computationally efficient nonlinear bell inequalities for quantum networks the correlations in quantum networks have attracted strong interest with new types of violations of the locality the standard bell inequalities cannot characterize the multipartite correlations that are generated by multiple sources the main problem is that no computationally efficient method is available for constructing useful bell inequalities for general quantum networks in this work we show a significant improvement by presenting new explicit bell type inequalities for general networks including cyclic networks these nonlinear inequalities are related to the matching problem of an equivalent unweighted bipartite graph that allows constructing a polynomial time algorithm for the quantum resources consisting of bipartite entangled pure states and generalized greenberger horne zeilinger ghz states we prove the generic nonmultilocality of quantum networks with multiple independent observers using new bell inequalities the violations are maximal with respect to the presented tsirelson s bound for einstein podolsky rosen states and ghz states moreover these violations hold for werner states or some general noisy states our results suggest that the presented bell inequalities can be used to characterize experimental quantum networks

analysis of momentum adaptive filtering algorithms this article analyzes the momentum lms algorithm and other momentum algorithms using asymptotic techniques that provide information regarding the almost sure behavior of the parameter estimates and their asymptotic distribution the analysis does not make any assumptions on the autocorrelation function of the input process

image representation by a new optimal non uniform morphological sampling abstract this paper presents a new non uniform subsampling strategy based on mathematical morphology this sampling scheme is determinist and iterative at each iteration a sample position is determined in order to minimize the overall absolute reconstruction error we show that satisfying this criterion is equivalent to maximizing the volume of reconstructed image the sample selection strategy is repeated until reaching either a previously determined number of samples or a maximal admissible error the correspondent reconstruction procedure is also described the algorithm is first presented using only one structuring element then extended to the case of a family of structuring elements experiments on the choice of structuring elements in the family allow us to choose the optimal description set finally we present an application of this novel image representation method on image compression a comparison of results with jpeg standard shows the good performance of our approach especially for high compression ratios

spectral decomposition of bell operators for multiqubit systems the spectral decomposition of multipartite bell operators for two dichotomic observables per site as introduced by werner and wolf phys rev a 64 032112 2001 is done implications on the characterization of bell inequalities as criteria of entanglement are discussed

the general uq sl 2 invariant xxz integrable quantum spin chain the boundary conditions are constructed for the general xxz quantum integrable spin chain such that the resulting system is invariant under the quantum algebra uq sl 2 action the result generalizes that due to pasquier and saleur 1990 obtained for spin 1 2 and spin 1

generalized block coding of black and white images a generalized approach to block coding of two tone images is introduced binary n sequences blocks are described various conventional block coding techniques are shown to be particular cases of this approach numerical examples confirm that based on the approach the coding technique outperforms existing techniques generalized block coding is proved to be near optimum for encoding sparse binary patterns and advantageous for sources with unknown models

violation of bell s inequalities and distillability for n qubits we consider quantum systems composed of n qubits and the family of all bell s correlation inequalities for two two valued measurements per site we show that if an n qubit state violates any of these inequalities then it is at least bipartite distillable indeed there exists a link between the amount of bell s inequality violation and the degree of distillability thus we strengthen the interpretation of bell s inequalities as detectors of useful entanglement

yang baxterization of reflection equations for r with two distinct eigenvalues a condition of yang baxterization of reflection equations for r with two distinct eigenvalues is given constant solutions to reflection equations for r related to fundamental representations of slq n and slq 1 1 and for r of the eight vertex model are yang baxterized

fusion procedure for the belavin model with open boundary conditions we have recently used unitarity and cross unitarity properties of an symmetric r matrix to construct the transfer matrix t u for an n site open spin chain here we give a fusion procedure for such a chain and we prove that the fused transfer matrix is commutative with the original transfer matrix t u

boundary conditions for integrable quantum systems a new class of boundary conditions is described for quantum systems integrable by means of the quantum inverse scattering r matrix method the method proposed allows the author to treat open quantum chains with appropriate boundary terms in the hamiltonian the general considerations are applied to the xxz and xyz models the nonlinear schrodinger equation and toda chain

a block coding technique for encoding sparse binary patterns an efficient method is presented for encoding sparse binary patterns this method is very simple to implement and performs in a near optimum way the sparse pattern is assumed to be a memoryless binary source this kind of pattern is found in a three dimensional authentication scheme in the data compression area the patterns are usually not memoryless sources however when lpc linear prediction coding is applied the resulting error pattern is very close to a memoryless model

a comparison of two quantized state adaptive algorithms quantized state qs adaptive algorithms reduce the numerical complexity and dynamic range requirements of least mean squares lms adaptation by replacing multiplications with shifts bit comparisons or table lookups a theoretical foundation with which to distinguish two primary qs algorithm forms and to predict which algorithm is most appropriate in a given context is presented an extended lyapunov approach is used to derive a persistence of excitation pe condition which guarantees linear stability of the quantized error qe form averaging theory is then used to derive pe condition which guarantees exponential stability of the quantized regressor qreg form failure to meet this latter condition which is not equivalent to the spectral richness pe condition for lms can result in exponential instability the qe and qreg algorithms are then compared in terms of conditions for stability convergence properties of the prediction and parameter errors convergence rates and steady state errors

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

reflection quadratic algebra associated with z2 model the reflection quadratic algebra a r associated with the z2 model is formulated from the reflection equation it is proved that a r is isomorphic to the matrix element algebra a r of the quantum group related to r and thus its coalgebra structure is obtained a new a r comodule structure of a r is revealed

quantifying multipartite nonlocality the nonlocal correlations of multipartite entangled states can be reproduced by a classical model if sufficiently many parties join together or if sufficiently many parties broadcast their measurement inputs the maximal number m of groups and the minimal number k of broadcasting parties that allow for the reproduction of a given set of correlations quantify their multipartite nonlocal content we show how upper bounds on m and lower bounds on k can be computed from the violation of the mermin svetlichny inequalities while n partite greenberger horne zeilinger states violate these inequalities maximally we find that w states violate them only by a very small amount

solving large scale optimization problems related to bell s theorem impossibility of finding local realistic models for quantum correlations due to entanglement is an important fact in foundations of quantum physics gaining now new applications in quantum information theory we present an in depth description of a method of testing the existence of such models which involves two levels of optimization a higher level non linear task and a lower level linear programming lp task the article compares the performances of the existing implementation of the method where the lps are solved with the simplex method and our new implementation where the lps are solved with an innovative matrix free interior point method we describe in detail how the latter can be applied to our problem discuss the basic scenario and possible improvements and how they impact on overall performance significant performance advantage of the matrix free interior point method over the simplex method is confirmed by extensive computational results the new method is able to solve substantially larger problems consequently the noise resistance of the non classicality of correlations of several types of quantum states which has never been computed before can now be efficiently determined an extensive set of data in the form of tables and graphics is presented and discussed the article is intended for all audiences no quantum mechanical background is necessary

nonclassical correlations from randomly chosen local measurements we show that correlations inconsistent with any locally causal description can be a generic feature of measurements on entangled quantum states specifically spatially separated parties who perform local measurements on a maximally entangled state using randomly chosen measurement bases can with significant probability generate nonclassical correlations that violate a bell inequality for n parties using a greenberger horne zeilinger state this probability of violation rapidly tends to unity as the number of parties increases we also show that even with both a randomly chosen two qubit pure state and randomly chosen measurement bases a violation can be found about 10 of the time among other applications our work provides a feasible alternative for the demonstration of bell inequality violation without a shared reference frame

new concise upper bounds on quantum violation of general multipartite bell inequalities last years bounds on the maximal quantum violation of general bell inequalities were intensively discussed in the literature via different mathematical tools in the present paper we analyze quantum violation of general bell inequalities via the lqhv local quasi hidden variable modelling framework correctly reproducing the probabilistic description of every quantum correlation scenario the lqhv mathematical framework allows us to derive for all d and n a new upper bound 2d 1 n 1 on the maximal violation by an n qudit state of all general bell inequalities also new upper bounds on the maximal violation by an n qudit state of general bell inequalities for s settings per site these new upper bounds essentially improve all the known precise upper bounds on quantum violation of general multipartite bell inequalities for some s d and n the new upper bounds are attainable

do all pure entangled states violate bell s inequalities for correlation functions any pure entangled state of two particles violates a bell inequality for two particle correlation functions gisin s theorem we show that there exist pure entangled ng2 qubit states that do not violate any bell inequality for n particle correlation functions for experiments involving two dichotomic observables per local measuring station we also find that mermin ardehali belinskii klyshko inequalities may not always be optimal for refutation of local realistic description

finite dimensional irreducible representations of reflection algebra for su 1 1 q vertex model classification boson fermion realizations and yang baxterization finite dimensional irreducible representations of a reflection algebra related to the reflection equation for the su 1 1 q model are classified it is proven that this algebra has two inequivalent one dimensional and one two dimensional irreducible representations some indecomposable representations are also constructed and the q boson fermion realizations are explicitly presented finally the yang baxterization of this algebra and its constant solutions the one dimensional representations is investigated

bell klyshko inequalities to characterize maximally entangled states of n qubits this letter presents the first rigorous proof of the conjecture raised by gisin and bechmann pasquinucci phys lett a 246 1 1998 that the greenberger horne zeilinger states of n qubits and the states obtained from them by local unitary transformations are the unique states that maximally violate the bell klyshko inequalities the proof is obtained by using the certain algebraic properties that pauli s matrices satisfy and some subtle mathematical techniques since all states obtained by local unitary transformations of a maximally entangled state are equally valid entangled states we thus give a characterization of maximally entangled states of n qubits in terms of the bell type inequality

adaptive filtering with binary reinforcement recently there has been increased interest in high speed adaptive filtering where the usual stochastic gradient or least mean square lms algorithm is replaced with the simpler algorithm where adaptation is guided only by the polarity of the error signal in this paper the convergence of this binary reinforcement br algorithm is proved under the usual independence assumption and the surprising observation is made that unlike the lms algorithm convergence occurs for any positive value of the step size parameter while the stochastic gradient algorithm attempts to minimize a mean square error cost function the binary reinforcement algorithm in fact attempts to minimize a mean absolute error cost function it is proved for the binary reinforcement algorithm that the tap weight vector converges in distribution to a random vector that is suitably concentrated about the optimal value based on a least mean absolute error cost function for a sufficiently small step size the expected cost of the asymptotic weight vector can be made as close as desired to thc minimum cost attain ed by the optimum weight vector

differential block coding of bilevel images in this correspondence a simple one dimensional 1 d differencing operation is applied to bilevel images prior to block coding to produce a sparse binary image that can be encoded efficiently using any of a number of well known techniques the difference image can be encoded more efficiently than the original bilevel image whenever the average run length of black pixels in the original image is greater than two compression is achieved because the correlation between adjacent pixels is reduced compared with the original image the encoding decoding operations are described and compression performance is presented for a set of standard bilevel images

the covering problem and spl mu dependent adaptive algorithms the paper presents a family of techniques called adaptive covering algorithms which solve a particular covering problem how to best cover a target shape using a set of simply parameterized elements the algorithms inspired by adaptive filtering techniques provide a computationally simple robust and efficient alternative to more traditional methods such as bayesian approaches convex hulls and multi layer perceptrons the paper develops a theoretical understanding of the adaptive covering algorithms by relating their behavior via weak convergence techniques to the evolution of a deterministic ordinary differential equation ode in the process the authors give new convergence results for a class of step size dependent recursive algorithms stability and instability of the ode can be interpreted in terms of the local stability instability of the algorithm in terms of the covering problem candidate coverings tend to improve as more data is gathered whenever the ode is stable several examples are given which demonstrate the ideas and which verify that the analysis accurately predicts the true behavior of the algorithms

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

chain of hardy type local reality constraints for n qubits nonlocality without inequality is an elegant argument introduced by hardy for two qubit systems and later generalised to n qubits to establish contradiction of quantum theory with local realism interestingly for n 2 this argument is actually a corollary of bell type inequalities viz the ch hardy inequality involving bell correlations but for n greater than two it involves n particle probabilities more general than bell correlations in this paper we first derive a chain of completely new local realistic inequalities involving joint probabilities for n qubits and then associated with each such inequality we provide a new hardy type local reality constraint without inequalities quantum mechanical maximal violations of the chain of inequalities and of the associated constraints are also studied by deriving appropriate cirel son type theorems these results involving joint probabilities more general than bell correlations are expected to provide a new systematic tool to investigate entanglement

on quantum groups for zn models the quantum group for the zn model is studied from the braid group representation the fundamental representation is constructed from the weyl relation zx omega xz with omega being an nth root of unity in the case of n 2 the eight vertex model the quantum group is shown to be a homomorphic image of the glq 2 with q2 1

spectral decomposition of bell s operators for qubits the spectral decomposition is given for the n qubit bell operators with two observables per qubit it is found that the eigenstates when non degenerate are n qubit ghz states even for those operators that do not allow the maximal violation of the corresponding inequality we present two applications of this analysis in particular we discuss the existence of pure entangled states that do not violate the mermin klyshko inequality for n 3

on spin systems related to the temperley lieb algebra the spectrum of the transfer matrices constructed from the spectral parameter dependent temperley lieb r matrix is found using functional relations identical to those of the spin 1 2 xxz magnet

asymptotic analysis of stochastic gradient based adaptive filtering algorithms with general cost functions this paper presents an analysis of stochastic gradient based adaptive algorithms with general cost functions the analysis holds under mild assumptions on the inputs and the cost function the method of analysis is based on an asymptotic analysis of fixed stepsize adaptive algorithms and gives almost sure results regarding the behavior of the parameter estimates whereas previous stochastic analyses typically considered mean and mean square behavior the parameter estimates are shown to enter a small neighborhood about the optimum value and remain there for a finite length of time furthermore almost sure exponential bounds are given for the rate of convergence of the parameter estimates the asymptotic distribution of the parameter estimates is shown to be gaussian with mean equal to the optimum value and covariance matrix that depends on the input statistics specific adaptive algorithms that fall under the framework of this paper are signed error least mean square lms dual sign lms quantized state lms least mean fourth dead zone algorithms momentum algorithms and leaky lms

tight multipartite bell s inequalities involving many measurement settings which quantum states do not allow a local realistic lr description this question still remains open mainly because our present tools to test local realism are not optimal most of bell s inequalities are for the case in which only two measurement settings can be chosen by each observer e g the clauser horneshimony holt chsh inequality 1 inequalities for bipartite higher dimensional systems 2 multipartite bell s inequalities 3 6 one can call such inequalities standard ones one can expect that allowing the observers to choose between more than two observables should give more stringent constraints on lr models thus new inequalities may extend the class of nonseparable states which cannot be described by lr variables violation of local realism is an important ingredient for building quantum information protocols that decrease the communication complexity 7 and is a criterion for the efficient quantum key distribution 8 multisetting bell s inequalities may lead to such novel schemes although various nonstandard bell s inequalities are known 9 13 we still lack an efficient method for their derivation a general way is to define the facets of the correlation polytope 9 13 yet this is a computationally hard np problem 14 recently wu and zong 15 derived an inequality for three parties which involves four local settings for two observers and two settings for the third one and showed that it is stronger than the standard three particle bell inequalities here by generalizing the method of ref 15 we derive a wide class of tight bell s inequalities for n 2 parties and many measurement settings we find a single general bell s inequality that generates all inequalities from this class we also give a necessary and sufficient condition for the violation of the new inequalities by quantum predictions most importantly the inequalities reveal violation of local realism for the classes of states for which all standard bell s inequalities 5 6 are satisfied we start with the case ofn 3 observers suppose that the first two observers can choose between four settings and the third one between two settings we denote such problem as 4 4 2 l etai withi 2f 1 2 3 4g stand for the predetermined local realistic values for the first observer under the local settingi bj withj 2f 1 2 3 4g for similar values for the second observer and ck withk 2 f1 2g for the values for the third observer for the given run of the experiment we assume thata i b j a ndc k can take values 1 or 1 then the lr values satisfy the following algebraic identity a12 s 0 x k l 1 2 s 0 k l a1 1 k a 2 b1 1 l b 2 4

weak convergence and local stability properties of fixed step size recursive algorithms a recursive equation that subsumes several common adaptive filtering algorithms is analyzed for general stochastic inputs and disturbances by relating the motion of the parameter estimate errors to the behavior of an unforced deterministic ordinary differential equation ode the odes describing the motion of several common adaptive filters are examined in some simple settings including the least mean square lms algorithm and all three of its signed variants the signed regressor the signed error and the sign sign algorithms stability and instability results are presented in terms of the eigenvalues of a correlation like matrix this generalizes known results for lms signed regressor lms and signed error lms and gives new stability criteria for the sign sign algorithm the ability of the algorithms to track moving parameterizations can be analyzed in a similar manner by relating the time varying system to a forced ode the asymptotic distribution about the forced ode is an ornstein uhlenbeck process the properties of which can be described in a straightforward manner

a hybrid lossless lossy binary image compression scheme in this paper the authors present a binary image compression scheme that can be used either for lossless or lossy compression requirements this scheme contains five new contributions the lossless component of the scheme partitions the input image into a number of non overlapping rectangles using a new line by line method the upper left and the lower right vertices of each rectangle are identified and the coordinates of which are efficiently encoded using three methods of representation and compression the lossy component on the other hand provides higher compression through two techniques 1 it reduces the number of rectangles from the input image using our mathematical regression models these mathematical models guarantees image quality so that rectangular reduction should not produce visual distortion in the image the mathematical models have been obtained through subjective tests and regression analysis on a large set of binary images 2 further compression gain is achieved through discarding isolated pixels and 1 pixel rectangles from the image simulation results show that the proposed schemes provide significant improvements over previously published work for both the lossy and the lossless components

quantum and braided linear algebra quantum matrices a r are known for every r matrix obeying the quantum yang baxter equations it is also known that these act on vectors given by the corresponding zamalodchikov algebra this interpretation is developed in detail distinguishing between two forms of this algebra v r vectors and v r covectors a r v r21 v r is an algebra homomorphism i e quantum matrices are realized by the tensor product of a quantum vector with a quantum covector while the inner product of a quantum covector with a quantum vector transforms as a scaler it is shown that if v r and v r are endowed with the necessary braid statistics then their braided tensor product v r v r is a realization of the braided matrices b r introduced previously while their inner product leads to an invariant quantum trace introducing braid statistics in this way leads to a fully covariant quantum braided linear algebra the braided groups obtained from b r act on themselves by conjugation in a way impossible

irregular uq sl 3 representations at roots of unity via gel fand weyl zetlin basis the gel fand weyl zetlin gwz description of the uq sl 3 irregular irreps at roots of unity is explicitly given those are irreps fixed by the same parameters as the unitary irreducible representations uirs of su 3 yet having dimensions smaller than their classical counterparts the reason being that to obtain an irregular irrep one has to make factorization of an additional submodule this description is made geometrically transparent by an arrangement of the standard su 3 gwz basis in a hexagonal pyramid which is valid for any q and seems new even for q 1 the pyramid has as a base the standard hexagon which gives the weight space of the uirs of su 3 in the plane of third component of isospin iz and hypercharge y while third dimension of this pyramid is related to the isospin i algebraically this arrangement is related to a one to one correspondence between the abstract gwz states and monomials in the algebra of raising generators uq g however those monomials are not in the standard poi

embedded elliptic curves and the yang baxter equations abstract the completely z n symmetric s matrix defined by belavin is shown to satisfy the yang baxter equations in the projective space of boltzmann weights the curves on which there exist commuting transfer matrices are shown to be embedded elliptic curves explicit polynomial equations for these curves are given for n 2 these results reduce to the results of baxter for the symmetric eight vertex model