limits for entanglement measures the basic principle of entanglement processing says that entanglement cannot increase under local operations and classical communication based on this principle we show that any entanglement measure e suitable for the regime of a high number of identically prepared entangled pairs satisfies ed or e or ef where ed and ef are the entanglement of distillation and formation respectively moreover we exhibit a theorem establishing a very general form of bounds for distillable entanglement

the weak metric approximation property we introduce and investigate the weak metric approximation property of banach spaces which is strictly stronger than the approximation property and at least formally weaker than the metric approximation property among others we show that if a banach space has the approximation property and is 1 complemented in its bidual then it has the weak metric approximation property we also study the lifting of the weak metric approximation property from banach spaces to their dual spaces this enables us in particular to show that the subspace of c0 constructed by johnson and schechtman does not have the weak metric approximation property

a solid like fem for geometrically non linear 3d frames abstract this study presents a solid like finite element formulation to solve geometric non linear three dimensional inhomogeneous frames to achieve the desired representation unconstrained vectors are used instead of the classic rigid director triad as a consequence the resulting formulation does not use finite rotation schemes high order curved elements with any cross section are developed using a full three dimensional constitutive elastic relation warping and variable thickness strain modes are introduced to avoid locking the warping mode is solved numerically in fem pre processing computational code which is coupled to the main program the extra calculations are relatively small when the number of finite elements with the same cross section increases the warping mode is based on a 2d free torsion saint venant problem that considers inhomogeneous material a scheme that automatically generates shape functions and its derivatives allow the use of any degree of approximation for the developed frame element general examples are solved to check the objectivity path independence locking free behavior generality and accuracy of the proposed formulation

on commuting approximation properties of banach spaces let a c 0 and let b be a compact set of scalars we show that if x is a banach space such that the canonical projection from x onto x satisfies the inequality and 1 b c then every commuting bounded compact approximation of the identity of x is shrinking this generalizes a theorem by godefroy and saphar from 1988 as an application we show that under the conditions described above both x and x have the metric compact approximation property mcap relying on the willis construction we show that the commuting mcap does not imply the approximation property

frame potential for finite dimensional banach spaces abstract we define the frame potential for a schauder frame on a finite dimensional banach space as the square of the 2 summing norm of the frame operator as is the case for frames for hilbert spaces we prove that the frame potential can be used to characterize finite unit norm tight frames funtfs for finite dimensional banach spaces we prove the existence of funtfs for a variety of spaces and in particular that every n dimensional complex banach space with a 1 unconditional basis has a funtf of n vectors for every n n however many interesting results on funtfs and sums of rank one projections for hilbert spaces remain unknown for banach spaces and we conclude the paper with multiple open questions

intersection properties of ball sequences and uniqueness of hahn banach extensions let x be a banach space and y a closed subspace we introduce an intrinsic geometric property of y the k ball sequence property which is a weakening of the famous k ball property due to alfsen effros we prove that y satisfies the 2 ball sequence property if and only if y has the phelps uniqueness property u i e every continuous linear functional g y has a unique norm preserving extension f x we prove that y is an ideal having property u if and only if y satisfies the 3 ball sequence property and in this case y satisfies the k ball sequence property for all k

quantifying entanglement resources we present an overview of the quantitative theory of single copy entanglement in finite dimensional quantum systems in particular we emphasize the point of view that different entanglement measures quantify different types of resources which leads to a natural interdependence of entanglement classification and quantification apart from the theoretical basis we outline various methods for obtaining quantitative results on arbitrary mixed states this article is part of a special issue of journal of physics a mathematical and theoretical devoted to 50 years of bell s theorem

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

asymptotic relative entropy of entanglement we present an analytical formula for the asymptotic relative entropy of entanglement with respect to positive partial transpose states for werner states of arbitrary dimension we then demonstrate its validity using methods from convex optimization this is the first case in which the asymptotic value of a subadditive entanglement measure has been calculated

useful states and entanglement distillation we derive general upper bounds on the distillable entanglement of a mixed state under one way and two way local operations and classical communication locc in both cases the upper bound is based on a convex decomposition of the state into useful and useless quantum states by useful we mean a state whose distillable entanglement is non negative and equal to its coherent information and thus given by a single letter tractable formula on the other hand useless states are undistillable i e their distillable entanglement is zero we prove that in both settings the distillable entanglement is convex on such decompositions hence an upper bound on the distillable entanglement is obtained from the contributions of the useful states alone being equal to the convex combination of their coherent informations optimizing over all such decompositions of the input state yields our upper bound the useful and useless states are given by degradable and antidegradable states in the one way locc setting and by maximally correlated and positive partial transpose ppt states in the two way locc setting respectively we also illustrate how our method can be extended to quantum channels interpreting our upper bound as a convex roof extension we show that it reduces to a particularly simple non convex optimization problem for the classes of isotropic states and werner states in the one way locc setting this non convex optimization yields an upper bound on the quantum capacity of the qubit depolarizing channel that is strictly tighter than previously known bounds for large values of the depolarizing parameter in the two way locc setting the non convex optimization achieves the ppt relative entropy of entanglement for both isotropic and werner states

faithful squashed entanglement squashed entanglement is a measure for the entanglement of bipartite quantum states in this paper we present a lower bound for squashed entanglement in terms of a distance to the set of separable states this implies that squashed entanglement is faithful that is it is strictly positive if and only if the state is entangled we derive the lower bound on squashed entanglement from a lower bound on the quantum conditional mutual information which is used to define squashed entanglement the quantum conditional mutual information corresponds to the amount by which strong subadditivity of von neumann entropy fails to be saturated our result therefore sheds light on the structure of states that almost satisfy strong subadditivity with equality the proof is based on two recent results from quantum information theory the operational interpretation of the quantum mutual information as the optimal rate for state redistribution and the interpretation of the regularised relative entropy of entanglement as an error exponent in hypothesis testing the distance to the set of separable states is measured in terms of the locc norm an operationally motivated norm giving the optimal probability of distinguishing two bipartite quantum states each shared by two parties using any protocol formed by local quantum operations and classical communication locc between the parties a similar result for the frobenius or euclidean norm follows as an immediate consequence the result has two applications in complexity theory the first application is a quasipolynomial time algorithm solving the weak membership problem for the set of separable states in locc or euclidean norm the second application concerns quantum merlin arthur games here we show that multiple provers are not more powerful than a single prover when the verifier is restricted to locc operations thereby providing a new characterisation of the complexity class qma

finite elasticity in spatial description linearization aspects with 3 d membrane applications the treatment of finite hyperelasticity set on the spatial configuration is described the fully consistent linearization of the corresponding field equations is carried out in detail it provides the basis of the exact newton raphson procedure for solution of the associated boundary value problem a membrane formulation is presented in which the incompressibility constraint usually employed in the description of rubber like materials is satisfied trivially the excellent performance of the proposed framework is demonstrated by means of 3 d membrane finite element simulations

on m ideals of compact operators in lorentz sequence spaces abstract let x d v p and y d w q be lorentz sequence spaces we investigate when the space k x y of compact linear operators acting from x to y forms or does not form an m ideal in the space of bounded linear operators we show that k x y fails to be a non trivial m ideal whenever p 1 or p q in the case when 1 p q we establish a general essential condition guaranteeing that k x y is not an m ideal in contrast we prove that non trivial m ideals k x y do exist whenever 1 p q and we give a description of them

causal limit on quantum communication the capacity of a channel is known to be equivalent to the highest rate at which it can generate entanglement analogous to entanglement the notion of a causality measure characterizes the temporal aspect of quantum correlations despite holding an equally fundamental role in physics temporal quantum correlations have yet to find their operational significance in quantum communication here we uncover a connection between quantum causality and channel capacity we show the amount of temporal correlations between two ends of the noisy quantum channel as quantified by a causality measure implies a general upper bound on its channel capacity the expression of this new bound is simpler to evaluate than most previously known bounds we demonstrate the utility of this bound by applying it to a class of shifted depolarizing channels which results in improvement over previously known bounds for this class of channels

on ideals of compact operators satisfying them r s inequality abstract letr s 0 1 we prove that a banach spacexsatisfies them r s inequality i e formula where is the canonical projection ofx ontox wheneverr s 2 1 and there exists a norm one projectionpon l x with ker p k x satisfying formula we characterize the last property of k x in l x by a strong version of the metric compact approximation property ofx our results extend some well known results onm ideals

entanglement cost under positive partial transpose preserving operations we study the entanglement cost under quantum operations preserving the positivity of the partial transpose ppt operations we demonstrate that this cost is directly related to the logarithmic negativity thereby providing the operational interpretation for this entanglement measure as examples we discuss general werner states and arbitrary bipartite gaussian states then we prove that for the antisymmetric werner state ppt cost and ppt entanglement of distillation coincide this is the first example of a truly mixed state for which entanglement manipulation is asymptotically reversible which points towards a unique entanglement measure under ppt operations

on the static interaction of fluid and gas loaded multi chamber systems in large deformation finite element analysis abstract completing previous studies d berry h yang formulation and experimental verification of a pneumatic finite element int j numer methods engrg 39 1996 1097 1114 j bonet r d wood j mahaney p heywood finite element analysis of air supported membrane structures comput methods appl mech engrg 190 2000 579 595 t rumpel effiziente diskretisierung von statischen fluid struktur problemen bei grosen deformationen ph d thesis institut fur mechanik der universitat karlsruhe th 2003 t rumpel k schweizerhof volume dependent pressure loading and its influence on the stability of structures int j numer methods engrg 56 2003 211 238 t rumpel k schweizerhof hydrostatic fluid loading in non linear finite element analysis int j numer methods engrg 59 2004 849 870 on the deformation dependence of gas or fluid loadings with the assumption of finite gas and fluid volumes the current contribution focuses on the influence of modifications of the size and shape of a finite structure filled with combinations of gas and incompressible or compressible heavy fluid in contrast to the previous contributions berry and yang 1996 bonet et al 2000 rumpel 2003 rumpel and schweizerhof 2003 rumpel and schweizerhof 2004 where different finite element formulations for some specific load cases were derived this derivation provides a general formulation of a multi chamber system filled with gas and additional compressible heavy fluid by introducing two stiffness parameters it is possible to reduce the formulation to the pure pneumatic or hydrostatic load cases described in earlier works further on it will be shown how to manage the modification of the load cases during the loading process the linearization of the corresponding virtual work expression necessary for a newton type solution algorithm leads to additional terms for the volume dependence bonet et al 2000 rumpel 2003 rumpel and schweizerhof 2003 and the expected fully symmetric stiffness matrix the discretization of the solid structures with finite elements leads to standard stiffness matrix forms for the structures plus the so called load stiffness matrices k schweizerhof e ramm displacement dependent pressure loads in non linear finite element analyses comput struct 18 1984 1099 1114 and several dyadic rank updates depending on the type of filling for each filled structure part assuming that loaded surface segments are identical with the element surfaces a further focus is on a specific solution scheme exploiting the dyadic rank update structure some numerical examples show the effectiveness of the approach and the necessity to take the corresponding terms in the variational expression and in the linearization into account

condition on the renyi entanglement entropy under stochastic local manipulation the r enyi entanglement entropy ree is an entanglement quantifier considered as a natural generalization of the entanglement entropy when it comes to stochastic local operations and classical communication slocc however only a limited class of the rees satisfy the monotonicity condition while their statistical properties beyond mean values have not been fully investigated here we establish a general condition that the probability distribution of the ree of any order obeys under slocc the condition is obtained by introducing a family of entanglement monotones that contain the higher order moments of the rees the contribution from the higher order moments imposes a strict limitation on entanglement distillation via slocc we find that the upper bound on success probabilities for entanglement distillation exponentially decreases as the amount of raised entanglement increases which cannot be captured from the monotonicity of the ree based on the strong restriction on entanglement transformation under slocc we design a new method to estimate entanglement in quantum many body systems from experimentally observable quantities

lifting convex approximation properties from banach spaces to their dual spaces and the related local reflexivity abstract our main result demonstrates that rather weak forms of the extendable local reflexivity and of the principle of local reflexivity are needed for the lifting of bounded convex approximation properties from banach spaces to their dual spaces this provides a unified approach to the lifting of various bounded approximation properties including besides the classical ones the approximation property for pairs of banach spaces and the positive approximation property of banach lattices

the infinite number of generalized dimensions of fractals and strange attractors abstract we show that fractals in general and strange attractors in particular are characterized by an infinite number of generalized dimensions dq q 0 to this aim we develop a rescaling transformation group which yields analytic expressions for all the quantities dq we prove that lim q 0 dq fractal dimension d limq 1dq information dimension and dq 2 correlation exponent v dq with other integer q s correspond to exponents associated with ternary quaternary and higher correlation functions we prove that generally dq dq for any q q for homogeneous fractals dq dq a particularly interesting dimension is dq for two examples feigenbaum attractor generalized baker s transformation we calculate the generalized dimensions and find that d is a non trivial number all the other generalized dimensions are bounded between the fractal dimension and d

generalized quantum entropy the generalized quantum entropies are introduced in this paper some important properties such as nonnegativity continuity and concavity are proved but different from the von neumann entropy the subadditivity and additivity fail for the quantum unified r s entropy in general

form finding of membrane structures by the updated reference method with minimum mesh distortion this paper presents a new technique for the solution of the well known form finding problem in membrane structures the technique proposed is based on the updated reference configuration method proposed by bletzinger proceedings of the iass colloquium on structural morphology towards the new millenium nottingham 1997 in which an area functional is minimised within the context of a finite element discretisation in this paper an additional functional term is introduced with the aim of minimising the mesh distortion during the form finding process this new term provides in plane stiffness which prevents the emergence of mechanisms without the need for ad hoc changes of the tangent matrix as a consequence of this additional strain energy term the form finding process can be viewed as a standard large strain membrane analysis with a specific choice of hyperelastic strain energy function this implies that it can be implemented in any standard code as an additional constitutive model two well known simple examples of form finding will be presented to illustrate the method proposed

bounds on relative entropy of entanglement for multi party systems we present upper and lower bounds to the relative entropy of entanglement of multi party systems in terms of the bi partite entanglements of formation and distillation and entropies of various subsystems we point out implications of our results to the local reversible convertibility of multi party pure states and discuss their physical basis in terms of deleting information

monotonically equivalent entropies and solution of additivity equation generalized entropies are studied as lyapunov functions for the master equation markov chains three basic properties of these lyapunov functions are taken into consideration universality independence of the kinetic coefficients trace form the form of sum over the states and additivity for composition of independent subsystems all the entropies which have all three properties simultaneously and are defined for positive probabilities are found they form a one parametric family we consider also pairs of entropies s1 s2 which are connected by the monotonous transformation s2 f s1 equivalent entropies all classes of pairs of universal equivalent entropies one of which has a trace form and another is additive these entropies can be different one from another were found these classes consist of two one parametric families the family of entropies which are equivalent to the additive trace form entropies and the family of renyi tsallis entropies

geometry of two qubit states with negative conditional entropy we review the geometric features of negative conditional entropy and the properties of the conditional amplitude operator proposed by cerf and adami for two qubit states in comparison with entanglement and nonlocality of the states we identify the region of negative conditional entropy in the tetrahedron of locally maximally mixed two qubit states within this set of states negative conditional entropy implies nonlocality and entanglement but not vice versa and we show that the cerf adami conditional amplitude operator provides an entanglement witness equivalent to the peres horodecki criterion outside of the tetrahedron this equivalence is generally not true

on quantum renyi entropies a new generalization and some properties the renyi entropies constitute a family of information measures that generalizes the well known shannon entropy inheriting many of its properties they appear in the form of unconditional and conditional entropies relative entropies or mutual information and have found many applications in information theory and beyond various generalizations of renyi entropies to the quantum setting have been proposed most prominently petz s quasi entropies and renner s conditional min max and collision entropy however these quantum extensions are incompatible and thus unsatisfactory we propose a new quantum generalization of the family of renyi entropies that contains the von neumann entropy min entropy collision entropy and the max entropy as special cases thus encompassing most quantum entropies in use today we show several natural properties for this definition including data processing inequalities a duality relation and an entropic uncertainty relation

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

the operational meaning of min and max entropy in this paper we show that the conditional min entropy h min a b of a bipartite state rhoab is directly related to the maximum achievable overlap with a maximally entangled state if only local actions on the b part of rhoab are allowed in the special case where a is classical this overlap corresponds to the probability of guessing a given b in a similar vein we connect the conditional max entropy h max a b to the maximum fidelity of rhoab with a product state that is completely mixed on a in the case where a is classical this corresponds to the security of a when used as a secret key in the presence of an adversary holding b because min and max entropies are known to characterize information processing tasks such as randomness extraction and state merging our results establish a direct connection between these tasks and basic operational problems for example they imply that the logarithm of the probability of guessing a given b is a lower bound on the number of uniform secret bits that can be extracted from a relative to an adversary holding b

synthesis of linear coherent quantum control systems using a differential evolution algorithm we propose a new method to construct an optimal linear coherent quantum controller based on an evolutionary optimization method namely a differential evolution algorithm the aim is to provide a straightforward approach to deal with both nonlinear and nonconvex constraints arising in the coherent quantum controller synthesis the solution to this control problem involves a complex algebraic riccati equation which corresponds to a physical realizability condition for the coherent quantum controller the proposed method is demonstrated through an example of an entanglement control problem for a quantum network comprising two cascaded optical parametric amplifiers

the asymptotically commuting bounded approximation property of banach spaces abstract we introduce and study the asymptotically commuting bounded approximation property of banach spaces this property is e g enjoyed by any dual space with the bounded approximation property the principal result is the following if a banach space x has the asymptotically commuting bounded approximation property then x is saturated with locally complemented separable subspaces enjoying the commuting bounded approximation property

lifting bounded approximation properties from banach spaces to their dual spaces based on a new reformulation of the bounded approximation property we develop a unified approach to the lifting of bounded approximation properties from a banach space x to its dual x this encompasses cases when x has the unique extension property or x is extendably locally reflexive in particular it is shown that the unique extension property of x permits to lift the metric a approximation property from x to x for any operator ideal a and that there exists a banach space x such that x x are extendably locally reflexive but x x are not

quantification of gaussian quantum steering einstein podolsky rosen steering incarnates a useful nonclassical correlation which sits between entanglement and bell nonlocality while a number of qualitative steering criteria exist very little has been achieved for what concerns quantifying steerability we introduce a computable measure of steering for arbitrary bipartite gaussian states of continuous variable systems for two mode gaussian states the measure reduces to a form of coherent information which is proven never to exceed entanglement and to reduce to it on pure states we provide an operational connection between our measure and the key rate in one sided device independent quantum key distribution we further prove that peres conjecture holds in its stronger form within the fully gaussian regime namely steering bound entangled gaussian states by gaussian measurements is impossible

finite element analysis of air supported membrane structures this paper deals with the finite element analysis of closed membrane structures that contain an enclosed fluid such as air the change in the fluid pressure resulting from the application of external forces is evaluated and taken into account in the formulation of the equilibrium equations the membrane formulation presented avoids the need for local co ordinate axes by using the isoparametric finite element plane as a material reference configuration the membrane material is modelled using standard large strain hyperelastic constitutive equations the volume of fluid is obtained by integrating over the membrane surface and boyle s law is used to determine the changes in air pressure that result from changes in volume full linearization of the internal pressure forces and the resulting additional term in the tangent operator are derived this new component leads to a full but rank one matrix and an algorithm to solve the resulting linear system is provided a number of numerical examples using the theory presented are considered

on α nuclear operators with applications to vector valued function spaces abstract let x be a banach space and let y be a closed subspace of a banach space z let be a tensor norm our main result is as follows assume that x or z has the approximation property if there is a bounded linear extension operator from y to z then any bounded linear operator t x y is nuclear whenever t is nuclear from x to z using this result we characterize the space c p x respectively uc p x of continuous functions from a compact hausdorff space into a banach space x whose range is p compact respectively unconditionally p compact

banach spaces with separable duals it is proved that every banach space with a separable dual em beds into a space with a shrinking basis it follows that every separable re flexive space can be embedded in a reflexive space with a basis

an explicit expression for the relative entropy of entanglement in all dimensions the relative entropy of entanglement is defined in terms of the relative entropy between an entangled state and its closest separable state css given a multipartite state on the boundary of the set of separable states we find an explicit expression for all the entangled states for which this state is a css our formula holds for multipartite states in all dimensions for the bipartite case of two qubits our formula reduce to the one given by miranowicz and ishizaka phys rev a 78 032310 2008

path integral approach to the nonextensive canonical density matrix abstract feynman s path integral is herein generalized to the nonextensive canonical density matrix based on tsallis entropy this generalization is done in two ways by using unnormalized and normalized constraints firstly we consider the path integral formulation with unnormalized constraints and this generalization is worked out through two different ways which are shown to be equivalent these formulations with unnormalized constraints are solutions to the two generalized bloch equations proposed in this work the first form of the generalized bloch equation is linear but with a temperature dependent effective hamiltonian the second form is nonlinear and resembles the anomalous correlated diffusion equation porous medium equation furthermore we can extend these results to the prescription of field theory using integral representations the second development is dedicated to analyzing the path integral formulation with normalized constraints to illustrate the methods introduced here we analyze the free particle case and a non interacting scalar field the results herein obtained are expected to be useful in the discussion of generic nonextensive contexts

theory and finite element formulation of rubberlike membrane shells using principal stretches a theory of rubberlike membrane shells undergoing large elastic deformations is derived the stresses are deduced from ogden s material law which is formulated in terms of the principal values of the right stretch tensor incompressibility is fulfilled exactly using the plane stress constraint furthermore a finite element formulation of the membrane theory is given the use of the tangential stiffness matrix derived analytically provides a quadratically convergent solution process several numerical examples show the robustness of the developed finite element

hydrostatic fluid loading in non linear finite element analysis deformation dependent pressure loading on solid structures is created by the interaction of fluids with the deformable surface of a structure such fairly simple load models are valid for static and quasi static analyses and they are a very efficient tool to represent the influence of a fluid on the behaviour of structures completing previous studies on the deformation dependence of the loading with the assumption of finite gas volumes the current contribution focuses on the influence of modifications of the size and shape of a finite structure containing an incompressible fluid with a free surface the linearization of the corresponding virtual work expression necessary for a newton type solution leads to additional terms for the volume dependence investigating these terms the conservativeness of the problem can be proven by the symmetry of the linearized form similarly to gas loading the discretization of the structure with finite elements leads to standard stiffness matrix forms plus the so called load stiffness matrices and a rank one update for each filled structure part if the loaded surface segments are identical with element surfaces some numerical examples show the effectiveness of the approach and the necessity to take the corresponding terms in the variational expression and the following linearization into account copyright 2004 john wiley sons ltd

some properties of q logarithm and q exponential functions in tsallis statistics we present some formulae which q logarithmic and q exponential functions introduced in tsallis statistics satisfy exact expression of the mellin transform of q exponential function is given moreover the q generalization of the digamma function is presented

an entanglement measure based on two order minors in this paper a new entanglement measure called emm the entanglement measure based on minors has been constructed by the convex roof method and proved to be a good entanglement measure according to the axiomatic point of view computation of emm can be finished directly by the two order minors of a coefficient matrix instead of the eigenvalues of the density operator required by most of the other entanglement measures so it is very fast and very easy on the other hand emm is related to the modified bures distance between and the closest separable state so it has geometry meaning we also investigate the relations between emm and the entanglement of formation negativity and logarithmic negativity and discover that emm is always smaller than or equal to them emm is equivalent to concurrence however their definitions and methods of proof are completely different emm will improve the efficiency of searching for maximally entangled multipartite states

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

hilbert s projective metric in quantum information theory we introduce and apply hilbert s projective metric in the context of quantum information theory the metric is induced by convex cones such as the sets of positive separable or positive partial transpose operators it provides bounds on measures for statistical distinguishability of quantum states and on the decrease of entanglement under protocols involving local quantum operations and classical communication or under other cone preserving operations the results are formulated in terms of general cones and base norms and lead to contractivity bounds for quantum channels for instance improving ruskai s trace norm contraction inequality a new duality between distinguishability measures and base norms is provided for two given pairs of quantum states we show that the contraction of hilbert s projective metric is necessary and sufficient for the existence of a probabilistic quantum operation that maps one pair onto the other inequalities between hilbert s projective metric and the chernoff bound the

student s t and r distributions unified derivation from an entropic variational principle abstract the optimization of the recently generalized entropy of the form s q 1 dx p x q q 1 with the constraints dx p x 1 and x 2 q dx x 2 p x q 1 yields the student s t distribution for q 1 and the r distribution for q

the asymptotic entanglement cost of preparing a quantum state we give a detailed proof of the conjecture that the asymptotic entanglement cost of preparing a state is equal to limn ef n n where ef is the entanglement of formation

fractal structure with a typical scale in order to understand the characteristics common to distributions which have both fractal and non fractal scale regions in a unified framework we introduce the concept of a typical scale we employ a model of 2d gravity modified by the r2 term as a tool to understand such distributions through the typical scale this model is obtained by adding an interaction term with a typical scale to a scale invariant system a distribution derived in the model provides power law one in the large scale region but weibull like one in the small scale region as examples of distributions which have both fractal and non fractal regions we take those of personal income and citation number of scientific papers we show that these distributions are fitted fairly well by the distribution curves derived analytically in the r2 2d gravity model as a result we consider that the typical scale is a useful concept to understand various distributions observed in the real world in a unified way we also point out that the r2 2d gravity model provides us with an effective tool to read the typical scales of various distributions in a systematic way

monogamy of multi qubit entanglement using renyi entropy we introduce a class of bipartite entanglement measures based on renyi entropy namely renyi entanglement with an analytic formula in two qubit systems for 1 we also show that multi qubit entanglement has a monogamy inequality in terms of renyi entanglement for all 2

multiwavelet packet entropy and its application in transmission line fault recognition and classification multiwavelets possess better properties than traditional wavelets multiwavelet packet transformation has more high frequency information spectral entropy can be applied as an analysis index to the complexity or uncertainty of a signal this paper tries to define four multiwavelet packet entropies to extract the features of different transmission line faults and uses a radial basis function rbf neural network to recognize and classify 10 fault types of power transmission lines first the preprocessing and postprocessing problems of multiwavelets are presented shannon entropy and tsallis entropy are introduced and their difference is discussed second multiwavelet packet energy entropy time entropy shannon singular entropy and tsallis singular entropy are defined as the feature extraction methods of transmission line fault signals third the plan of transmission line fault recognition using multiwavelet packet entropies and an rbf neural network is proposed finally the experimental results show that the plan with the four multiwavelet packet energy entropies defined in this paper achieves better performance in fault recognition the performance with sa4 symmetric antisymmetric multiwavelet packet tsallis singular entropy is the best among the combinations of different multiwavelet packets and the four multiwavelet packet entropies

operator monotones the reduction criterion and the relative entropy we introduce the theory of operator monotone functions and employ it to derive a new inequality relating the quantum relative entropy and the quantum conditional entropy we present applications of this new inequality and in particular we prove a new lower bound on the relative entropy of entanglement and other properties of entanglement measures

remarks on entanglement measures and non local state distinguishability we investigate the properties of three entanglement measures that quantify the statistical distinguishability of a given state with the closest disentangled state that has the same reductions as the primary state in particular we concentrate on the relative entropy of entanglement with reversed entries we show that this quantity is an entanglement monotone which is strongly additive thereby demonstrating that monotonicity under local quantum operations and strong additivity are compatible in principle in accordance with the presented statistical interpretation which is provided this entanglement monotone however has the property that it diverges on pure states with the consequence that it cannot distinguish the degree of entanglement of different pure states we also prove that the relative entropy of entanglement with respect to the set of disentangled states that have identical reductions to the primary state is an entanglement monotone we finally investigate the trace norm measure and demonstrate that it is also a proper entanglement monotone

logarithmic negativity a full entanglement monotone that is not convex it is proven that logarithmic negativity does not increase on average under a general positive partial transpose preserving operation a set of operations that incorporate local operations and classical communication as a subset and in the process a further proof is provided that the negativity does not increase on average under the same set of operations given that the logarithmic negativity is not a convex function this result is surprising as it is generally considered that convexity describes the local physical process of losing information the role of convexity and in particular its relation or lack thereof to physical processes is discussed and importance of continuity in this context is stressed

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

monogamy inequality for distributed gaussian entanglement we show that for all n mode gaussian states of continuous variable systems the entanglement shared among n parties exhibits the fundamental monogamy property the monogamy inequality is proven by introducing the gaussian tangle an entanglement monotone under gaussian local operations and classical communication which is defined in terms of the squared negativity in complete analogy with the case of n qubit systems our results elucidate the structure of quantum correlations in many body harmonic lattice systems

norm preserving extensions of functionals and denting points of convex sets let w and z be banach spaces and let x subset w and y subset z be closed subspaces let mathcal l be a subspace of mathcal l w z the banach space of bounded linear operators from w to z containing x otimes y we describe for x in x and y in y all norm preserving extensions of x otimes y in x otimes y ast to the space mathcal l in terms of convergence of convex combinations we also characterize denting points of bounded convex subsets of banach spaces in similar terms various applications are presented

the emergence of typical entanglement in two party random processes we investigate the entanglement within a system undergoing a random local process we find that there is initially a phase of very fast generation and spread of entanglement at the end of this phase the entanglement is typically maximal in oliveira et al 2007 phys rev lett 98 130502 we proved that the maximal entanglement is reached to a fixed arbitrary accuracy within o n3 steps where n is the total number of qubits here we provide a detailed and more pedagogical proof we demonstrate that one can use the so called stabilizer gates to simulate this process efficiently on a classical computer furthermore we discuss three ways of identifying the transition from the phase of rapid spread of entanglement to the stationary phase i the time when saturation of the maximal entanglement is achieved ii the cutoff moment when the entanglement probability distribution is practically stationary and iii the moment block entanglement exhibits volume scaling we furthermore investigate the mixed state and multipartite setting numerically we find that the mutual information appears to behave similarly to the quantum correlations and that there is a well behaved phase space flow of entanglement properties towards an equilibrium we describe how the emergence of typical entanglement can be used to create a much simpler tripartite entanglement description the results form a bridge between certain abstract results concerning typical also known as generic entanglement relative to an unbiased distribution on pure states and the more physical picture of distributions emerging from random local interactions

ideals of operators and the metric approximation property abstract we prove that a banach space x has the metric approximation property if and only if f y x the space of all finite rank operators is an ideal in l y x the space of all bounded operators for every banach space y moreover x has the shrinking metric approximation property if and only if f x y is an ideal in l x y for every banach space y similar results are obtained for u ideals and the corresponding unconditional metric approximation properties

independence of work and entropy for equal energetic finite quantum systems passive state energy as an entanglement quantifier although entropy is a necessary and sufficient quantity to characterize the order of work content for equal energetic ee states in the asymptotic limit for the finite quantum systems the relation is not so linear and requires detailed investigation toward this we have considered a resource theoretic framework taking the energy preserving operations epos as free to compare the amount of extractable work from two different quantum states under the epo majorization becomes a necessary criterion for state transformation it is also shown that the passive state energy is a concave function and for ee states it becomes proportional to the ergotropy in absolute sense invariance of the passive state energy under unitary action on the given state makes it an entanglement measure for the pure bipartite states furthermore due to the nonadditivity of passive state energy for the different system hamiltonians one can generate vidal s monotones which would give the optimal probability for pure entangled state transformation this measure also quantifies the ergotropic gap which is employed to distinguish some specific classes of three qubit pure entangled states

entropy correlation and entanglement for mixed states in an algebraic model as an alternative with potential connections to actual experiments other than the systems more usually used in the field of entanglement the dynamics of entropy correlation and entanglement between two anharmonic vibrations in a well established algebraic model with parameters extracted from fitting to highly excited spectral experimental results for molecules h2o and so2 is studied in terms of the linear entropy and two negativities for various initial states that are respectively taken to be the mixed density matrices of thermal states and squeezed states on each mode for a suitable parameter in initial states the entropies in two stretches can show positive correlation or anti correlation and the linear entropy of each mode is positively correlated with the negativities just for the mixed squeezed states with small parameters in h2o while they do not display any correlation in other cases for the mixed squeezed states the negativities exhibit dominantly positive correlations with an effective mutual entropy the differences in the linear entropy and the negativities between h2o and so2 are discussed as well those are useful for molecular quantum computing and quantum information processing

an edge based smoothed finite element method es fem using 3 node triangular elements for 3d non linear analysis of spatial membrane structures an edge based smoothed finite element method using 3 node triangular membrane elements es fem t3 is proposed to analyze three dimensional 3d spatial membrane structures under large deflection rotation and strain in our 3d formulation co rotational local coordinate systems associated with the edge based smoothing domains are constructed edge based gradient smoothing for the spatial membrane structure is performed in global cartesian coordinate system and transformed into the co rotational local coordinate system the smoothed strain and stress can then be properly evaluated in the co rotational local coordinate system after the elimination of the rigid body motions simply by coordinates transformation explicit time integration scheme is used to compute the transient response of the 3d spatial membrane structure to time domain excitations and the dynamic relaxation method is employed to obtain steady state solutions the numerical results demonstrate that the proposed method produces much better solution accuracy and computational efficiency than the standard fem using t3 membrane element copyright 2010 john wiley sons ltd

some general properties of unified entropies basic properties of the unified entropies are examined the consideration is mainly restricted to the finite dimensional quantum case bounds in terms of ensembles of quantum states are given both the continuity in fannes sense and stability in lesche s sense are shown for wide ranges of parameters in particular uniform estimates are obtained for the quantum renyi entropies stability properties in the thermodynamic limit are discussed as well it is shown that the unified entropies enjoy both the subadditivity and triangle inequality for a certain range of parameters non decreasing of all the unified entropies under projective measurements is proved

on convex optimization problems in quantum information theory convex optimization problems arise naturally in quantum information theory often in terms of minimizing a convex function over a convex subset of the space of hermitian matrices in most cases finding exact solutions to these problems is usually impossible as inspired by earlier investigations into the relative entropy of entanglement ree miranowicz and ishizaka 2008 phys rev a 78 032310 we introduce a general method to solve the converse problem rather than find explicit solutions that is given a matrix in a convex set we determine a family of convex functions that are minimized at this point this method allows us find explicit formulae for the ree and the rains bound two well known upper bounds on the distillable entanglement and yields interesting information about these quantities such as the fact that they coincide in the case where at least one subsystem of a multipartite state is a qubit