on the minimum output entropy of random orthogonal quantum channels we consider the sequences of random quantum channels defined by using the stinespring formula with haar distributed random orthogonal matrices for any fixed sequence of input states we study the asymptotic eigenvalue distribution of the outputs through the tensor powers of random channels we show that the input states achieving minimum output entropy are tensor products of maximally entangled states bell states when the tensor power is even this phenomenon is completely different from the one for random quantum channels constructed from haar distributed random unitary matrices which leads us to formulate some conjectures about the regularized minimum output entropy

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

coexistence does not imply joint measurability one of the hallmarks of quantum theory is the realization that distinct measurements cannot in general be performed simultaneously in stark contrast to classical physics in this context the notions of coexistence and joint measurability are employed to analyze the possibility of measuring together two general quantum observables characterizing different degrees of compatibility between measurements it is known that two jointly measurable observables are always coexistent and that the converse holds for various classes of observables including the case of observables with two outcomes here we resolve in the negative the open question of whether this equivalence holds in general our resolution strengthens the notions of coexistence and joint measurability by showing that both are robust against small imperfections in the measurement setups

intrinsic volumes of symmetric cones and applications in convex programming we express the probability distribution of the solution of a random standard gaussian instance of a convex cone program in terms of the intrinsic volumes and curvature measures of the reference cone we then compute the intrinsic volumes of the cone of positive semidefinite matrices over the real numbers over the complex numbers and over the quaternions in terms of integrals related to mehta s integral in particular we obtain a closed formula for the probability that the solution of a random standard gaussian semidefinite program has a certain rank

discontinuous displacement approximation for capturing plastic localization it is proposed to capture localized plastic deformation via the inclusion of regularized displacement discontinuities at element boundaries interfaces of the finite element subdivision the regularization is based on a kinematic assumption for an interface that resembles that which is pertinent to the classical shear band concept as a by product of the regularization an intrinsic band width is introduced as a constitutive property rather than a geometric feature of the finite element mesh in this way the spurious mesh sensitivity which is obtained when the displacement approximation is continuous can be avoided another consequence is that the interfacial relation between the elements is derived directly from the conventional constitutive properties of the continuously deforming material an interesting feature is that the acoustic tensor will not only play a role for diagnosing discontinuous bifurcation but will also serve as the tangent stiffness tensor of the interface up to within a scalar factor an analytical investigation of the behaviour of the interface is carried out and it is shown that dilatation may indeed accompany slip within a shear band for a general plasticity model the significance of proper mesh alignment is demonstrated for a simple problem in plane strain and plane stress it is shown that a unique structural post peak response in accordance with non linear fracture mechanics can be achieved when the plastic softening modulus is properly related to the bandwidth the paper concludes with a numerical simulation of the gradual development of a shear band in a soil slope

entanglement breaking channels with general outcome operator algebras a unit preserving and completely positive linear map or a channel a ain between c algebras a and ain is called entanglement breaking eb if idb is a separable state for any c algebra b and any state on the injective c tensor product ain b in this paper we establish the equivalence of the following conditions for a channel with a quantum input space and with a general outcome c algebra generalizing the known results in finite dimensions i is eb ii has a measurement prepare form holevo form iii n copies of are compatible for all 2 n iv countably infinite copies of are compatible by using this equivalence we also show that the set of randomization equivalence classes of normal eb channels with a fixed input von neumann algebra is upper and lower dedekind closed i e the supremum or infimum of any randomization increasing or decreasing net of eb channels is also eb as an example we construct an injective normal eb channel with an arbitrary outcome operator algebra m acting on an infinite dimensional separable hilbert space by using the coherent states and the bargmann measure

localisation in a cosserat continuum under static and dynamic loading conditions abstract localisation studies have been carried out for an unconstrained elasto plastic strain softening cosserat continuum because of the presence of an internal length scale in this continuum model a perfect convergence is found upon mesh refinement a finite constant width of the localisation zone and a finite energy dissipation are computed under static as well as under transient loading conditions because of the existence of rotational degrees of freedom in a cosserat continuum additional wave types arise and wave propagation becomes dispersive this has been investigated analytically and numerically for an elastic cosserat continuum and an excellent agreement has been found between both solutions

the norm 1 property of a quantum observable a normalized positive operator measure x e x has the norm 1 property if e x 1 whenever e x o this property reflects the fact that the measurement outcome probabilities for the values of such observables can be made arbitrarily close to one with suitable state preparations some general implications of the norm 1 property are investigated as case studies localization observables phase observables and phase space observables are considered

preparation uncertainty implies measurement uncertainty in a class of generalized probabilistic theories in quantum theory it is known for a pair of noncommutative observables that there is no state on which they take simultaneously definite values and that there is no joint measurement of them they are called preparation uncertainty and measurement uncertainty respectively and research has unveiled that they are not independent from but related with each other in a quantitative way this study aims to reveal whether similar relations to quantum ones hold also in generalized probabilistic theories gpts in particular a certain class of gpts is considered which can be characterized by transitivity and self duality and regarded as extensions of quantum theory it is proved that there are close connections expressed quantitatively between two types of uncertainty on a pair observables also in those theories if preparation uncertainty exists then measurement uncertainty also exists and they are described by similar inequalities our results manifest that their correspondences are not specific to quantum theory but more universal ones

hastings s additivity counterexample via dvoretzky s theorem the goal of this note is to show that hastings s counterexample to the additivity of minimal output von neumann entropy can be readily deduced from a sharp version of dvoretzky s theorem

random positive operator valued measures we introduce several notions of random positive operator valued measures povms and we prove that some of them are equivalent we then study statistical properties of the effect operators for the canonical examples starting from the limiting eigenvalue distribution we derive the large system limit for several quantities of interest in quantum information theory such as the sharpness the noise content and the probability range finally we study different compatibility criteria and we compare them for generic povms

a novel boundary element approach to time harmonic dynamics of incremental nonlinear elasticity the role of pre stress on structural vibrations and dynamic shear banding a new boundary element technique is developed to analyze two dimensional time harmonic small amplitude vibrations superimposed upon a homogeneously pre stressed orthotropic and incompressible elastic solid new expressions for the green s functions for incremental applied tractions are obtained in which static and dynamic contributions are uncoupled the dynamic contributions are regular whereas the static terms are strongly singular and are solved in closed form expressions particularly useful for numerical calculations as a consequence of the static dynamic de coupling these expressions turn out to be useful also for quasi static deformation the formulation is tested for different boundary value problems these include a problem with certain boundary conditions investigated by ryzhak in the static case for which an analytic solution is proposed here in the time harmonic regime the effect of pre stress is shown to strongly influence the vibrational response of elastic structures it is shown that natural frequencies strongly decrease when pre stress approaches quasi static bifurcation loads and wave propagation speeds tend to vanish when the boundary of ellipticity is approached near this boundary but still within the elliptic region we observe a focussing of vibrations along plane waves parallel to the shear bands 2007 elsevier b v all rights reserved

nonlocality distillation and postquantum theories with trivial communication complexity we first present a protocol for deterministically distilling nonlocality building upon a recent result of forster et al phys rev lett 102 120401 2009 our protocol which is optimal for two copy distillation works efficiently for a specific class of postquantum nonlocal boxes which we term correlated nonlocal boxes in the asymptotic limit all correlated nonlocal boxes are distilled to the maximally nonlocal box of popescu and rohrlich then taking advantage of a result of brassard et al phys rev lett 96 250401 2006 we show that all correlated nonlocal boxes make communication complexity trivial and therefore appear very unlikely to exist in nature astonishingly some of these nonlocal boxes are arbitrarily close to the set of classical correlations this result therefore gives new insight to the problem of why quantum nonlocality is limited

an analysis of strong discontinuities in multiplicative finite strain plasticity and their relation with the numerical simulation of strain localization in solids abstract this paper presents an analysis of strong discontinuities in inelastic solids at finite strains solutions exhibiting this type of discontinuities characterized by a discontinuous displacement field are shown to make physical and mathematical sense in a classical multiplicative plasticity continuum model if the softening modulus is reinterpreted as a singular distribution physically the strainsoftening is localized along the discontinuity conditions for the appearance of strong discontinuities in the geometrically nonlinear range are characterized as it is the response of the material during localization in addition these analytical results are exploited in the design of a new class of finite element methods the proposed methods fall within the class of enhanced strain methods and lead to solutions independent of the mesh size and insensitive to mesh alignment without requiring any regularization of the solutions by numerical parameters like a characteristic length

an implicit bem formulation for gradient plasticity and localization phenomena the aim of this paper is to discuss a boundary element formulation for non linear structural problems involving localization phenomena in order to overcome the well known mesh dependency observed in local plasticity a gradient plasticity model is used an implicit boundary element formulation is proposed and the underlying consistent tangent operator defined this formulation is based on the classical displacement and strain integral representations combined with an integral representation of the plastic multiplier first numerical examples are presented to illustrate the application of the method copyright 2001 john wiley sons ltd

effects of pre stress on crack tip fields in elastic incompressible solids abstract a closed form asymptotic solution is provided for velocity fields and the nominal stress rates near the tip of a stationary crack in a homogeneously pre stressed configuration of a nonlinear elastic incompressible material in particular a biaxial pre stress is assumed with stress axes parallel and orthogonal to the crack faces two boundary conditions are considered on the crack faces namely a constant pressure or a constant dead loading both preserving an homogeneous ground state starting from this configuration small superimposed mode i or mode ii deformations are solved in the framework of biot s incremental theory of elasticity in this way a definition of an incremental stress intensity factor is introduced slightly different for pressure or dead loading conditions on crack faces specific examples are finally developed for various hyperelastic materials including the j2 deformation theory of plasticity the presence of pre stress is shown to strongly influence the angular variation of the asymptotic crack tip fields even if the nominal stress rate displays a square root singularity as in the infinitesimal theory relationships between the solution with shear band formation at the crack tip and instability of the crack surfaces are given in evidence

on fixed points of luders operation in this paper we give a concrete example of a luders operation la with n 3 such that la b b does not imply that b commutes with all e1 e2 and e3 in a this example answers an open problem of professor gudder

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

product of random projections jacobi ensembles and universality problems arising from free probability we consider the product of two independent randomly rotated projectors the square of its radial part turns out to be distributed as a jacobi ensemble we study its global and local properties in the large dimension scaling relevant to free probability theory we establish asymptotics for one point and two point correlation functions as well as properties of largest and smallest eigenvalues

fixed points of quantum operations quantum operations frequently occur in quantum measurement theory quantum probability quantum computation and quantum information theory if an operator a is invariant under a quantum operation we call a a fixed point physically the fixed points are the operators that are not disturbed by the action of our main purpose is to answer the following question if a is a fixed point is a compatible with the operation elements of we shall show in general that the answer is no and we shall give some sufficient conditions under which the answer is yes our results will follow from some general theorems concerning completely positive maps and injectivity of operator systems and von neumann algebras

coexistence on reflecting hyperplane in generalized probability theories the coexistence of effects in a certain class of generalized probability theories is investigated the effect space corresponding to an even sided regular polygon state space has a central hyperplane that contains all the nontrivial extremal effects the existence of such a hyperplane called a reflecting hyperplane is closely related to the point symmetry of the corresponding state space the effects on such a hyperplane can be regarded as the generalized unbiased effects a necessary and sufficient condition for a pair of unbiased effects in the even sided regular polygon theories is presented this result reproduces a low dimensional analogue of known results of qubit effects in a certain limit the coexistence of effects in a certain class of generalized probability theories is investigated the effect space corresponding to an even sided regular polygon state space has a central hyperplane that contains all the nontrivial extremal effects the existence of such a hyperplane called a reflecting hyperplane is closely related to the point symmetry of the corresponding state space the effects on such a hyperplane can be regarded as the generalized unbiased effects a necessary and sufficient condition for a pair of unbiased effects in the even sided regular polygon theories is presented this result reproduces a low dimensional analogue of known results of qubit effects in a certain limit

a full tangent stiffness field boundary element formulation for geometric and material non linear problems of solid mechanics the field boundary element method naturally admits the solution algorithm in the incompressible regimes of fully developed plastic flow this is not the case with the generally popular finite element method without further modifications to the method such as reduced integration or a mixed method for treating the dilatational deformation the analyses by the field boundary element method for geometric and material non linear problems are generally carried out by an incremental algorithm where the velocities or displacement increments on the boundary are treated as the primary variables and an initial strain iteration method is commonly used to obtain the state of equilibrium for problems such as buckling and diffused tensile necking involving very large strains such a solution scheme may not be able to capture the bifurcation phenomena or the convergence will be unacceptably slow when the post bifurcation behaviour needs to be analysed to avoid this predicament a full tangent stiffness field boundary element formulation which takes the initial stress velocity gradient displacement gradient coupling terms accurately into account is presented in this paper here the velocity field both inside and on the boundary are treated as primary variables the large strain plasticity constitutive equation employed is based on an endochronic model of combined isotropic kinematic hardening plasticity using the concepts of material director triad and the associated plastic spin a generalized mid point radial return algorithm is presented for determining the objective increments of stress from the computed velocity gradients numerical results are presented for problems of diffuse necking involving very large strains and plastic instability in initially perfect elastic plastic plates under tension these results demonstrate the clear superiority of the full tangent stiffness algorithm over the initial strain algorithm in the context of the integral equation formulations for large strain plasticity

implicit bem formulations for usual and sensitivity problems in elasto plasticity using the consistent tangent operator concept this paper presents boundary element method bem formulations for usual and sensitivity problems in small strain elasto plasticity using the concept of the local consistent tangent operator cto usual problems here refer to analysis of nonlinear problems in structural and solid continua for which simo and taylor first proposed the use of the cto within the context of the finite element method fem a new implicit bem scheme for such problems using the cto is presented first a formulation for sensitivity analysis follows it is shown that the sensitivity of the strain increment associated with an infinitesimal variation of some design parameter solves a linear problem which is governed by the converged value of the same global cto as the one that appears in the usual problem numerical results for both usual and sensitivity problems are shown for a one dimensional example they demonstrate the effectiveness of the present approach in particular accurate sensitivities with respect to material parameters e g exponent of the power type hardening law are obtained even with few integration cells and for large load increments

optimal quantum state tomography with known parameters it is a well known fact that the optimal positive operator valued measure povm for quantum state tomography is the symmetric informationally complete povm sic povm we investigate the same problem only in the case when there is some a priori information about the state specifically when some parameters are known in this paper we mainly focus on solving a three dimensional optimization problem which gives us a non trivial example for the so called conditional sic povms a straightforward generalization of the concept of sic povms we also present other special cases to show further applications of the proposed numerical methods and to illustrate the complexity of this topic

on the discrete constitutive models induced by strong discontinuity kinematics and continuum constitutive equations on the basis of continuum constitutive models stress vs strain the introduction of strong discontinuity kinematics considering jumps in the displacement fields across a discontinuity interface induces projected discrete constitutive models traction displacement jumps in a consistent manner therefore this projection provides possible links between the classical continuum strain localization analysis and the non linear decohesive fracture mechanics techniques the strong discontinuity analysis shows that bandwidth based regularization of the hardening softening parameter is the crucial modification to be done on the continuum model to achieve such a projection and it also provides the strong discontinuity conditions that set restrictions on the stress state compatible with bifurcations in a strong discontinuity format the methodology is illustrated on the basis of two classical families of non linear constitutive models scalar continuum damage and elasto plasticity for which the corresponding discrete constitutive models and the strong discontinuity conditions are derived

bounding the set of quantum correlations we introduce a hierarchy of conditions necessarily satisfied by any distribution p ensuremath alpha ensuremath beta representing the probabilities for two separate observers to obtain outcomes ensuremath alpha and ensuremath beta when making local measurements on a shared quantum state each condition in this hierarchy is formulated as a semidefinite program among other applications our approach can be used to obtain upper bounds on the quantum violation of an arbitrary bell inequality it yields for instance tight bounds for the violations of the collins et al inequalities

a new boundary element technique without domain integrals for elastoplastic solids summary a simple idea is proposed to solve boundary value problems for elastoplastic solids via boundary elements namely to use the green s functions corresponding to both the loading and unloading branches of the tangent constitutive operator to solve for plastic and elastic regions respectively in this way domain integrals are completely avoided in the boundary integral equations though a discretization of the region where plastic flow occurs still remains necessary to account for the inhomogeneity of plastic deformation the elastoplastic analysis reduces in essence to a straightforward adaptation of techniques valid for anisotropic linear elastic constitutive equations the loading branch of the elastoplastic constitutive operator may be viewed formally as a type of anisotropic elastic law numerical examples using j2 flow theory with linear hardening demonstrate that the proposed method retains all the advantages related to boundary element formulations is stable and performs well the method presented is for simplicity developed for the associative flow rule however a full derivation of green s function and boundary integral equations is also given for the general case of non associative flow rule it is shown that in the non associative case a domain integral unavoidably arises in the formulation copyright 2005 john wiley sons ltd

entanglement of random subspaces via the hastings bound recently hastings a counterexample to additivity of minimum output entropy nat phys 5 255 2009 e print arxiv 0809 3972v3 proved the existence of random unitary channels which violate the additivity conjecture in this paper we use hastings method to derive new bounds for the entanglement of random subspaces of bipartite systems as an application we use these bounds to prove the existence of nonunital channels which violate additivity of minimal output entropy

induced measures in the space of mixed quantum states we analyse several product measures in the space of mixed quantum states in particular we study measures induced by the operation of partial tracing the natural rotationally invariant measure on the set of all pure states of a n k composite system induces a unique measure in the space of n n mixed states or in the space of k k mixed states if the reduction takes place with respect to the first subsystem for k n the induced measure is equal to the hilbert schmidt measure which is shown to coincide with the measure induced by singular values of non hermitian random gaussian matrices pertaining to the ginibre ensemble we compute several averages with respect to this measure and show that the mean entanglement of n n pure states behaves as lnn 1 2

quantum channels with polytopic images and image additivity we study quantum channels with respect to their image i e the image of the set of density operators under the action of the channel we first characterize the set of quantum channels having polytopic images and show that additivity of the minimal output entropy can be violated in this class we then provide a complete characterization of quantum channels t that are universally image additive in the sense that for any quantum channel s the image of t otimes s is the convex hull of the tensor product of the images of t and s these channels turn out to form a strict subset of entanglement breaking channels with polytopic images and a strict superset of classical quantum channels

on coexistence and joint measurability of rank 1 quantum observables we show that a rank 1 quantum observable povm is jointly measurable with a quantum observable exactly when is a smearing of if is extreme rank 1 and discrete then and are coexistent if and only if they are jointly measurable

on the zeros of the riemann zeta function in the critical strip iv etude de la localisation des zeros complexes de la fonction zeta de riemann verification numerique de l hypothese de riemann pour les 1 500 000 001 premiers zeros de la forme it dans la bande critique avec 0 t 545 439 823 215 tous ces zeros ayant pour partie reelle 1 2

random repeated quantum interactions and random invariant states we consider a generalized model of repeated quantum interactions where a system mathcal h is interacting in a random way with a sequence of independent quantum systems mathcal k n n geq 1 two types of randomness are studied in detail one is provided by considering haar distributed unitaries to describe each interaction between mathcal h and mathcal k n the other involves random quantum states describing each copy mathcal k n in the limit of a large number of interactions we present convergence results for the asymptotic state of mathcal h this is achieved by studying spectral properties of random quantum channels which guarantee the existence of unique invariant states finally this allows to introduce a new physically motivated ensemble of random density matrices called the asymptotic induced ensemble

fast algorithms for multiple evaluations of the riemann zeta function the best previously know algorithm for evaluating the riemann zeta function it with bounded and t large to moderate accuracy was based on the rienmann siegel formula and required on the order of t 1 2 operations for each value that was computed new algorithms are presented in this paper which enable one to compute any single value of it with fixed and t t t t 1 2 in o te operations on numbers of o log t bits for any e 0 for example these algorithms lead to methods for numerically verifying the riemann hypothesis for the first n zeros in what is expected to be o n 1 e operations

entanglement thresholds for random induced states for a random quantum state on h c d otimes c d obtained by partial tracing a random pure state on h otimes c s we consider the whether it is typically separable or typically entangled for this problem we show the existence of a sharp threshold s 0 s 0 d of order roughly d 3 more precisely for any a 0 and for d large enough such a random state is entangled with very large probability when s 1 a s 0 one consequence of this result is as follows for a system of n identical particles in a random pure state there is a threshold k 0 k 0 n sim n 5 such that two subsystems of k particles each typically share entanglement if k k 0 and typically do not share entanglement if k k 0 our methods work also for multipartite systems and for unbalanced systems such as c d otimes c d d neq d the arguments rely on random matrices classical convexity high dimensional probability and geometry of banach spaces some of the auxiliary results may be of reference value a high level non technical overview of the results of this paper and of a related article arxiv 1011 0275 can be found in arxiv 1112 4582

unifying typical entanglement and coin tossing on randomization in probabilistic theories it is well known that pure quantum states are typically almost maximally entangled and thus have close to maximally mixed subsystems we consider whether this is true for probabilistic theories more generally and not just for quantum theory we derive a formula for the expected purity of a subsystem in any probabilistic theory for which this quantity is well defined it applies to typical entanglement in pure quantum states coin tossing in classical probability theory and randomization in post quantum theories a simple generalization yields the typical entanglement in anti symmetric quantum subspaces the formula is exact and simple only containing the number of degrees of freedom and the information capacity of the respective systems it allows us to generalize statistical physics arguments in a way which depends only on coarse properties of the underlying theory the proof of the formula generalizes several randomization notions to general probabilistic theories this includes a generalization of purity contributing to the recent effort of finding appropriate generalized entropy measures

eigenvectors and eigenvalues in a random subspace of a tensor product given two positive integers n and k and a parameter t 0 1 we choose at random a vector subspace v n k n of dimension n tnk we show that the set of k tuples of singular values of all unit vectors in v n fills asymptotically as n tends to infinity a deterministic convex set k k t that we describe using a new norm in k

commutators of free random variables let a be a unital c algebra given together with a specified state a c consider two selfadjoint elements a b of a which are free with respect to in the sense of the free probability theory of voiculescu let us denote c i ab ba where the i in front of the commutator is introduced to make c selfadjoint in this paper we show how the spectral distribution of c can be calculated from the spectral distributions of a and b some properties of the corresponding operation on probability measures are also discussed the methods we use are combinatorial based on the description of freeness in terms of non crossing partitions an important ingredient is the notion of r diagonal pair introduced and studied in our previous paper 12

nondisturbing quantum measurements we consider pairs of discrete quantum observables povms and analyze the relation between the notions of nondisturbance joint measurability and commutativity we specify conditions under which these properties coincide or differ depending for instance on the interplay between the number of outcomes and the hilbert space dimension or on algebraic properties of the effect operators we also show that non disturbance is in general not a symmetric relation and that it can be decided and quantified by means of a semidefinite program

measurement uncertainty relations for discrete observables relative entropy formulation we introduce a new information theoretic formulation of quantum measurement uncertainty relations based on the notion of relative entropy between measurement probabilities in the case of a finite dimensional system and for any approximate joint measurement of two target discrete observables we define the entropic divergence as the maximal total loss of information occurring in the approximation at hand for fixed target observables we study the joint measurements minimizing the entropic divergence and we prove the general properties of its minimum value such a minimum is our uncertainty lower bound the total information lost by replacing the target observables with their optimal approximations evaluated at the worst possible state the bound turns out to be also an entropic incompatibility degree that is a good information theoretic measure of incompatibility indeed it vanishes if and only if the target observables are compatible it is state independent and it enjoys all the invariance properties which are desirable for such a measure in this context we point out the difference between general approximate joint measurements and sequential approximate joint measurements to do this we introduce a separate index for the tradeoff between the error of the first measurement and the disturbance of the second one by exploiting the symmetry properties of the target observables exact values lower bounds and optimal approximations are evaluated in two different concrete examples 1 a couple of spin 1 2 components not necessarily orthogonal 2 two fourier conjugate mutually unbiased bases in prime power dimension finally the entropic incompatibility degree straightforwardly generalizes to the case of many observables still maintaining all its relevant properties we explicitly compute it for three orthogonal spin 1 2 components

entanglement and the three dimensionality of the bloch ball we consider a very natural generalization of quantum theory by letting the dimension of the bloch ball be not necessarily three we analyze bipartite state spaces where each of the components has a d dimensional euclidean ball as state space in addition to this we impose two very natural assumptions the continuity and reversibility of dynamics and the possibility of characterizing bipartite states by local measurements we classify all these bipartite state spaces and prove that except for the quantum two qubit state space none of them contains entangled states equivalently in any of these non quantum theories interacting dynamics is impossible this result reveals that existence of entanglement is the requirement with minimal logical content which singles out quantum theory from our family of theories

integration with respect to the haar measure on unitary orthogonal and symplectic group we revisit the work of the first named author and using simpler algebraic arguments we calculate integrals of polynomial functions with respect to the haar measure on the unitary group u d the previous result provided exact formulas only for 2d bigger than the degree of the integrated polynomial and we show that these formulas remain valid for all values of d also we consider the integrals of polynomial functions on the orthogonal group o d and the symplectic group sp d we obtain an exact character expansion and the asymptotic behavior for large d thus we can show the asymptotic freeness of haar distributed orthogonal and symplectic random matrices as well as the convergence of integrals of the itzykson zuber type

generalized probability theories what determines the structure of quantum theory the framework of generalized probabilistic theories is a powerful tool for studying the foundations of quantum physics it provides the basis for a variety of recent findings that significantly improve our understanding of the rich physical structure of quantum theory this review paper tries to present the framework and recent results to a broader readership in an accessible manner to achieve this we follow a constructive approach starting from a few basic physically motivated assumptions we show how a given set of observations can be manifested in an operational theory furthermore we characterize consistency conditions limiting the range of possible extensions in this framework classical and quantum theory appear as special cases and the aim is to understand what distinguishes quantum mechanics as the fundamental theory realized in nature it turns out that non classical features of single systems can equivalently result from higher dimensional classical theories that have been restricted entanglement and non locality however are shown to be genuine non classical features

a field boundary element formulation for material nonlinear problems at finite strains abstract a boundary element formulation for geometrical nonlinear problems is presented which is applicable for arbitrary constitutive equations based on the concept of hyperelastic response relative to an intermediate configuration this includes purely hyperelastic problems at large elastic strains in contrast to other formulations the total lagrange framework employed in this work significantly increases the numerical efficiency as the system matrices remain constant during the incremental solution and have to be computed only once a nonlinear set of equations with an identical structure for both boundary and internal unknowns is derived the basic unknowns are displacement gradients which are calculated via integral equations and not by differentiation of the shape functions the formulation can be consistently linearised to allow for the implementation of efficient iteration schemes using gradients e g the newton raphson scheme

a boundary element technique for incremental non linear elasticity part i formulation abstract incremental elastic deformations superimposed upon a given homogeneous strain are analyzed with a boundary element technique this is based on a recently developed green s function for non linear incremental elastic deformations plane strain perturbations are considered of a broad class of incompressible material behaviours including hyper hypoelastic and navier stokes constitutive equations within the elliptic range numerical treatment of the problem is detailed a possibility of employing the method in the fully non linear range is outlined which yields a boundary element approach where the use of domain integrals is avoided at least in a conventional sense the methods for bifurcation and shear band analyses will be reported in part ii

a galerkin symmetric boundary element method in elasticity formulation and implementation a symmetric boundary element method based on a weighted residual galerkin approach for elastoplastic analysis is revisited and its computer implementation for two dimensional homogeneous problems is described

on the asymptotic distribution of the commutator and anticommutator of random matrices we study in the limit of infinite matrix order the normalized eigenvalue counting measures of the commutator and anticommutator of two hermitian or real symmetric matrices rotated independently one respect to another by the random unitary or orthogonal haar distributed matrix we establish the convergence with probability 1 to a limiting nonrandom measure we obtain and analyze the functional equations for the stieltjes transforms of the limiting measures

multivariate analysis and jacobi ensembles largest eigenvalue tracy widom limits and rates of convergence abstract let a and b be independent central wishart matrices in p variables with common covariance and having m and n degrees of freedom respectively the distribution of the largest eigenvalue of a b 1 b has numerous applications in multivariate statistics but is difficult to calculate exactly suppose that m and n grow in proportion to p we show that after centering and scaling the distribution is approximated to second order o p 2 3 by the tracy widom law the results are obtained for both complex and then real valued data by using methods of random matrix theory to study the largest eigenvalue of the jacobi unitary and orthogonal ensembles asymptotic approximations of jacobi polynomials near the largest zero play a central role

on the distribution of spacings between zeros of the zeta function etude numerique de la distribution des espacements des zeros de la fonction zeta de riemann observation de certains phenomenes inatendus

estimates for the eigenvalues of the jordan product of hermitian matrices n alikakos and p w bates department of mathematics heriot watt university edinburgh scotland submitted by richard a brualdi abstract given hermitian matrices a and b professor taussky todd posed the problem of estimating the eigenvalues of their jordan product ab ba here we establish bounds for all the eigenvalues of the jordan product when both a and b are positive definite at the same time we give a more straightforward proof and an improvement of estimates given by d w nicholson for the smallest eigenvalue 0 introduction given hermitian matrices a and b their

adaptive meshing for dynamic strain localization a mesh enrichment procedure is developed to capture the shear band for strain localization in elasto visco plastic solids the enriched mesh comprises four and five noded quadrilateral elements which can be adaptively refined in the localized zone the criterion for mesh adaption combines three well known localization characteristics to predict the onset of localization in individual elements a modified procedure for transferring state variables between two successive refined meshes is proposed the procedure is tested by solving several sample problems consistent and stable solutions are obtained in particular shear band widths and plastic strains are found to converge to stable values the results are compared with solutions using the enriched displacement procedure defined in l the efficiency of the global adaptive scheme is tested on initial and boundary value problems that involve different material properties and geometries

a case of indispensable localized instability in elastic plastic solids abstract the primary instability in homogeneous elastic plastic bodies with prescribed boundary displacements is studied in this event instability is known to arise when hadamards inequality is first violated this violation being the very condition for the localized instability to be possible in principle the question is posed whether localized instability is the only possible type of instability under specified conditions or diffuse instability is equally possible which is true for elastic bodies in order to state a rational criterion for distinction between localized and diffuse instability modes ims which are treated in full generality as mutually complementary notions without any a priori prescriptions regarding the mode of deformation it is proposed to characterize ims by means of some quantitative measure of localization named the localizational volume the latter evaluates the volume of that part of a body where relatively great incremental strains are concentrated this property of proposed measure is proved the main result established is that in the problem under consideration any primary im is characterized by infinitesimal value of localizational volume i e all the primary ims appear to be localized in such a volumetric sense which means at least the absence of diffuse ims the conclusion is drawn that indispensability of such a localization treated in the sense of small localizational volume is a global essentially non linear effect boundary constraint piecewise linear constitutive relation

a symmetric galerkin boundary domain element method for finite elastic deformations abstract the symmetric galerkin boundary element method sgbem is reformulated for problems of finite elasticity with hyperelastic material and incompressibility using fundamental solutions related to a fictitious homogeneous isotropic and compressible linear elastic material the proposed formulation contains besides the standard boundary integrals domain integrals which account for the problem s nonlinearities through some fictitious initial strain and stress fields required to satisfy appropriate consistency equations the boundary domain integral equation problem so obtained is shown to admit a stationarity principle a consequence of the hu washizu one which covers a number of particular cases including the compressible case as well as the fully linear case either incompressible and compressible so recovering known results of the literature the continuum rate problem is also addressed and suitably discretized by boundary and domain elements the related algebraic solving equation system is shown to exhibit symmetry and some sign definiteness features it is formally solved in terms of the node values of the displacement gradient the idrostatic pressure the initial strain and stress fields a long with the unknown boundary displacements and tractions details regarding the fundamental solutions and the stationarity principle are reported in three appendices at the end of the paper

finite element simulation of strain localization with large deformation capturing strong discontinuity using a petrov galerkin multiscale formulation the finite element model for strain localization analysis developed in a previous work is generalized to the finite deformation regime strain enhancements via jumps in the displacement field are captured and condensed on the material level leading to a formulation that does not require static condensation to be performed on the element level a general evolution condition is first formulated laying out conditions for the continued activation of a strong discontinuity then a multiscale finite element model is formulated to describe the post bifurcation behavior highlighting the key roles played by the continuous and conforming deformation maps on the characterization of the finite deformation kinematics of a localized element traced by a strong discontinuity the resulting finite element equation exhibits the features of a petrov galerkin formulation in which the gradient of the weighting function is evaluated over the continuous part of the deformation map whereas the gradient of the trial function is evaluated over the conforming part of the same map in the limit of infinitesimal deformations the formulation reduces to the standard galerkin approximation described in a previous work numerical examples are presented demonstrating absolute objectivity with respect to mesh refinement and insensitivity to mesh alignment of finite element solutions 2002 elsevier science b v all rights reserved

the riemann zeros and eigenvalue asymptotics comparison between formulae for the counting functions of the heights tn of the riemann zeros and of semiclassical quantum eigenvalues en suggests that the tn are eigenvalues of an unknown hermitean operator h obtained by quantizing a classical dynamical system with hamiltonian hcl many features of hcl are provided by the analogy for example the riemann dynamics should be chaotic and have periodic orbits whose periods are multiples of logarithms of prime numbers statistics of the tn have a similar structure to those of the semiclassical en in particular they display random matrix universality at short range and nonuniversal behaviour over longer ranges very refined features of the statistics of the tn can be computed accurately from formulae with quantum analogues the riemann siegel formula for the zeta function is described in detail its interpretation as a relation between long and short periodic orbits gives further insights into the quantum spectral fluctuations we speculate that the riemann dynamics is related to the trajectories generated by the classical hamiltonian hcl xp

lorentz invariant hamiltonian and riemann hypothesis we have given some arguments that a two dimensional lorentz invariant hamiltonian may be relevant to the riemann hypothesis concerning zero points of the riemann zeta function some eigenfunction of the hamiltonian corresponding to infinite dimensional representation of the lorentz group have many interesting properties especially a relationship exists between the zero zeta function condition and the absence of trivial representations in the wavefunction we also give a heuristic argument for the validity of the hypothesis

almost one bit violation for the additivity of the minimum output entropy in a previous paper we proved that in the appropriate asymptotic regime the limit of the collection of possible eigenvalues of output states of a random quantum channel is a deterministic compact set kk t we also showed that the set kk t is obtained up to an intersection as the unit ball of the dual of a free compression norm in this paper we identify the maximum of ell p norms on the set kk t and prove that the maximum is attained on a vector of shape a b b where a b in particular we compute the precise limit value of the minimum output entropy of a single random quantum channel as a corollary we show that for any varepsilon 0 it is possible to obtain a violation for the additivity of the minimum output entropy for an output dimension as low as 183 and that for appropriate choice of parameters the violation can be as large as log 2 varepsilon conversely our result implies that with probability one in the limit one does not obtain a violation of additivity using conjugate random quantum channels and the bell state in dimension 182 and less

perfectly matched layers for flexural waves in kirchhof love plates abstract we propose perfectly matched layers pmls for flexural waves in plate structures the analytical model is based on transformation optics techniques applied to the biharmonic fourth order partial differential equation describing flexural vibrations in kirchhoff love plates we show that perfect boundary conditions are not an optimal solution since they depend on the incident waves the full analytical form of pmls and zero reflection conditions at the boundary between homogeneous and pml domains are given the implementation in a finite element fem code is described and an eigenfrequency analysis is given as a possible methodology to check the implementation itself a measure of the performances of the pmls is introduced and the effects of element discretization boundary conditions frequency dimension of the pml amount of transformation and dissipation are detailed it is shown that the model gives excellent results also when the applied load approaches the pml domain

complete characterization of extreme quantum observables in infinite dimensions we give a complete characterization for extreme quantum observables i e for normalized positive operator valued measures povms which are extremals in the convex set of all povms the characterization is valid both in discrete and continuous cases and also in the case of an infinite dimensional hilbert space we show that sharp povms are pre processing clean i e they cannot be irreversibly connected to other povms via quantum channels

counterexamples to the maximal p norm multiplicativity conjecture for all p 1 for all p 1 we demonstrate the existence of quantum channels with non multiplicative maximal output p norms equivalently for all p 1 the minimum output renyi entropy of order p of a quantum channel is not additive the violations found are large in all cases the minimum output renyi entropy of order p for a product channel need not be significantly greater than the minimum output entropy of its individual factors since p 1 corresponds to the von neumann entropy these counterexamples demonstrate that if the additivity conjecture of quantum information theory is true it cannot be proved as a consequence of any channel independent guarantee of maximal p norm multiplicativity we also show that a class of channels previously studied in the context of approximate encryption lead to counterexamples for all p 2