multiqubit nonlocality in families of 3 and 4 qubit entangled states we investigate genuine multiqubit nonlocality in families of entangled 3 and 4 qubit pure states by analyzing a bell type inequality that is violated only if all qubits are nonlocally correlated we present detailed numerical studies of the relationship between entanglement and violation of the svetlichny bell type inequality in an experimentally accessible set of 3 qubit pure states and identify the special nonlocality property of the maximal slice states in the space of all 3 qubit pure states we also analyze nonlocal correlations in 3 qubit generalized greenberger horne zeilinger ghz states and extend our analysis to the case of 4 qubit generalized ghz states we show that like the 3 qubit case some 4 qubit generalized ghz states do not violate a bell inequality that tests for genuine 4 qubit nonlocality furthermore the location of the boundary between the states that do violate the inequality and those that do not is the same for the 3 and 4 qubit generalized ghz states

model selection and akaike s information criterion aic the general theory and its analytical extensions during the last fifteen years akaike s entropy based information criterion aic has had a fundamental impact in statistical model evaluation problems this paper studies the general theory of the aic procedure and provides its analytical extensions in two ways without violating akaike s main principles these extensions make aic asymptotically consistent and penalize overparameterization more stringently to pick only the simplest of the true models these selection criteria are called caic and caicf asymptotic properties of aic and its extensions are investigated and empirical performances of these criteria are studied in choosing the correct degree of a polynomial model in two different monte carlo experiments under different conditions

multipartite generalization of the schmidt decomposition we find a canonical form for pure states of a general multipartite system in which the constraints on the coordinates with respect to a factorizable orthonormal basis are simply that certain ones vanish and certain others are real for identical particles they are invariant under permutations of the particles as an application we find the dimension of the generic local equivalence class

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

concurrence vectors in arbitrary multipartite quantum systems for a given pure state of a multipartite system the concurrence vector is defined by employing the defining representation of generators of the corresponding rotation groups the norm of a concurrence vector is considered as a measure of entanglement for the multipartite pure state the concurrence vector is regarded as the direct sum of concurrence subvectors in the sense that each subvector is associated with a pair of particles it is proposed to use the norm of each subvector as the contribution of the corresponding pair in entanglement of the system

general paradigm for distilling classical key from quantum states in this paper we develop a formalism for distilling a classical key from a quantum state in a systematic way expanding on our previous work on a secure key from bound entanglement horodecki et al 2005 more detailed proofs discussion and examples are provided of the main results namely we demonstrate that all quantum cryptographic protocols can be recast in a way which looks like entanglement theory with the only change being that instead of distilling einstein podolsky rosen epr pairs the parties distill private states the form of these general private states are given and we show that there are a number of useful ways of expressing them some of the private states can be approximated by certain states which are bound entangled thus distillable entanglement is not a requirement for a private key we find that such bound entangled states are useful for a cryptographic primitive we call a controlled private quantum channel pqc we also find a general class of states which have negative partial transpose are npt but which appear to be bound entangled the relative entropy distance is shown to be an upper bound on the rate of a key this allows us to compute the exact value of a distillable key for a certain class of private states

wegner type bounds for a multi particle continuous anderson model with an alloy type external potential we consider an n particle quantum systems in d with interaction and in presence of a random external alloy type potential a continuous n particle anderson model we establish wegner type bounds inequalities for such models giving upper bounds for the probability that random spectra of hamiltonians in finite volumes intersect a given set

a bayesian multidimensional scaling procedure for the spatial analysis of revealed choice data we present a new bayesian formulation of a vector multidimensional scaling procedure for the spatial analysis of binary choice data the gibbs sampler is gainfully employed to estimate the posterior distribution of the specified scalar products bilinear model parameters the computational procedure allows for the explicit estimation of a covariance matrix which can accommodate violations of iia due to context effects in addition posterior standard errors can be estimated which reflect differential degrees of consumer choice uncertainty and or brand position instability a marketing application concerning the analysis of consumers consideration sets for luxury automobiles is provided to illustrate the use of the proposed methodology

polynomial invariants of quantum codes the weight enumerators shor and laflamme 1997 of a quantum code are quite powerful tools for exploring its structure as the weight enumerators are quadratic invariants of the code this suggests the consideration of higher degree polynomial invariants we show that the space of degree k invariants of a code of length n is spanned by a set of basic invariants in one to one correspondence with s sub k sup n we then present a number of equations and inequalities in these invariants in particular we give a higher order generalization of the shadow enumerator of a code and prove that its coefficients are nonnegative we also prove that the quartic invariants of a 4 4 2 sub 2 code are uniquely determined an important step in a proof that any 4 4 2 sub 2 code is additive rains 1999

the geometry of multi qubit entanglement this paper a continuation of a previous one iwai 2007 j phys a math theor 40 1361 studies the geometry of multi qubit entanglement with respect to bipartite partitions an n qubit system c2 n is isomorphic with the linear space of 2l 2m complex matrices where l m n according to the isomorphism the local transformation group u 2l u 2m acts on the space of normalized states in let m and g denote the space of normalized states and the local transformation group acting on m respectively according to the orbit types m is stratified into strata among which a principal stratum and the sets of separable states and maximally entangled states will be identified for a function f c det i cc proves to serve as a measure of entanglement where i denotes the 2l 2l identity matrix the f c attains the minimal and the maximal values respectively on the sets of separable states and maximally entangled states and further takes no extremal values on the principal stratum the f c projects to a function on the factor space g m a naturally defined metric on m also projects to that on g m which serves to measure the distance between the separable states f 1 0 and the states f 1 k of prescribed value k of measure to be precise one has to restrict m to the principal stratum when projecting the metric three and four qubit systems will be studied intensively and then multi qubit systems discussed

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

classification of general n qubit states under stochastic local operations and classical communication in terms of the rank of coefficient matrix we solve the entanglement classification under stochastic local operations and classical communication slocc for general n qubit states for two arbitrary pure n qubit states connected via local operations we establish an equation between the two coefficient matrices associated with the states the rank of the coefficient matrix is preserved under slocc and gives rise to a simple way of partitioning all the pure states of n qubits into different families of entanglement classes as exemplified here when applied to the symmetric states this approach reveals that all the dicke states ensuremath ell n with ensuremath ell 1 dots n 2 are inequivalent under slocc

local unitary symmetries and entanglement invariants we investigate the relation between local unitary symmetries and entanglement invariants of multi qubit systems the hilbert space of such systems can be stratified in terms of states with different types of symmetry we review the connection between this stratification and the ring of entanglement invariants and the corresponding geometric description in terms of algebraic varieties on a stratum of a non trivial symmetry group the invariants of the symmetry preserving operations gives a sufficient description of entanglement finding these invariants is often a simpler problem than finding the invariants of the local unitary group the conditions as given by the luna richardson theorem for when the ring of such invariants is isomorphic to the ring of local unitary invariants on the stratum are discussed as an example we consider symmetry groups that can be diagonalized by local unitary operations and for which the group action on each qubit is non trivial on the stratum of such a symmetry the entanglement can be described in terms of a canonical form and the invariants of the symmetry preserving operations this canonical form and the invariants are directly determined by the symmetry group further we briefly discuss how some recently proposed entanglement classification schemes capture symmetry properties

the uniqueness theorem for entanglement measures we explore and develop the mathematics of the theory of entanglement measures after a careful review and analysis of definitions of preliminary results and of connections between conditions on entanglement measures we prove a sharpened version of a uniqueness theorem which gives necessary and sufficient conditions for an entanglement measure to coincide with the reduced von neumann entropy on pure states we also prove several versions of a theorem on extreme entanglement measures in the case of mixed states we analyze properties of the asymptotic regularization of entanglement measures proving for example convexity for the entanglement cost and for the regularized relative entropy of entangle ment

asymptotic entanglement manipulation of bipartite pure states entanglement of pure states of bipartite quantum systems has been shown to have a unique measure in terms of the von neumann entropy of the reduced states of either of its subsystems the measure is established under entanglement manipulation of an asymptotically large number of copies of the bipartite pure state in this paper two different asymptotic measures of entanglement for arbitrary sequences of bipartite pure states are established these are shown to coincide only when the sequence is information stable in terms of the quantum spectral information rates of its corresponding sequence of subsystem states additional bounds on the optimal rates of entanglement manipulation protocols in quantum information theory are also presented these include bounds given by generalizations of the coherent information bounds rains bound and the relative entropy of entanglement

eigenfunctions in a two particle anderson tight binding model we establish the phenomenon of anderson localisation for a quantum two particle system on a lattice mathbb z d with short range interaction and in presence of an iid external potential with sufficiently regular marginal distribution

characterization of entanglement transformation via group representation theory entanglement transformation of composite quantum systems is investigated in the context of group representation theory representation of the direct product group sl 2 c sl 2 c composed of local operators acting on the binary composite system is realized in the four dimensional complex space in terms of a set of novel bases that are pseudo orthonormalized the two to one homomorphism is then established for the group sl 2 c sl 2 c onto the so 4 c it is shown that the resulting representation theory leads to the complete characterization for the entanglement transformation of the binary composite system

on the geometry of four qubit invariants the geometry of four qubit entanglement is investigated we replace some of the polynomial invariants for four qubits introduced recently by new ones of direct geometrical meaning it is shown that these invariants describe four points six lines and four planes in complex projective space cp3 for the generic entanglement class of stochastic local operations and classical communication they take a very simple form related to the elementary symmetric polynomials in four complex variables moreover suitable powers of their magnitudes are entanglement monotones that fit nicely into the geometric set of n qubit ones related to grassmannians of l planes found recently we also show that in terms of these invariants the hyperdeterminant of order 24 in the four qubit amplitudes takes a more instructive form than the previously published expressions available in the literature finally in order to understand two three and four qubit entanglement in geometric terms we propose a unified setting based on cp3 furnished with a fixed quadric

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

scalable programmable quantum gates and a new aspect of the additivity problem for the classical capacity of quantum channels we consider two apparently separated problems in the first part of the article we study the concept of a scalable approximate programmable quantum gate spqg these are special approximate programmable quantum gates with nice properties that could have implications on the theory of universal computation unfortunately as we prove such objects do not exist in the domain of usual quantum theory in the second part the problem of noisy dense coding and generalizations is addressed we observe that the additivity problem for the classical capacity obtained is of apparently greater generality than for the usual quantum channel completely positive maps i e the latter occurs as a special case of the former but as we shall argue with the help of the nonexistence result of the first part the former cannot be reduced to an instance of the latter we conclude by suggesting that the additivity problem for the classical capacity of quantum channels as posed until now may conceptually not be in its appropriate generality

classification of multipartite entanglement of all finite dimensionality we provide a systematic classification of multiparticle entanglement in terms of equivalence classes of states under stochastic local operations and classical communication slocc we show that such a slocc equivalency class of states is characterized by ratios of homogenous polynomials that are invariant under local action of the special linear group we then construct the complete set of all such sl invariant polynomials slips our construction is based on schur weyl duality and applies to any number of qudits in all finite dimensions in addition we provide an elegant formula for the dimension of the homogenous slips space of a fixed degree as a function of the number of qudits the expressions for the slips involve in general many terms but for the case of qubits we also provide much simpler expressions

method of convex rigid frames and applications in studies of multipartite qunit pure states in this letter we suggest a method of convex rigid frames in the studies of multipartite qunit pure states we illustrate what the convex rigid frames are and what is their method as applications we use this method to solve some basic problems and give some new results three theorems the problem of the partial separability of the multipartite qunit pure states and its geometric explanation the problem of the classification of multipartite qunit pure states giving a perfect explanation of the local unitary transformations thirdly we discuss the invariants of classes and give a possible physical explanation

relative entropy of entanglement and restricted measurements we introduce variants of relative entropy of entanglement based on the optimal distinguishability from unentangled states by means of restricted measurements in this way we are able to prove that the standard regularized entropy of entanglement is strictly positive for all multipartite entangled states this implies that the asymptotic creation of a multipartite entangled state by means of local operations and classical communication always requires the consumption of a nonlocal resource at a strictly positive rate

a new proof of localization in the anderson tight binding model we give a new proof of exponential localization in the anderson tight binding model which uses many ideas of the frohlich martinelli scoppola and spencer proof but is technically simpler particularly the probabilistic estimates

the geometry of concurrence as a measure of entanglement it is widely recognized that concurrence can be regarded as a measure of two qubit entanglement this paper studies the geometry of concurrence for a two qubit system to show that the concurrence serves as a coordinate of the factor space where is the space of normalized two qubit states and where g u 1 su 2 su 2 any monotonically increasing function of the concurrence can serve as a measure for entanglement from the viewpoint of riemannian geometry a state with concurrence r is shown to be distant from the separable states by where r ranges over 0 r 1 in addition measures of entanglement for n qubits are discussed on the basis of a bipartite decomposition with m n they are invariant under the local unitary transformation group u 2 u 2m

a comparison of the entanglement measures negativity and concurrence in this paper we investigate two different entanglement measures in the case of mixed states of two qubits we prove that the negativity of a state can never exceed its concurrence and is always larger than 1 c 2 c2 1 c where c is the concurrence of the state furthermore we derive an explicit expression for the states for which the upper or lower bound is satisfied finally we show that similar results hold if the relative entropy of entanglement and the entanglement of formation are compared

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

absence of diffusion in the anderson tight binding model for large disorder or low energy we prove that the green s function of the anderson tight binding hamiltonian decays exponentially fast at long distances on v with probability 1 we must assume that either the disorder is large or the energy is sufficiently low our proof is based on perturbation theory about an infinite sequence of block hamiltonians and is related to kam methods

application of model selection criteria to some problems in multivariate analysis a review of model selection criteria is presented with a view toward showing their similarities it is suggested that some problems treated by sequences of hypothesis tests may be more expeditiously treated by the application of model selection criteria consideration is given to application of model selection criteria to some problems of multivariate analysis especially the clustering of variables factor analysis and more generally describing a complex of variables

local symmetry properties of pure three qubit states entanglement types of pure states of three spin particles are classified by means of their stabilizers in the group of local unitary transformations it is shown that the stabilizer is generically discrete and that a larger stabilizer indicates a stationary value for some local invariant we describe all the exceptional states with enlarged stabilizers

application of the conditional population mixture model to image segmentation the problem of image segmentation is considered in the context of a mixture of probability distributions the segments fall into classes a probability distribution is associated with each class of segment parametric families of distributions are considered a set of parameter values being associated with each class with each observation is associated an unobservable label indicating from which class the observation arose segmentation algorithms are obtained by applying a method of iterated maximum likelihood to the resulting likelihood function a numerical example is given choice of the number of classes using akaike s information criterion aic for model identification is illustrated

revised geometric measure of entanglement we present a revised geometric measure of entanglement rgme which is just certain generalization of geometric measure of entanglement gme the revised version is an entanglement monotone some useful inequalities about rgme are deduced for example we give the formulae of rgme for the two parameter class of states in a 2 n quantum system the two particles high dimensional maximally entangled mixed state the isotropic state including the n particle d level case and two multipartite bound entangled states the results show there is a relation and then rgme is an appropriate measure of entanglement

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

a complete set of covariants of the four qubit system we obtain a complete and minimal set of 170 generators for the algebra of sl 2 4 covariants of a binary quadrilinear form interpreted in terms of a four qubit system this describes in particular the algebraic varieties formed by the orbits of local filtering operations in its projective hilbert space also this sheds some light on the local unitary invariants and provides all the possible building blocks for the construction of entanglement measures for such a system

a new class of entanglement measures we introduce new entanglement measures on the set of density operators on tensor product hilbert spaces these measures are based on the greatest cross norm on the tensor product of the sets of trace class operators on hilbert space we show that they satisfy the basic requirements on entanglement measures discussed in the literature including convexity invariance under local unitary operations and nonincrease under local quantum operations and classical communication

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

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

a bayesian vector multidimensional scaling procedure incorporating dimension reparameterization with variable selection we propose a two way bayesian vector spatial procedure incorporating dimension reparameterization with a variable selection option to determine the dimensionality and simultaneously identify the significant covariates that help interpret the derived dimensions in the joint space map we discuss how we solve identifiability problems in a bayesian context that are associated with the two way vector spatial model and demonstrate through a simulation study how our proposed model outperforms a popular benchmark model in addition an empirical application dealing with consumers ratings of large sport utility vehicles is presented to illustrate the proposed methodology we are able to obtain interpretable and managerially insightful results from our proposed model with variable selection in comparison with the benchmark model

a latent class approach to fitting the weighted euclidean model clascal a weighted euclidean distance model for analyzing three way proximity data is proposed that incorporates a latent class approach in this latent class weighted euclidean model the contribution to the distance function between two stimuli is per dimension weighted identically by all subjects in the same latent class this model removes the rotational invariance of the classical multidimensional scaling model retaining psychologically meaningful dimensions and drastically reduces the number of parameters in the traditional indscal model the probability density function for the data of a subject is posited to be a finite mixture of spherical multivariate normal densities the maximum likelihood function is optimized by means of an em algorithm a modified fisher scoring method is used to update the parameters in the m step a model selection strategy is proposed and illustrated on both real and artificial data

entangled three qubit states without concurrence and three tangle we provide a complete analysis of mixed three qubit states composed of a greenberger horne zeilinger state and a w state orthogonal to the former we present optimal decompositions and convex roofs for the three tangle further we provide an analytical method to decide whether or not an arbitrary rank 2 state of three qubits has vanishing three tangle these results highlight intriguing differences compared to the properties of two qubit mixed states and may serve as a quantitative reference for future studies of entanglement in multipartite mixed states by studying the coffman kundu wootters inequality we find that while the amounts of inequivalent entanglement types strictly add up for pure states this monogamy can be lifted for mixed states by virtue of vanishing tangle measures

random effects diagonal metric multidimensional scaling models by assuming a distribution for the subject weights in a diagonal metric indscal multidimensional scaling model the subject weights become random effects including random effects in multidimensional scaling models offers several advantages over traditional diagonal metric models such as those fitted by the indscal alscal and other multidimensional scaling programs unlike traditional models the number of parameters does not increase with the number of subjects and because the distribution of the subject weights is modeled the construction of linear models of the subject weights and the testing of those models is immediate here we define a random effects diagonal metric multidimensional scaling model give computational algorithms describe our experiences with these algorithms and provide an example illustrating the use of the model and algorithms

a latent class multidimensional scaling model for two way one mode continuous rating dissimilarity data in this paper we propose a cluster mds model for two way one mode continuous rating dissimilarity data the model aims at partitioning the objects into classes and simultaneously representing the cluster centers in a low dimensional space under the normal distribution assumption a latent class model is developed in terms of the set of dissimilarities in a maximum likelihood framework in each iteration the probability that a dissimilarity belongs to each of the blocks conforming to a partition of the original dissimilarity matrix and the rest of parameters are estimated in a simulated annealing based algorithm a model selection strategy is used to test the number of latent classes and the dimensionality of the problem both simulated and classical dissimilarity data are analyzed to illustrate the model

localization bounds for multiparticle systems we consider the spectral and dynamical properties of quantum systems of n particles on the lattice mathbb z d of arbitrary dimension with a hamiltonian which in addition to the kinetic term includes a random potential with iid values at the lattice sites and a finite range interaction two basic parameters of the model are the strength of the disorder and the strength of the interparticle interaction it is established here that for all n there are regimes of high disorder and or weak enough interactions for which the system exhibits spectral and dynamical localization the localization is expressed through bounds on the transition amplitudes which are uniform in time and decay exponentially in the hausdorff distance in the configuration space the results are derived through the analysis of fractional moments of the n particle green function and related bounds on the eigenfunction correlators

entanglement swapping between multi qudit systems we generalize the entanglement swapping scheme originally proposed for two pairs of qubits to an arbitrary number q of systems composed from an arbitrary number mj of qudits each of the systems is supposed to be prepared in a maximally entangled state of mj qudits while different systems are not correlated at all we show that when a set of qj 1 aj particles from each of the q systems aj particles are measured is subjected to a generalized bell type measurement the resulting set of qj 1 mj aj particles will collapse into a maximally entangled state

characterization of partial positive transposition states and measures of entanglement a detailed characterization of partial positive transposition ppt states both in the heisenberg and in the schrodinger picture is given measures of entanglement are defined and discussed in details illustrative examples are provided

localization at large disorder and at extreme energies an elementary derivation the work presents a short proof of localization under the conditions of either strong disorder 0 or extreme energies for a wide class of self adjoint operators with random matrix elements acting inl 2 spaces a prototypical example is the discrete schrodinger operatorh u 0 x v x onz d d 1 withu 0 x a specified background potential and v x generated as random variables the general results apply to operators with replaced by a non local self adjoint operatort whose matrix elements satisfy y t x y s const uniformly inx for somes 1 localization means here that within a specified energy range the spectrum ofh is of the pure point type or equivalently the wave functions do not spread indefinitely under the unitary time evolution generated byh the effect is produced by strong disorder in either the potential or in the off diagonal matrix elementst x y under rapid decay oft x y the corresponding eigenfunctions are also proven to decay exponentially the method is based on resolvent techniques the central technical ideas include the use of low moments of the resolvent kernel i e g e x y s withs small enough 1 to avoid the divergence caused by the distribution s cauchy tails and an effective use of the simple form of the dependence ofg e x y on the individual matrix elements ofh in elucidating the implications of the fundamental equation h e g e x x 0 x x0 this approach simplifies previous derivations of localization results avoiding the small denominator difficulties which have been hitherto encountered in the subject it also yields some new results which include localization under the following sets of conditions i potentials with an inhomogeneous non random partu 0 x ii the bethe lattice iii operators with very slow decay in the off diagonal terms t x y 1 x y d e and iv localization produced by disordered boundary conditions

bayesian multidimensional scaling and choice of dimension multidimensional scaling is widely used to handle data that consist of similarity or dissimilarity measures between pairs of objects we deal with two major problems in metric multidimensional scaling configuration of objects and determination of the dimension of object configuration within a bayesian framework a markov chain monte carlo algorithm is proposed for object configuration along with a simple bayesian criterion called mdsic for choosing their dimension simulation results are presented as are real data our method provides better results than does classical multidimensional scaling and alscal for object configuration and mdsic seems to work well for dimension choice in the examples considered

monotones and invariants for multi particle quantum states we introduce new entanglement monotones which generalize to the case of many parties those which give rise to the majorization based partial ordering of bipartite states entanglement we give some examples of restrictions they impose on deterministic and probabilistic conversion between multipartite states via local actions and classical communication these include restrictions which do not follow from any bipartite considerations we derive supermultiplicativity relations between each state s monotones and the monotones for collective processing when the parties share several states we also investigate polynomial invariants under local unitary transformations and show that a large class of these are invariant under collective unitary processing and also multiplicative putting restrictions for example on the exact conversion of multiple copies of one state to multiple copies of another

the reduction of the closest disentangled states we study the closest disentangled state to a given entangled state in any system multi party with any dimension we obtain the set of equations the closest disentangled state must satisfy and show that its reduction is strongly related to the extremal condition of the local filtering on each party although the equations we obtain are not still tractable we find some sufficient conditions for which the closest disentangled state has the same reduction as the given entangled state further we suggest a prescription to obtain a tight upper bound of the relative entropy of entanglement in two qubit systems

local unitary equivalence of multipartite pure states necessary and sufficient conditions for the equivalence of arbitrary n qubit pure quantum states under local unitary lu operations are derived first an easily computable standard form for multipartite states is introduced two generic states are shown to be lu equivalent iff their standard forms coincide the lu equivalence problem for nongeneric states is solved by presenting a systematic method to determine the lu operators if they exist which interconvert the two states

bell s theorem for general n qubit states we derive a single general bell inequality which is a sufficient and necessary condition for the correlation function for n particles to be describable in a local and realistic picture for the case in which measurements on each particle can be chosen between two arbitrary dichotomic observables we also derive a necessary and sufficient condition for an arbitrary n qubit mixed state to violate this inequality this condition is a generalization and reformulation of the horodecki family condition for two qubits

entanglement of pure states for a single copy an optimal local conversion strategy between any two pure states of a bipartite system is presented it is optimal in that the probability of success is the largest achievable if the parties which share the system and which can communicate classically are only allowed to act locally on it the study of optimal local conversions sheds some light on the entanglement of a single copy of a pure state we propose a quantification of such an entanglement by means of a finite minimal set of new measures from which the optimal probability of conversion follows

on asymptotic continuity of functions of quantum states a useful kind of continuity of quantum states functions in asymptotic regime is so called asymptotic continuity in this letter we provide general tools for checking if a function possesses this property first we prove equivalence of asymptotic continuity with so called robustness under admixture this allows us to show that relative entropy distance from a convex set including a maximally mixed state is asymptotically continuous subsequently we consider arrowing a way of building a new function out of a given one the procedure originates from constructions of intrinsic information and entanglement of formation we show that arrowing preserves asymptotic continuity for a class of functions so called subextensive ones the result is illustrated by means of several examples

tripartite entanglement dependence of tripartite non locality in non inertial frames the three tangle dependence of smax max s where s is a svetlichny operator is explicitly derived when one party moves with a uniform acceleration with respect to other parties in a generalized greenberger horne zeilinger and maximally slice states the tangle dependence of smax is also derived implicitly from this dependence we conjecture that multipartite entanglement is not the only physical resource for quantum mechanical multipartite non locality

estimating entanglement measures in experiments we present a method to estimate entanglement measures in experiments we show how a lower bound on a generic entanglement measure can be derived from the measured expectation values of any finite collection of entanglement witnesses hence witness measurements are given a quantitative meaning without the need of further experimental data we apply our results to a recent multiphoton experiment m bourennane et al phys rev lett 92 087902 2004 giving bounds on the entanglement of formation and the geometric measure of entanglement in this experiment

classification of n qubit states with minimum orbit dimension the group of local unitary transformations acts on the space of n qubit pure states decomposing it into orbits in a previous paper we proved that a product of singlet states together with an unentangled qubit for a system with an odd number of qubits achieves the smallest possible orbit dimension equal to 3n 2 for n even and 3n 1 2 for n odd where n is the number of qubits in this paper we show that any state with minimum orbit dimension must be of this form and furthermore such states are classified up to local unitary equivalence by the sets of pairs of qubits entangled in singlets

a bipartite class of entanglement monotones for n qubit pure states we construct a class of algebraic invariants for n qubit pure states based on bipartite decompositions of the system we show that they are entanglement monotones and that they differ from the well known linear entropies of the sub systems they therefore capture new information on the non local properties of multipartite systems

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

when is a pure state of three qubits determined by its single particle reduced density matrices using techniques from symplectic geometry we prove that a pure state of three qubits is up to local unitaries uniquely determined by its one particle reduced density matrices exactly when their ordered spectra belong to the boundary of the so called kirwan polytope otherwise the states with given reduced density matrices are parameterized up to local unitary equivalence by two real variables given inevitable experimental imprecision this means that already for three qubits a pure quantum state can never be reconstructed from single particle tomography we moreover show that the knowledge of the reduced density matrices is always sufficient if one is given the additional promise that the quantum state is not convertible to the greenberger horne zeilinger state by stochastic local operations and classical communication and discuss generalizations of our results to an arbitrary number of qubits

highly entangled multi qubit states with simple algebraic structure recent works by brown et al 2005 j phys a math gen 38 1119 and borras et al 2007 j phys a math theor 40 13407 have explored numerical optimization procedures to search for highly entangled multi qubit states according to some computationally tractable entanglement measure we present an alternative scheme based upon the idea of searching for states having not only high entanglement but also simple algebraic structure we report results for 4 5 6 7 and 8 qubits discovered by this approach showing that many of such states do exist in particular we find a maximally entangled 6 qubit state with an algebraic structure simpler than the best results known so far for the case of 7 qubits we discover states with high but not maximum entanglement and simple structure as well as other desirable properties some preliminary results are shown for the case of 8 qubits

modeling viewpoint shifts in probabilistic choice a number of mathematical models for overcoming intransitive choice have been proposed and tested in the literature of decision theory this article presents the development of a new stochastic choice model based on multidimensional scaling this allows decision makers to have multiple viewpoints whereas current multidimensional scaling models are based on the assumption that a subject or group of subjects has only one viewpoint the implication of our model is that subjects make an intransitive choice because they are able to shift their viewpoint this paper also presents the maximum likelihood estimation of the proposed model and reanalyzes tversky s gamble experiment data

why two qubits are special we analyze some special properties of a system of two qubits and in particular of the so called bell basis for this system and discuss the possibility of extending these properties to higher dimensional systems we give a general construction for orthonormal bases of maximally entangled vectors which works in any dimension and is based on latin squares and complex hadamard matrices however for none of these bases the special properties of the operation of complex conjugation in bell basis hold namely that maximally entangled vectors have up to a phase real coefficients and that factorizable unitaries have real matrix elements

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

entanglement bell inequality and all that we start from the geometrical observation that a finite set of pure states correspond to some points on a sphere and their convex span cannot be the whole set of states if we call the left over entangled we can pursue this picture from the simplest case of a two dimensional hilbert space to the usual alice and bob game of entangled states and then move to bigger systems and finely to quantum field theory where almost everything is entangled on the way we encounter more or less known old friends up from the shell structure of states to the monogamy of squashed entanglement we study how entanglement can be concentrated on a small slice and how it depends on the particular factorization of the hilbert space

an extension of multiple correspondence analysis for identifying heterogeneous subgroups of respondents an extension of multiple correspondence analysis is proposed that takes into account cluster level heterogeneity in respondents preferences choices the method involves combining multiple correspondence analysis and k means in a unified framework the former is used for uncovering a low dimensional space of multivariate categorical variables while the latter is used for identifying relatively homogeneous clusters of respondents the proposed method offers an integrated graphical display that provides information on cluster based structures inherent in multivariate categorical data as well as the interdependencies among the data an empirical application is presented which demonstrates the usefulness of the proposed method and how it compares to several extant approaches

geometry of the three qubit state entanglement and division algebras we present a generalization to three qubits of the standard bloch sphere representation for a single qubit and of the seven dimensional sphere representation for two qubits presented in mosseri et al mosseri r and dandoloff r 2001 j phys a math gen 34 10243 the hilbert space of the three qubit system is the 15 dimensional sphere s15 which allows for a natural last hopf fibration with s8 as base and s7 as fibre a striking feature is as in the case of one and two qubits that the map is entanglement sensitive and the two distinct ways of un entangling three qubits are naturally related to the hopf map we define a quantity that measures the degree of entanglement of the three qubit state conjectures on the possibility of generalizing the construction for higher qubit states are also discussed

tripartite entanglement versus tripartite nonlocality in three qubit greenberger horne zeilinger class states we analyze the relationship between tripartite entanglement and genuine tripartite nonlocality for three qubit pure states in the greenberger horne zeilinger class we consider a family of states known as the generalized greenberger horne zeilinger states and derive an analytical expression relating the three tangle which quantifies tripartite entanglement to the svetlichny inequality which is a bell type inequality that is violated only when all three qubits are nonlocally correlated we show that states with three tangle less than 1 2 do not violate the svetlichny inequality on the other hand a set of states known as the maximal slice states does violate the svetlichny inequality and exactly analogous to the two qubit case the amount of violation is directly related to the degree of tripartite entanglement we discuss further interesting properties of the generalized greenberger horne zeilinger and maximal slice states

on local invariants of pure three qubit states we study invariants of three qubit states under local unitary transformations i e functions on the space of entanglement types which is known to have dimension six we show that there is no set of six algebraically independent polynomial invariants of degree 6 and find such a set with maximum degree eight we describe an intrinsic definition of a canonical state on each orbit and discuss the non polynomial invariants associated with it

quantum entanglement the unitary 8 vertex braid matrix with imaginary rapidity we study quantum entanglements induced on product states by the action of 8 vertex braid matrices rendered unitary with purely imaginary spectral parameters rapidity the unitarity is displayed via the canonical factorization of the coefficients of the projectors spanning the basis this adds one more new facet to the famous and fascinating features of the 8 vertex model the double periodicity and the analytic properties of the elliptic functions involved lead to a rich structure of the 3 tangle quantifying the entanglement we thus explore the complex relationship between topological and quantum entanglement

constructive proof of localization in the anderson tight binding model we prove that for large disorder or near the band tails the spectrum of the anderson tight binding hamiltonian with diagonal disorder consists exclusively of discrete eigenvalues the corresponding eigenfunctions are exponentially well localized these results hold in arbitrary dimension and with probability one in one dimension we recover the result that all states are localized for arbitrary energies and arbitrarily small disorder our techniques extend to other physical systems which exhibit localization phenomena such as infinite systems of coupled harmonic oscillators or random schrodinger operators in the continuum

a simple test for quantum channel capacity based on state and channel isomorphism we point out that semidefinite programming can be used as a quick test for nonzero one way quantum channel capacity this can be achieved by searching for symmetric extensions of states isomorphic to a given quantum channel with this method we provide examples of quantum channels that can lead to high entanglement transmission but still have zero one way capacity in particular regions of symmetric extendibility for isotropic states in arbitrary dimensions are presented further we derive a new entanglement parameter based on normalized relative entropy distance to the set of states that have symmetric extensions and show explicitly the symmetric extension of isotropic states being the nearest to singlets in the set of symmetrically extendible states the suitable regularization of the parameter provides a new upper bound on one way distillable entanglement

constrained latent class analysis simultaneous classification and scaling of discrete choice data a reparameterization of a latent class model is presented to simultaneously classify and scale nominal and ordered categorical choice data latent class specific probabilities are constrained to be equal to the preference probabilities from a probabilistic ideal point or vector model that yields a graphical multidimensional representation of the classification results in addition background variables can be incorporated as an aid to interpreting the latent class specific response probabilities the analyses of synthetic and real data sets illustrate the proposed method

finite volume fractional moment criteria for anderson localization a technically convenient signature of localization exhibited by discrete operators with random potentials is exponential decay of the fractional moments of the green function within the appropriate energy ranges known implications include spectral localization absence of level repulsion strong form of dynamical localization and a related condition which plays a significant role in the quantization of the hall conductance in two dimensional fermi gases we present a family of finite volume criteria which under some mild restrictions on the distribution of the potential cover the regime where the fractional moment decay condition holds the constructive criteria permit to establish this condition at spectral band edges provided there are sufficient lifshitz tail estimates on the density of states they are also used here to conclude that the fractional moment condition and thus the other manifestations of localization are valid throughout the regime covered by the multiscale analysis in the converse direction the analysis rules out fast power law decay of the green functions at mobility edges

propagation of a quantum state in a continuum of coupled oscillators and applications to entanglement the exponential hilbert space approach is used to link quantum mechanics in a small system with d dimensional hilbert space with the collective quantum behaviour in a large system comprised of d coupled oscillators with hilbert space h in the large system the expectation value of the mode position operator describes the location of a quantum state within the chain of d oscillators and the expectation value of the mode momentum operator describes the change of the mode position with time a continuum of modes d is also considered and in this case these operators obey the commutation relation a consequence of this is that uncertainties in the location of a state and in its momentum obey an uncertainty relation displacements and squeezing in the mode phase space are discussed for a certain hamiltonian the obey equations of motion which are very similar to those of a harmonic oscillator if the system is in an entangled state the formalism can be used to quantify concepts like the location of entanglement and the speed with which the entanglement propagates

multiclus a new method for simultaneously performing multidimensional scaling and cluster analysis this paper develops a maximum likelihood based method for simultaneously performing multidimensional scaling and cluster analysis on two way dominance or profile data this multiclus procedure utilizes mixtures of multivariate conditional normal distributions to estimate a joint space of stimulus coordinates andk vectors one for each cluster or group in at dimensional space the conditional mixture maximum likelihood method is introduced together with an e m algorithm for parameter estimation a monte carlo analysis is presented to investigate the performance of the algorithm as a number of data parameter and error factors are experimentally manipulated finally a consumer psychology application is discussed involving consumer expertise experience with microcomputers

quantum harmonic oscillator systems with disorder we study many body properties of quantum harmonic oscillator lattices with disorder a sufficient condition for dynamical localization expressed as a zero velocity lieb robinson bound is formulated in terms of the decay of the eigenfunction correlators for an effective one particle hamiltonian we show how state of the art techniques for proving anderson localization can be used to prove that these properties hold in a number of standard models we also derive bounds on the static and dynamic correlation functions at both zero and positive temperature in terms of one particle eigenfunction correlators in particular we show that static correlations decay exponentially fast if the corresponding effective one particle hamiltonian exhibits localization at low energies regardless of whether there is a gap in the spectrum above the ground state or not our results apply to finite as well as to infinite oscillator systems the eigenfunction correlators that appear are more general than those previously studied in the literature in particular we must allow for functions of the hamiltonian that have a singularity at the bottom of the spectrum we prove exponential bounds for such correlators for some of the standard models

algebraic invariants of five qubits we consider the action of the group on fifth rank tensors on a two dimensional space that is the hilbert space of a five qubit system the hilbert series of the algebra of polynomial invariants of five qubits pure states is obtained and the simplest invariants are computed