely preparing arbitrary d dimensional pure quantum states using approximately log d bits of communication and log d ebits of entanglement

the capacity of the quantum depolarizing channel the information carrying capacity of the d dimensional depolarizing channel is computed it is shown that this capacity can be achieved by encoding messages as products of pure states belonging to an orthonormal basis of the state space and using measurements which are products of projections onto this same orthonormal basis in other words neither entangled signal states nor entangled measurements give any advantage for information capacity the result follows from an additivity theorem for the product channel spl delta spl ominus spl psi where spl delta is the depolarizing channel and spl psi is a completely arbitrary channel we establish the amosov holevo werner see probl inform transm vol 36 p 305 313 2000 p norm conjecture for this product channel for all p spl ges 1 and deduce from this the additivity of the minimal entropy and of the holevo quantity spl chi sup

an adaptive edge element method with perfectly matched absorbing layers for wave scattering by biperiodic structures an edge element adaptive strategy with error control is developed for wave scattering by biperiodic structures the unbounded computational domain is truncated to a bounded one by a perfectly matched layer pml technique the pml parameters such as the thickness of the layer and the medium properties are determined through sharp a posteriori error estimates numerical experiments are presented to illustrate the competitive behavior of the proposed adaptive method

pml method for electromagnetic scattering problem in a two layer medium the perfectly matched layer pml method is well studied for acoustic scattering problems electromagnetic scattering problems and more recently elastic scattering problems with homogeneous background media the purpose of this paper is to present the stability and exponential convergence of the pml method for a three dimensional electromagnetic scattering problem in a two layer medium the main contributions of this paper are threefold first we establish the well posedness of the original scattering problem for any dirichlet boundary value in boldsymbol h 1 2 rm div gamma d where gamma d stands for the boundary of the scatterer second we propose a new weak formulation for the original problem where the dirichlet to neumann operator is proposed on a truncation boundary inside the pml this argument is favorable in the analysis of the pml dirichlet to neumann operator the inf sup condition is proved for the bilinear form third we establish the well posedness of the pml problem a

classical communication over a quantum interference channel calculating the capacity of interference channels is a notorious open problem in classical information theory such channels have two senders and two receivers and each sender would like to communicate with a partner receiver the capacity of such channels is known exactly in the settings of very strong and strong interference while the han kobayashi coding strategy gives the best known achievable rate region in the general case here we introduce and study the quantum interference channel a natural generalization of the interference channel to the setting of quantum information theory we restrict ourselves for the most part to channels with two classical inputs and two quantum outputs in order to simplify the presentation of our results though generalizations of our results to channels with quantum inputs are straightforward we are able to determine the exact classical capacity of this channel in the settings of very strong and strong interference by exploiting winter s successive decoding strategy and a novel two sender quantum simultaneous decoder respectively we provide a proof that a han kobayashi strategy is achievable with holevo information rates up to a conjecture regarding the existence of a three sender quantum simultaneous decoder this conjecture holds for a special class of quantum multiple access channels with average output states that commute and we discuss some other variations of the conjecture that hold finally we detail a connection between the quantum interference channel and prior work on the capacity of bipartite unitary gates

adaptive perfectly matched layer method for multiple scattering problems a uniaxial perfectly matched layer upml method is proposed for solving three dimensional helmholtz equation with multiple scatterers the exterior domain is truncated to enclose each scatterer by a bounded domain individually based on reliable a posteriori error estimate an efficient adaptive finite element algorithm is proposed to solve the multiple scattering problem the efficiency of the adaptive pml method is demonstrated by extensive numerical experiments

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

integrated semantics and logic metric spaces the concept of tautology degree of an abstract proposition is proposed in this paper by means of integral of the corresponding function with respect to certain semantics over 0 1 then a pseudo metric among abstract propositions is introduced and the r logic metric space is proposed where r is a suitable implication operator finally a new theoretical framework for approximate reasoning in the r logic metric space is provided

the capacity of the quantum channel with general signal states it is shown that the capacity of a classical quantum channel with arbitrary possibly mixed states equals the maximum of the entropy bound with respect to all a priori distributions this completes the recent result of hausladen jozsa schumacher westmoreland and wootters 1996 who proved the equality for the pure state channel

near field imaging of infinite rough surfaces this paper is concerned with an inverse rough surface scattering problem in near field optical imaging which is to reconstruct the scattering surface with a resolution beyond the diffraction limit the surface is assumed to be a small and smooth deformation of a plane surface based on a transformed field expansion the boundary value problem with complex scattering surface is converted into a successive sequence of two point boundary value problems in the frequency domain where an analytic solution for the direct scattering problem is derived from the method of integrated solution by neglecting the high order terms in the power series expansion the nonlinear inverse problem is linearized and an explicit inversion formula is obtained a spectral cut off regularization is adopted to suppress the exponential growth of the noise in the evanescent wave components which carry high spatial frequency of the scattering surface and contribute to the superresolution in the near field regime the method works f

fuzzy logic and the calculi of fuzzy rules fuzzy graphs and fuzzy probabilities the past few years have witnessed a rapid growth in the number and variety of applications of fuzzy logic ranging from consumer products and industrial process control to medical instrumentation information systems and decision analysis the foundations of fuzzy logic have become firmer and its impact within the basic sciences and especially in mathematical and physical sciences has become more visible and more substantive and yet there are still many misconceptions about the aims of fuzzy logic and misjudgments of its strengths and limitations one of the common misconceptions is rooted in semantics as a label fuzzy logic fl has two different meanings more specifically in a narrow sense fuzzy logic fln is a logical system which aims at a formalization of approximate reasoning in this sense fuzzy logic is an extension of multivalued logic but its agenda is quite different from that of conventional multivalued systems in a wide sense fuzzy logic flw is coextensive with fuzzy set theory fst flw is far broader than fln and contains fln as one of its branches today the term fuzzy logic is used predominantly in its wide sense thus effectively fl flw fst another important point is that any field x can be fuzzified by replacing crisp sets in x by fuzzy sets for example through fuzzification arithmetic can be generalized to fuzzy arithmetic topology to fuzzy topology control theory to fuzzy control theory etc in this perspective the calculi of fuzzy rules cfr fuzzy graphs cfg and fuzzy probabilities cfp may be viewed as generalizations of the calculi of rules graphs and probabilities the importance of cfr cfg and cfp derives from the fact that they play a central role in most of the applications of fl in particular the calculus of fuzzy graphs which is a subset of the calculus of fuzzy rules accounts for most of the applications of fuzzy logic in control systems analysis and related fields central to the calculus of fuzzy rules is a language referred to as the fuzzy dependency and command language fdcl the syntax of fdcl is concerned with the form of rules while the semantics of fdcl is concerned with their meaning an important issue in cfr is that of the induction of rules from observations in cfg a fuzzy graph is defined as the disjunction of cartesian products of fuzzy sets in effect a fuzzy graph may be viewed as a compressed representation of a functional or relational dependence operations on fuzzy graphs play an important role in cfg in the calculus of fuzzy probabilities probabilities are assumed to be represented as fuzzy rather than crisp numbers in a related way probability distributions are represented as fuzzy graphs a major aim of cfp is to provide a framework for linguistic decision analysis a type of qualitative analysis in which fuzzy numbers and fuzzy graphs are employed to represent both probabilities and utilities in an essential way the methodologies of fuzzy rules fuzzy graphs and fuzzy probabilities reflect the fact that 1 a imprecision and uncertainty are pervasive and 2 b precision and certainty carry a cost in the final analysis the principal aim of these methodologies is to exploit the tolerance for imprecision and uncertainty to achieve tractability robustness and low solution cost

an adaptive perfectly matched layer technique for 3 d time harmonic electromagnetic scattering problems an adaptive perfectly matched layer pml technique for solving the time harmonic electromagnetic scattering problems is developed the pml parameters such as the thickness of the layer and the fictitious medium property are determined through sharp a posteriori error estimates combined with the adaptive finite element method the adaptive pml technique provides a complete numerical strategy to solve the scattering problem in the framework of fem which produces automatically a coarse mesh size away from the fixed domain and thus makes the total computational costs insensitive to the thickness of the pml absorbing layer numerical experiments are included to illustrate the competitive behavior of the proposed adaptive method

variational approximation of maxwell s equations in biperiodic structures consider a plane wave incident on a biperiodic diffractive structure the diffraction problem may be modeled by maxwell s equations with transparent boundary conditions and solved by a finite element method in this paper a variational approximation is studied the well posedness of the continuous and discretized problems is established in the following sense in the continuous case it is shown that the model problem attains a unique cal h 1 solution for all but possibly a discrete set of frequencies in the discrete case error estimates for the variational finite element approximation of the model problem with or without truncation of the nonlocal boundary operators are obtained

potential capacities of quantum channels we introduce potential capacities of quantum channels in an operational way and provide upper bounds for these quantities which quantify the ultimate limit of usefulness of a channel for a given task in the best possible context unfortunately except for a few isolated cases potential capacities seem to be as hard to compute as their plain analogues we thus study upper bounds on some potential capacities for the classical capacity we give an upper bound in terms of the entanglement of formation to establish a bound for the quantum and private capacity we first lift the channel to a hadamard channel and then prove that the quantum and private capacity of a hadamard channel is strongly additive implying that for these channels potential and plain capacity are equal employing these upper bounds we show that if a channel is noisy however close it is to the noiseless channel then it cannot be activated into the noiseless channel by any other contextual channel this conclusion holds for all the three capacities we also discuss the so called environment assisted quantum capacity because we are able to characterize its potential version

on the capacities of bipartite hamiltonians and unitary gates we consider interactions as bidirectional channels we investigate the capacities for interaction hamiltonians and nonlocal unitary gates to generate entanglement and transmit classical information we give analytic expressions for the entanglement generating capacity and entanglement assisted one way classical communication capacity of interactions and show that these quantities are additive so that the asymptotic capacities equal the corresponding 1 shot capacities we give general bounds on other capacities discuss some examples and conclude with some open questions

a dispersion minimizing finite difference scheme and preconditioned solver for the 3d helmholtz equation in this paper a new 27 point finite difference method is presented for solving the 3d helmholtz equation with perfectly matched layer pml which is a second order scheme and pointwise consistent with the equation an error analysis is made between the numerical wavenumber and the exact wavenumber and a refined choice strategy based on minimizing the numerical dispersion is proposed for choosing weight parameters a full coarsening multigrid based preconditioned bi cgstab method is developed for solving the linear system stemming from the helmholtz equation with pml by the finite difference scheme the shifted laplacian is extended to precondition the 3d helmholtz equation and a spectral analysis is given the discrete preconditioned system is solved by the bi cgstab method with a multigrid method used to invert the preconditioner approximately full coarsening multigrid is employed and a new matrix based prolongation operator is constructed accordingly numerical results are presented to demonstrate the efficiency of both the new 27 point finite difference scheme with refined parameters and the preconditioned bi cgstab method with the 3d full coarsening multigrid

an adaptive finite element method for the diffraction grating problem with transparent boundary condition the diffraction grating problem is modeled by a boundary value problem governed by a helmholtz equation with transparent boundary conditions an a posteriori error estimate is derived when the truncation of the nonlocal boundary operators takes place to overcome the difficulty caused by the fact that the truncated dirichlet to neumann dtn mapping does not converge to the original dtn mapping in its operator norm a duality argument without assuming more regularity than the weak solution is applied the a posteriori error estimate consists of two parts the finite element discretization error and the truncation error of boundary operators which decays exponentially with respect to the truncation parameter based on the a posteriori error control a finite element adaptive strategy is established for the diffraction grating problem such that the truncation parameter is determined through the truncation error and the mesh elements for local refinements are marked through the finite element discretization

social optimality in quantum bayesian games a b s t r a c t a significant aspect of the study of quantum strategies is the exploration of the gametheoretic solution concept of the nash equilibrium in relation to the quantization of a game pareto optimality is a refinement on the set of nash equilibria a refinement on the set of pareto optimal outcomes is known as social optimality in which the sum of players payoffs is maximized this paper analyzes social optimality in a bayesian game that uses the setting of generalized einstein podolsky rosen experiments for its physical implementation we show that for the quantum bayesian game a direct connection appears between the violation of bell s inequality and the social optimal outcome of the game and that it attains a superior socially optimal outcome

the generalized truth degree of quantitative logic in the logic system l n n valued nm logic system the concept of the truth degree of a formula is the crucial tool and the building block in quantitative logic from which the concept of logic metric in quantitative logic is derived logic metric takes an important role in quantitative logic related to which are other concepts in quantitative logic such as divergence consistency etc in the present paper having combined the theory of generalized tautologies with the theory of truth degrees in quantitative logic we have proposed the theory of s c truth degrees of formulas related to theory c in the logic system l n n valued nm logic system and discussed some of its properties with the help of the properties of s c truth degrees t c a email protected c a b email protected c b we have obtained the c logic metric on the set f s of formulas in the propositional logic system l n n valued nm logic system by the work of this paper we can generalize the theory of quantitative logic in all round way and establish an approximate reasoning s framework related to theory c in the logic system l n n valued nm logic system

approximate degradable quantum channels degradable quantum channels are an important class of completely positive trace preserving maps among other properties they offer a single letter formula for the quantum and the private classical capacity and are characterized by the fact that a complementary channel can be obtained from the channel by applying a degrading channel in this paper we introduce the concept of approximate degradable channels which satisfy this condition up to some finite varepsilon geq 0 that is there exists a degrading channel which upon composition with the channel is varepsilon close in the diamond norm to the complementary channel we show that for any fixed channel the smallest such varepsilon can be efficiently determined via a semidefinite program moreover these approximate degradable channels also approximately inherit all other properties of degradable channels as an application we derive improved upper bounds to the quantum and private classical capacity for certain channels of interest in quantum communication

clean positive operator valued measures in quantum mechanics the statistics of the outcomes of a measuring apparatus is described by a positive operator valued measure povm a quantum channel transforms povms into povms generally irreversibly thus losing some of the information retrieved from the measurement this poses the problem of which povms are undisturbed i e they are not irreversibly connected to another povm we will call such povms clean in a sense the clean povms would be perfect since they would not have any additional extrinsical noise quite unexpectedly it turns out that such a cleanness property is largely unrelated to the convex structure of povms and there are clean povms that are not extremal and vice versa in this article we solve the cleannes classification problem for number n of outcomes n d d dimension of the hilbert space and we provide a set of either necessary or sufficient conditions for n d along with an iff condition for the case of informationally complete povms for n d2

squashed entanglement an additive entanglement measure in this paper we present a new entanglement monotone for bipartite quantum states its definition is inspired by the so called intrinsic information of classical cryptography and is given by the halved minimum quantum conditional mutual information over all tripartite state extensions we derive certain properties of the new measure which we call squashed entanglement it is a lower bound on entanglement of formation and an upper bound on distillable entanglement furthermore it is convex additive on tensor products and superadditive in general continuity in the state is the only property of our entanglement measure which we cannot provide a proof for we present some evidence however that our quantity has this property the strongest indication being a conjectured fannes type inequality for the conditional von neumann entropy this inequality is proved in the classical case

pretty strong converse for the quantum capacity of degradable channels we exhibit a possible road toward a strong converse for the quantum capacity of degradable channels in particular we show that all degradable channels obey what we call a pretty strong converse when the code rate increases above the quantum capacity the fidelity makes a discontinuous jump from 1 to at most 1 2 asymptotically a similar result can be shown for the private classical capacity furthermore we can show that if the strong converse holds for symmetric channels which have quantum capacity zero then degradable channels obey the strong converse the above mentioned asymptotic jump of the fidelity at the quantum capacity then decreases from 1 to 0

optimizing the perfectly matched layer the berenger perfectly matched layer or pml 4 3 is used in computational electromagnetism as a sponge layer to terminate finite element approximations of scattering problems an infinite perfectly matched layer creates no reflection for incident waves of any frequency or any incident direction and the waves decay exponentially in magnitude into the layer this property is lost when the layer is truncated since the truncation boundary generates a reflected wave discretization of the differential equations further changes the reflection coefficient of the layer in this talk we shall describe the pml in the simple case of a two dimensional electromagnetic problem the first part of this abstract is expository we shall show how to derive the layer using a change of variable approach 5 9 6 after this derivation we describe some new analysis to show the effects of truncating and discretizing the pml 9 we end by showing how to compute an optimal layer and make some remarks about pml for the full maxwell system

numerical solution of nonlinear diffraction problems an adaptive finite element method is developed for solving maxwell s equations in a nonlinear periodic structure the medium or computational domain is truncated by a perfect matched layer pml technique error estimates are established numerical examples are provided which illustrate the efficiency of the method

entanglement assisted capacity of a quantum channel and the reverse shannon theorem the entanglement assisted classical capacity of a noisy quantum channel c sub e is the amount of information per channel use that can be sent over the channel in the limit of many uses of the channel assuming that the sender and receiver have access to the resource of shared quantum entanglement which may be used up by the communication protocol we show that the capacity c sub e is given by an expression parallel to that for the capacity of a purely classical channel i e the maximum over channel inputs spl rho of the entropy of the channel input plus the entropy of the channel output minus their joint entropy the latter being defined as the entropy of an entangled purification of spl rho after half of it has passed through the channel we calculate entanglement assisted capacities for two interesting quantum channels the qubit amplitude damping channel and the bosonic channel with amplification attenuation and gaussian noise we discuss how many independent parameters are required to completely characterize the asymptotic behavior of a general quantum channel alone or in the presence of ancillary resources such as prior entanglement in the classical analog of entanglement assisted communication communication over a discrete memoryless channel dmc between parties who share prior random information we show that one parameter is sufficient i e that in the presence of prior shared random information all dmcs of equal capacity can simulate one another with unit asymptotic efficiency

a posteriori error indicators for maxwell s equations abstract in this paper we shall analyze a class of a posteriori error indicators for an electromagnetic scattering problem for maxwell s equations in the presence of a bounded inhomogeneous and anisotropic scatterer problems of this type arise when computing the interaction of electromagnetic radiation with biological tissue we briefly recall existence and uniqueness theory associated with this problem then we show how a posteriori error indicators can be derived using an adjoint equation approach the error indicators use both the jump in normal and tangential components of the field across faces in the mesh

on quantum fidelities and channel capacities for the discrete memoryless quantum channel we show the equivalence of two different notions of quantum channel capacity that which uses the entanglement fidelity as its criterion for success in transmission and that which uses the minimum fidelity of pure states in a subspace of the input hilbert space as its criterion as a corollary any source with entropy rate less than the capacity may be transmitted with high entanglement fidelity we also show that a restricted class of encodings is sufficient to transmit any quantum source which may be transmitted on a given channel this enables us to simplify a known upper bound for the channel capacity it also enables us to show that the availability of an auxiliary classical channel from encoder to decoder does not increase the quantum capacity

on equivalent forms of fuzzy logic systems nm and imtl the nilpotent minima are important t norms in fuzzy logic and fuzzy reasoning two interesting formal systems nilpotent minimum logic nm and l based on nilpotent minima have been proposed and have been intensively studied in this paper their equivalence is pointed out moreover coincidence of two related algebraic structures nm and r0 algebras is also proved in addition we give an equivalent form of involutive monoidal t norm based logic imtl

on the efficiency of adaptive finite element methods for elliptic problems with discontinuous coefficients the successful implementation of adaptive finite element methods based on a posteriori error estimates depends on several ingredients an a posteriori error indicator a refinement coarsening strategy and the choice of various parameters the objective of the paper is to examine the influence of these factors on the performance of adaptive finite element methods for a model problem the linear elliptic equation with strongly discontinuous coefficients we derive a new a posteriori error estimator which depends locally on the oscillations of the coefficients around singular points extensive numerical experiments are reported to support our theoretical results and to show the competitive behaviors of the proposed adaptive algorithm

data oscillation and convergence of adaptive fem data oscillation is intrinsic information missed by the averaging process associated with finite element methods fem regardless of quadrature ensuring a reduction rate of data oscillation together with an error reduction based on a posteriori error estimators we construct a simple and efficient adaptive fem for elliptic partial differential equations pdes with linear rate of convergence without any preliminary mesh adaptation nor explicit knowledge of constants any prescribed error tolerance is thus achieved in a finite number of steps a number of numerical experiments in two and three dimensions yield quasi optimal meshes along with a competitive performance

potential output purity of completely positive maps the notion of potential output purity of a completely positive map is introduced as a generalization of the regularized output purity an upper bound is derived for this quantity and for several classes of maps including cq classical quantum qc quantum classical hadamard channels it is shown that potential purity does not exceed the standard output purity as an application the potential purity is used to bound the logarithmic sobolev constant of a product of depolarizing channel semigroups

cryptographic distinguishability measures for quantum mechanical states this paper mostly expository in nature surveys four measures of distinguishability for quantum mechanical states this is done from the point of view of the cryptographer with a particular eye on applications in quantum cryptography each of the measures considered is rooted in an analogous classical measure of distinguishability for probability distributions namely the probability of an identification error the kolmogorov distance the bhattacharyya coefficient and the shannon 1948 distinguishability as defined through mutual information these measures have a long history of use in statistical pattern recognition and classical cryptography we obtain several inequalities that relate the quantum distinguishability measures to each other one of which may be crucial for proving the security of quantum cryptographic key distribution in another vein these measures and their connecting inequalities are used to define a single notion of cryptographic exponential indistinguishability for two families of quantum states this is a tool that may prove useful in the analysis of various quantum cryptographic protocols

on converse bounds for classical communication over quantum channels we explore several new converse bounds for classical communication over quantum channels in both the one shot and asymptotic regimes first we show that the matthews wehner meta converse bound for entanglement assisted classical communication can be achieved by activated no signaling assisted codes suitably generalizing a result for classical channels second we derive a new efficiently computable meta converse on the amount of classical information unassisted codes can transmit over a single use of a quantum channel as applications we provide a finite resource analysis of classical communication over quantum erasure channels including the second order and moderate deviation asymptotics third we explore the asymptotic analogue of our new meta converse the upsilon information of the channel we show that its regularization is an upper bound on the classical capacity which is generally tighter than the entanglement assisted capacity and other known efficiently computable strong converse bounds for covariant channels we show that the upsilon information is a strong converse bound

comparison of information structures and completely positive maps a theorem of blackwell about comparison between information structures in classical statistics is given as an analogue in the quantum probabilistic set up the theorem provides an operational interpretation for trace preserving completely positive maps which are the natural quantum analogue of classical stochastic maps the proof of the theorem relies on the separation theorem for convex sets and on quantum teleportation

non fuzzy versions of fuzzy reasoning in classical logics abstract fuzzy reasoning features fuzzy logic in its narrow sense fln and fuzzy modus ponens fmp is the core of fuzzy reasoning as is well known fmp is far more general and complicated than the conventional rule of modus ponens mp and takes the latter as special case under certain conditions this paper proves that there exist non fuzzy versions of fmp in classical 2 valued logic as well as in conventional multivalued systems and reveals the roots of these seemingly surprising results

tight uniform continuity bounds for quantum entropies conditional entropy relative entropy distance and energy constraints we present a bouquet of continuity bounds for quantum entropies falling broadly into two classes first a tight analysis of the alicki fannes continuity bounds for the conditional von neumann entropy reaching almost the best possible form that depends only on the system dimension and the trace distance of the states almost the same proof can be used to derive similar continuity bounds for the relative entropy distance from a convex set of states or positive operators as applications we give new proofs with tighter bounds of the asymptotic continuity of the relative entropy of entanglement er and its regularization e r infty as well as of the entanglement of formation ef using a novel quantum coupling of density operators which may be of independent interest we extend the latter to an asymptotic continuity bound for the regularized entanglement of formation aka entanglement cost e c e f infty second we derive analogous continuity bounds for the von neumann entropy and conditional entropy in infinite dimensional systems under an energy constraint most importantly systems of multiple quantum harmonic oscillators while without an energy bound the entropy is discontinuous it is well known to be continuous on states of bounded energy however a quantitative statement to that effect seems not to have been known here under some regularity assumptions on the hamiltonian we find that quite intuitively the gibbs entropy at the given energy roughly takes the role of the hilbert space dimension in the finite dimensional fannes inequality

the time harmonic maxwell equations in a doubly periodic structure abstract consider the diffraction of a beam of particles in r 3 when the dielectric coefficient is a constant e1 above a surface s and a different constant e2 below s and the magnetic permeability is constant throughout r 3 s is assumed to be a doubly periodic surface say z f x y with f x ml1 y nl2 f x y for integers m n the existence and uniqueness of a solution satisfying a radiation condition at infinity is reduced to a system of fredholm equations thus for all but a discrete set of e s there exists a unique solution

unified forms of triple i method first the present paper provides unified forms of triple i method for fuzzy modus ponens and fuzzy modus tollens of which diverse implication operators can be employed second it is clarified that in a sense zadeh s cri method for fuzzy modus ponens can be brought into line with the unified form of the triple i method lastly a unified form of a triple i method is established as well and a duality result concerning a triple i solutions of fuzzy modus ponens and fuzzy modus tollens is obtained

asymptotic properties of nearly unstable multivariate ar processes abstract nearly unstable multidimensional ar models are studied where the coefficient matrices are given in jordan normal form weak convergence of the sequence of the appropriately normalized lses of the coefficient matrices is proved a natural connection between the discrete and the corresponding continuous time models is presented

analysis of the rigorous coupled wave approach for p polarized light in gratings abstract we study the convergence properties of the two dimensional rigorous coupled wave approach rcwa for s polarized monochromatic incident light the rcwa is widely used to solve electromagnetic boundary value problems where the relative permittivity varies periodically in one direction i e scattering by a grating this semi analytical approach expands all the electromagnetic field phasors as well as the relative permittivity as fourier series in the spatial variable along the direction of periodicity and also replaces the relative permittivity with a stairstep approximation along the direction normal to the direction of periodicity thus there is error due to fourier truncation and also due to the approximation of grating permittivity we prove that the rcwa is a galerkin scheme which allows us to employ techniques borrowed from the finite element method to analyze the error an essential tool is a rellich identity that shows that certain continuous problems have unique solutions that depend continuously on the data with a continuity constant having explicit dependence on the relative permittivity we prove that the rcwa converges with an increasing number of retained fourier modes and with a finer approximation of the grating interfaces numerical results show that our convergence results for increasing the number of retained fourier modes are seen in practice while our estimates of convergence in slice thickness are pessimistic

the r0 type fuzzy logic metric space and an algorithm for solving fuzzy modus ponens fuzzy modus ponens briefly fmp is the most fundamental form of fuzzy reasoning and has been extensively discussed by diverse researchers the aim of the present paper is to propose a formalized form of fmp called generalized modus ponens in the fuzzy logic system l and solve it in l and then provide its numerical version as a new algorithm for solving fmp as a preparation some related questions such as what is a fuzzy logic metric space why is r 0 implication operator selected and what kind of merits does the fuzzy pseudo metric logic space f s r possess etc are analyzed

monoidal t norm based logic towards a logic for left continuous t norms hajek s bl logic is the fuzzy logic capturing the tautologies of continuous t norms and their residua in this paper we investigate a weaker logic mtl which is intended to cope with the tautologies of left continuous t norms and their residua the corresponding algebraic structures mtl algebras are defined and completeness of mtl with respect to linearly ordered mtl algebras is proved besides several schematic extensions of mtl are also considered as well as their corresponding predicate calculi

heralded channel holevo superadditivity bounds from entanglement monogamy we introduce a class of channels called heralded channels which generalize the quantum erasure channel composed with an arbitrary other quantum channel we show that monogamy of squashed entanglem

an adaptive perfectly matched layer technique for time harmonic scattering problems we develop an adaptive perfectly matched layer pml technique for solving the time harmonic scattering problems the pml parameters such as the thickness of the layer and the fictitious medium property are determined through sharp a posteriori error estimates the derived finite element a posteriori estimate for adapting meshes has the nice feature that it decays exponentially away from the boundary of the fixed domain where the pml layer is placed this property makes the total computational costs insensitive to the thickness of the pml absorbing layers numerical experiments are included to illustrate the competitive behavior of the proposed adaptive method

convergence of the uniaxial perfectly matched layer method for time harmonic scattering problems in two layered media in this paper we propose a uniaxial perfectly matched layer pml method for solving the time harmonic scattering problems in two layered media the exterior region of the scatterer is divided into two half spaces by an infinite plane on two sides of which the wave number takes different values we surround the computational domain where the scattering field is interested by a pml with the uniaxial medium property by imposing homogeneous boundary condition on the outer boundary of the pml we show that the solution of the pml problem converges exponentially to the solution of the original scattering problem in the computational domain as either the pml absorbing coefficient or the thickness of the pml tends to infinity

additivity of the classical capacity of entanglement breaking quantum channels we show that for the tensor product of an entanglement breaking quantum channel with an arbitrary quantum channel both the minimum entropy of an output of the channel and the holevo schumacher westmoreland capacity are additive in addition for the tensor product of two arbitrary quantum channels we give a bound involving entanglement of formation for the amount of subadditivity for minimum entropy output or superadditivity for classical capacity that can occur

the quantum capacity with symmetric side channels in this paper we present an upper bound for the quantum channel capacity that is both additive and convex our bound can be interpreted as the capacity of a channel for high fidelity quantum communication when assisted by a family of channels that have no capacity on their own this family of assistance channels which we call symmetric side channels consists of all channels mapping symmetrically to their output and environment the bound seems to be quite tight and for degradable quantum channels it coincides with the unassisted channel capacity using this symmetric side channel capacity we find new upper bounds on the capacity of the depolarizing channel we also briefly indicate an analogous notion for distilling entanglement using the same class of one way channels yielding one of the few entanglement measures that is monotonic under local operations with one way classical communication 1 locc but not under the more general class of local operations with classical communication locc