paper pole assignment for distributed systems by finite dimensional control the question of pole assignment for a class of distributed systems by means of finite dimensional control is considered a finite dimensional compensator is usually designed based on a reduced order model and it is not a priori known what effect this will have on the original infinite dimensional system explicit formulas are derived which enable one to calculate the eigenvalues of the resulting closed loop system for a certain compensator design estimates are derived which can be used to guarantee stability a priori numerical results are also presented

lyapunov based boundary feedback design for parabolic pdes this paper presents a methodology for the construction of simple control lyapunov functionals clfs for boundary controlled parabolic partial differential equations pdes the proposed methodolog

an obstruction based approach to the kochen specker theorem in isham and butterfield 1998 int j theor phys 37 2669 733 it was shown that the kochen specker theorem can be written in terms of the non existence of global elements of a certain varying set over the category of boolean subalgebras of projection operators on some hilbert space in this paper we show how obstructions to the construction of such global elements arise and how this provides a new way of looking at proofs of the theorem

stabilization of a non linear distributed parameter vibratory system the feedback stabilization problem for a non linear elastic distributed parameter system including a destabilizing effect is studied the model is formulated as an evolution equation in a hilbert space semigroup theory is used to investigate an initial value problem for the equation moreover a control system with a finite dimensional controller is constructed it is then proved that the state of the overall system converges to zero with a desirable exponential decay rate as time tends to infinity

on design orthogonality maximin distance and projection uniformity for computer experiments space filling designs are widely used in both computer and physical experiments column orthogonality maximin distance and projection uniformity are three basic and popular space filling criteria

linear codes with covering radius 2 and other new covering codes infinite families of linear binary codes with covering radius r 2 and minimum distance d 3 and d 4 are given using the constructed codes with d 3 r 2 families of covering codes with r 2 are obtained the parameters of many constructed codes with r

proofs of the kochen specker theorem based on a system of three qubits a number of new proofs of the kochen specker theorem are given based on the observables of the three qubit pauli group each proof is presented in the form of a diagram from which it is obvious by inspection each of our observable based proofs leads to a system of projectors and bases that generally yields a large number of parity proofs of the kochen specker theorem some examples of such proofs are given and some of their applications are discussed

proposed experimental tests of the bell kochen specker theorem for a two particle two state system sets of compatible propositions exist for which quantum mechanics and noncontextual hidden variable theories make conflicting predictions for every individual system whatever its quantum state this permits a simple all or nothing state independent experimental verification of the bell kochen specker theorem

discord and nonclassicality in probabilistic theories quantum discord quantifies nonclassical correlations in quantum states we introduce discord for states in causal probabilistic theories inspired by the original definition proposed by h ollivier and w h zurek phys rev lett 88 017901 2001 we show that the only probabilistic theory in which all states have null discord is classical probability theory non null discord is then not just a quantum feature but a generic signature of nonclassicality

a classification of hidden variable properties hidden variables are extra components added to try to banish counterintuitive features of quantum mechanics we start with a quantum mechanical model and describe various properties that can be asked of a hidden variable model we present six such properties and a venn diagram of how they are related with two existence theorems and three no go theorems epr bell and kochen specker we show which properties of empirically equivalent hidden variable models are possible and which are not formally our treatment relies only on classical probability models and physical phenomena are used only to motivate which models to choose

stronger two observer all versus nothing violation of local realism we introduce a two observer all versus nothing proof of bell s theorem which reduces the number of required quantum predictions from 9 a cabello phys rev lett 87 010403 2001 z b chen et al phys rev lett 90 160408 2003 to 4 provides a greater amount of evidence against local realism reduces the detection efficiency requirements for a conclusive experimental test of bell s theorem and leads to a bell inequality which resembles mermin s inequality for three observers n d mermin phys rev lett 65 1838 1990 but requires only two observers

bipartite all versus nothing proofs of bell s theorem with single qubit measurements if n qubits were distributed between 2 parties which quantum pure states and distributions of qubits would allow all versus nothing or greenberger horne zeilinger like proofs of bell s theorem using only single qubit measurements we show a necessary and sufficient condition for the existence of these proofs for any number of qubits and provide all distinct proofs up to n 7 qubits remarkably there is only one distribution of a state of n 4 qubits and six distributions each for a different state of n 6 qubits which allow these proofs

multipartite nonlocality as a resource and quantum correlations having indefinite causal order the characterization of quantum correlations in terms of information theoretic resource has been a fruitful approach to understand the power of quantum correlations as a resource while bipartite entanglement and bell inequality violation in this setting have been extensively studied relatively little is known about their multipartite counterpart in this paper we apply and adapt the recently proposed definitions of multipartite nonlocality bancal et al 2013 phys rev a 88 014102 to the three and four partite scenarios to gain new insight on the resource aspect of multipartite nonlocal quantum correlations specifically we show that reproducing certain tripartite quantum correlations requires mixtures of classical resources be it the ability to change the groupings or the time orderings of measurements thus when seen from the perspective of biseparable one way classical signaling resources certain tripartite quantum correlations do not admit a definite causal order in the four partite scenario we obtain a superset description of the set of biseparable correlations which can be produced by allowing two groups of bipartite non signaling resources quantum violation of the resulting bell like inequalities is investigated as a byproduct we obtain some new examples of device independent witnesses for genuine four partite entanglement and also device independent witnesses that allow one to infer the structure of the underlying multipartite entanglement this article is part of a special issue of journal of physics a mathematical and theoretical devoted to 50 years of bell s theorem

strong orthogonal arrays and associated latin hypercubes for computer experiments this paper introduces constructs and studies a new class of arrays called strong orthogonal arrays as suitable designs for computer experiments a strong orthogonal array of strength t enjoys better space filling properties than a comparable orthogonal array in all dimensions lower than t while retaining the space filling properties of the latter in t dimensions latin hypercubes based on strong orthogonal arrays of strength t are more space filling than comparable orthogonal array based latin hypercubes in all g dimensions for any 2 g t 1 copyright 2013 oxford university press

global stabilization of a class of nonlinear reaction diffusion partial differential equations by boundary feedback this paper provides global exponential stabilization results by means of boundary feedback control for one dimensional nonlinear unstable reaction diffusion partial differential equations pdes wi

hardy is almost everywhere we show that all n qubit entangled states with the exception of tensor products of single qubit and bipartite maximally entangled states admit hardy type proofs of non locality without inequalities or probabilities more precisely we show that for all such states there are local one qubit observables such that the resulting probability tables are logically contextual in the sense of abramsky and brandenburger this being the general form of the hardy type property moreover our proof is constructive given a state we show how to produce the witnessing local observables in fact we give an algorithm to do this although the algorithm is reasonably straightforward its proof of correctness is non trivial a further striking feature is that we show that n 2 local observables suffice to witness the logical contextuality of any n qubit state two each for two for the parties and one each for the remaining n 2 parties

two simple proofs of the kochen specker theorem a new proof of the kochen specker theorem uses 33 rays instead of 117 in the original proof if the number of dimensions is increased from 3 to 4 only 24 rays are needed

the spectrum determined growth assumption for perturbations of analytic semigroups this short paper gives useful information concerning properties of perturbations of infinitesimal generators of analytic semigroups in particular it is shown that the spectrum determined growth assumption is retained not only under bounded perturbations but also under a class of unbounded perturbations which arise in control problems for parabolic systems where the control occurs pointwise or on the boundary

entropic tests of multipartite nonlocality and state independent contextuality we introduce a multipartite extension of an information theoretic distance introduced by zurek nature london 341 119 1989 we use it to develop a new tool for studying quantum correlations from an information theoretic perspective in particular we derive entropic tests of multipartite nonlocality for three qubits and for an arbitrary even number of qubits as well as a test of state independent contextuality in addition we rederive the tripartite mermin inequality and a state independent noncontextuality inequality by cabello phys rev lett 101 210401 2008 this suggests that the information theoretic distance approach to multipartite nonlocality and state independent contextuality can provide a more general treatment of nonclassical correlations than the orthodox approach based on correlation functions

perfect commuting operator strategies for linear system games linear system games are a generalization of mermin s magic square game introduced by cleve and mittal they show that perfect strategies for linear system games in the tensor product model of entanglement correspond to finite dimensional operator solutions of a certain set of non commutative equations we investigate linear system games in the commuting operator model of entanglement where alice and bob s measurement operators act on a joint hilbert space and alice s operators must commute with bob s operators we show that perfect strategies in this model correspond to possibly infinite dimensional operator solutions of the non commutative equations the proof is based around a finitely presented group associated with the linear system which arises from the non commutative equations

sensors and controllers location in distributed systems a survey a survey of the field of optimal sensors and or controllers location for dynamical distributed parameter systems modelled by partial differential equations is presented the recent contributions in this field are grouped according to the main goal for which the location problem is developed namely system identification state estimation and optimal control in order to pose the sensors and controllers location problem the semigroup approach for modelling distributed linear systems is briefly reviewed together with its equivalent infinite dimensional and approximate finite dimensional fourier expansion representations after presenting a concise general review of the several methods considered in the current literature a classification of methods is also proposed the main classifying factor concerns the use of n modal approximation schemes and the different stages of the optimization procedure in which they are required

inequalities for experimental tests of the kochen specker theorem we derive inequalities for n partite states under the assumption that the hidden variable theoretical joint probability distribution for any pair of commuting observables is equal to the quantum mechanical one fine showed that this assumption is connected to the no hidden variables theorem of kochen and specker ks theorem these inequalities give a way to experimentally test the ks theorem the fidelity to the bell states which is larger than 1 2 is sufficient for the experimental confirmation of the ks theorem hence the werner state is enough to test experimentally the ks theorem furthermore it is possible to test the ks theorem experimentally using uncorrelated states an n partite uncorrelated state violates the n partite inequality derived here by an amount that grows exponentially with n

modified gronwall s inequality and its application to stabilization problem for semilinear parabolic systems abstract this paper deals with the stabilization of semilinear parabolic distributed systems by means of boundary controls the partial differential equation describing the system is formulated as a semilinear evolution equation in a hilbert space by using a variable transformation here it is shown that the solution globally exists for the closed loop system which installs a finite dimensional dynamic compensator by using the properties of an analytic semigroup moreover a sufficient condition for stabilization of the system is derived by making use of the modified gronwall s inequality developed in this paper

stability analysis of linear parabolic systems and removement of singularities in substructure static feedback abstract we analyze stability property of a class of linear parabolic systems via static feedback stabilization via static feedback scheme is most difficult and challenging when both actuators and observation weights admit spillovers this arises typically in the boundary observation boundary feedback scheme we propose a simple static feedback law containing a parameter and enhance the stability property or achieve slightly stabilization in some situations the evolution of the substructure of finite dimension contains singularities regarding we show that these singularities are removed as long as the dimension is not large

hedging bets with correlated quantum strategies this paper studies the potential advantages of correlated answers in hypothetical tests of a simple interactive type in these tests an individual is presented with a question to which he or she must respond with an answer leading to an outcome of pass or fail in quantum information theoretic variants of these tests we show it is possible for an individual to correlate their answers across multiple tests in a way that produces a striking non classical behaviour specifically there exist tests for which no strategy can lead to the outcome pass with certainty but where answers to multiple independently administered tests can be correlated so that at least one test is passed with certainty this phenomenon which gives rise to a perfect form of hedging when considered in a game theoretic setting is quantum in nature it is not possible in classical variants of the tests we consider

the optimal projection equations for finite dimensional fixed order dynamic compensation of infinite dimensional systems one of the major difficulties in designing implementable finite dimensional controllers for distributed parameter systems is that such systems are inherently infinite dimensional while controller dimension is severely constrained by on line computing capability while some approaches to this problem initially seek a correspondingly infinite dimensional control law whose finite dimensional approximation may be of impractically high order the usual engineering approach involves first approximating the distributed parameter system with a high order discretized model followed by design ofa relatively low order dynamic controller among the numerous approaches suggested for the latter step are model controller reduction techniques used in conjunction with the standard lqg result an alternative approach developed in 36 relies upon the discovery in 31 that the necessary conditions for optimal fixed order dynamic compensation can be transformed into a set of equations possessing remarkable structural coherence the present paper generalizes this result to apply directly to the distributed parameter system itself in contrast to the pair of operator riccati equations for the full order lqg case the optimal finite dimensional fixed orderdynamic compensator is characterized byfour operator equations two modified riccati equations and two modified lyapunov equations coupled by an oblique projection whose rank is precisely equal to the order ofthe compensatorand which determines the optimal compensator gains this optimal projection is obtained by a full rank factorization of the product of the finite rank nonnegative definite hilbert space operators which satisfy the pair ofmodified lyapunov equations the coupling represents a graphic portrayal of the demise of the classical separation principle for the finite dimensional reduced order controller case the results obtained apply to a semigroup formulation in hilbert space and thus are applicable to control problems involving a broad range of specific partial and functional differential equations

a comparison of three methods for selecting values of input variables in the analysis of output from a computer code two types of sampling plans are examined as alternatives to simple random sampling in monte carlo studies these plans are shown to be improvements over simple random sampling with respect to variance for a class of estimators which includes the sample mean and the empirical distribution function

finite dimensional compensators for parabolic distributed systems with unbounded control and observation it is proved that for a class of parabolic distributed parameter systems with unbounded control and observation there exists a finite dimensional compensator using dynamic output feedback finite dimensional means here that the dynamics relating the input to the output is finite dimensional a constructive design algorithm is presented and several examples are considered

greenberger horne zeilinger paradoxes from qudit graph states one fascinating way of revealing quantum nonlocality is the all versus nothing test due to greenberger horne and zeilinger ghz known as the ghz paradox so far genuine multipartite and multilevel ghz paradoxes are known to exist only in systems containing an odd number of particles here we shall construct ghz paradoxes for an arbitrary number greater than 3 of particles with the help of qudit graph states on a special kind of graphs called ghz graphs furthermore based on the ghz paradox arising from a ghz graph we derive a bell inequality with two d outcome observables for each observer whose maximal violation attained by the corresponding graph state and a kochen specker inequality testing the quantum contextuality in a state independent fashion

simple unified form for the major no hidden variables theorems two examples are given that substantially simplify the no hidden variables theorem of kochen and specker greatly reducing the number of observables considered and requiring no intricate geometric argument while one of the examples also obeys a more powerful version of bell s theorem the other does not the examples provide a new perspective on both of these fundamental theorems and on the relation between them

bell kochen specker theorem for any finite dimension the bell kochen specker theorem against non contextual hidden variables can be proved by constructing a finite set of totally non colourable directions as kochen and specker did in a hilbert space of dimension n 3 we generalize kochen and specker s set to hilbert spaces of any finite dimension in a three step process that shows the relationship between different kinds of proofs continuum probabilistic state specific and state independent of the bell kochen specker theorem at the same time this construction of a totally non colourable set of directions in any dimension explicitly solves the question raised by zimba and penrose about the existence of such a set for n 5

fault detection for linear distributed parameter systems using finite dimensional functional observers abstractin this article finite dimensional residual generators are directly designed for riesz spectral systems with bounded input and output operators to detect faults this is achieved by using finite dimensional observers that can estimate linear functionals of the state without spillover these observers allow for a decoupling of the unknown disturbances from the estimation error dynamics under mild assumptions then a finite dimensional residual generator is obtained by approximately decoupling the state from the residual that is generated by the observer states and the outputs it is shown that the resulting approximation error can be made small by increasing the observer order then fault detection with the finite dimensional residual generator can be assured by introducing a time varying threshold a faulty euler bernoulli beam with structural damping illustrates the proposed finite dimensional fault detection approach

distributed system transfer functions of exponential order o is a real number we construct a transfer function algebra of fractions viz f o for modelling possibly unstable distributed systems such that i fcirc in f o is holomorphic in re s o i e is o stable iff fcirc is o exponentially stable and ii we allow delay in the direct input output transmission of the system this algebra is a a restriction of the algebra b o developed by callier and desoer 1978 1980 a b an extension of the algebra of proper rational functions such that the exponential order properties of the latter transfer functions of lumped systems are maintained the algebra f o can be used for modelling and feedback system design it is shown that standard semigroup systems are better modelled by a transfer function in f o rather than b o

feedback control of second order evolution equations with unbounded observation feedback control is developed for a class of distributed systems described by second order evolution equations with unbounded observation in order to increase the degree of stability of the system a dynamic compensator is designed on the basis of a finite dimensional model of the system and a feedback control system is constructed by using sensor outputs it is shown that the degree of stability of the whole system including the compensator is improved by modal control based on a finite dimensional modal model

noncontextual hidden variables and physical measurements meyer phys rev lett 83 3751 1999 recently showed that the kochen specker theorem which demonstrates the impossibility of a deterministic hidden variable description of ideal spin measurements on a spin 1 particle can be effectively nullified if only finite precision measurements are considered we generalize this result one can ascribe consistent outcomes to a dense subset of the set of projection valued measurements or to a dense subset of the set of positive operator valued measurements on any finite dimensional system hence no kochen specker like contradiction can rule out hidden variable theories indistinguishable from quantum theory by finite precision measurements in either class

a new algebraic approach to stabilization for boundary control systems of parabolic type abstract we study the stabilization problem of linear parabolic boundary control systems while the control system is described by a pair of standard linear differential operators l the corresponding semigroup generator generally admits no riesz basis of eigenvectors in the sense that very little information on the fractional powers of this generator is needed our approach has enough generality as a prototype to be used for other types of parabolic systems we propose in this paper a new algebraic approach to the stabilization which gives to the best of the author s knowledge the simplest framework of the problem the control system with the scheme of boundary observation boundary feedback is turned into the differential equations with no boundary input in usual and standard l 2 spaces in a readable manner

finite dimensional dual state feedback control of linear boundary control systems in this article the finite dimensional control of distributed parameter systems with boundary control and unbounded observation is considered this problem is solved by extending the concept of dual observer based compensators to infinite dimensions these compensators have the advantage that on the one hand the separation principle can be used to directly determine a finite dimensional compensator and on the other hand they can be directly applied to boundary control systems with a time derivative of the input in order to achieve a low controller order as well as a desired control performance a parametric approach is proposed to parameterise the degrees of freedom contained in the controller consequently desired design specifications can be achieved by using a parameter optimisation the proposed design of finite dimensional dual observer based compensators is demonstrated by means of a heat conducting system with neumann boundary control and boundary measurements

necessary conditions for extended noncontextuality in general sets of random variables in this paper we explore the graph approach to contextuality to restate the extended definition of noncontextuality as given by kujala et al phys rev lett 115 150401 2015 using graph theoretical terms this extended definition avoids the assumption of the pre sheaf or non disturbance condition which states that if two contexts overlap then the marginal distribution obtained for the intersection must be the same a restriction that will never be perfectly satisfied in real experiments with this we are able to derive necessary conditions for extended noncontextuality for any set of random variables based on the geometrical aspects of the graph approach which can be tested directly with experimental data in any contextuality experiment and which reduce to traditional necessary conditions for noncontextuality if the non disturbance condition is satisfied

strong orthogonal arrays of strength two plus strong orthogonal arrays were recently introduced and studied in he and tang biometrika100 2013 254 260 as a class of space filling designs for computer experiments to enjoy the benefits of better space filling properties when compared to ordinary orthogonal arrays strong orthogonal arrays need to have strength three or higher which may require run sizes that are too large for experimenters to afford to address this problem we introduce a new class of arrays called strong orthogonal arrays of strength two plus these arrays while being more economical than strong orthogonal arrays of strength three still enjoy the better two dimensional space filling property of the latter among the many results we have obtained on the characterizations and constructions of strong orthogonal arrays of strength two plus worth special mention is their intimate connection with second order saturated designs

an approximate predictor approach to reduced order models and controllers for distributed parameter systems two reduced order digital controllers for distributed parameter systems dps are described reduced order models approximate the optimal finite past predictor and error covariance for the full system to minimize an approximation to the kullback leibler information distance klid an lqg controller based on a reduced order system model is described a reduced order controller is found to minimize the klid between the closed loop system outputs with the full and reduced order controllers noncollocated control of a flexible beam is simulated

approximation of discrete time lqg compensators for distributed systems with boundary input and unbounded measurement abstract we consider the approximation of optimal discrete time linear quadratic gaussian lqg compensators for distributed parameter control systems with boundary input and unbounded measurement our approach applies to problems that can be formulated in a state space on which both the discrete time input and output operators are continuous approximating compensators are obtained via application of the lqg theory and associated approximation results for infinite dimensional discrete time control systems with bounded input and output numerical results for spline and modal approximation schemes used to compute optimal compensators for a one dimensional heat equation with either neumann or dirichlet boundary control and pointwise measurement of temperature are presented and discussed

geometry of uncertainty relations for linear combinations of position and momentum for a quantum particle with a single degree of freedom we derive preparational sum and product uncertainty relations satisfied by n linear combinations of position and momentum observables the state independent bounds depend on their degree of incompatibility defined by the area of a parallelogram in an n dimensional coefficient space maximal incompatibility occurs if the observables give rise to regular polygons in phase space we also conjecture a hirschman type uncertainty relation for n observables linear in position and momentum generalizing the original relation which lower bounds the sum of the position and momentum shannon entropies of the particle

constraints on quantum hidden variables and the bohm theory the no hidden variables arguments of mermin and peres 1990 are assessed in the light of the bohm formulation of quantum theory

feedback stabilization of linear diffusion systems this paper treats the feedback stabilization of linear diffusion systems by using a finite dimensional feedback dynamic controller we construct a finite dimensional observer using the output functions from sensors and the control inputs to the system are given by the feedback of the observer output assuming for some fixed finite number l that the first l modes are controllable and observable we prove that it is possible to construct a finite dimensional feedback dynamic controller such that the diffusion system has an arbitrarily large damping constant

stability and stabilizability of infinite dimensional systems in this paper we are concerned with stability problems for infinite dimensional systems first we review the theory for linear systems where the dynamics are governed by strongly continuous semigro

compensator design of semi linear parabolic systems the stabilization of semi linear parabolic distributed systems by means of boundary controls is treated formulating the partial differential equation describing the system as an evolution equation in a hilbert space here by using the properties of an analytic semigroup the global existence of the solution under static output feedback is shown moreover in the similar way the global existence of the solution and the stabihzability for the system which installs a finite dimensional dynamic compensator is shown

finite dimensional regulators for a class of infinite dimensional systems abstract we show that the direct approach developed by the author for stabilization of certain classes of distributed parameter systems can be extended to cover regulation problems as well an iterative design algorithm is presented together with proof that the algorithm will converge after a finite number of steps the procedure is illustrated with an example of a constant disturbance acting on a delay system

state independent proof of kochen specker theorem with 13 rays quantum contextuality as proved by kochen and specker and also by bell should manifest itself in any state in any system with more than two distinguishable states and recently has been experimentally verified however for the simplest system capable of exhibiting contextuality a qutrit the quantum contextuality is verified only state dependently in experiment because too many at least 31 observables are involved in all the known state independent tests here we report an experimentally testable inequality involving only 13 observables that is satisfied by all noncontextual realistic models while being violated by all qutrit states thus our inequality facilitates a state independent test of the quantum contextuality for an indivisible quantum system we also provide a record breaking state independent proof of the kochen specker theorem with 13 directions determined by 26 points on the surface of a magic cube

general conditions for maximal violation of non contextuality in discrete and continuous variables the contextuality of quantum mechanics can be shown by the violation of inequalities based on measurements of well chosen observables an important property of such observables is that their expectation value can be expressed in terms of probabilities for obtaining two exclusive outcomes examples of such inequalities have been constructed using either observables with a dichotomic spectrum or using periodic functions obtained from displacement operators in phase space here we identify the general conditions on the spectral decomposition of observables demonstrating state independent contextuality of quantum mechanics our results not only unify existing strategies for maximal violation of state independent non contextuality inequalities but also lead to new scenarios enabling such violations among the consequences of our results is the impossibility of having a state independent maximal violation of non contextuality in the peres mermin scenario with discrete observables of odd dimensions

mermin pentagrams arising from veldkamp lines for three qubits we study the geometry of the space of mermin pentagrams objects that are used to rule out the existence of noncontextual hidden variable theories as alternatives to quantum theory it is shown that this space of 12 096 possible pentagrams is organized into 1008 families with each family containing a double six of pentagrams the 1008 families are connected to a special set of veldkamp lines in the veldkamp space for three qubits an object well known to finite geometers but has only been introduced to physics recently due to the transitive action of the symplectic group on this set of veldkamp lines it is enough to study only one canonical double six configuration of pentagrams we prove that the geometry of this double six configuration is encapsulated in the weight diagram of the 20 dimensional irreducible representation of the group as an interesting by product of our approach we show that mermin pentagrams and a class of mermin squares labelled by three qubit pauli operators are inherently related we conjecture that by studying the representation theoretic content of other veldkamp lines of the veldkamp space for n qubits makes it possible to find new contextual configurations in a systematic manner

the construction of kochen specker noncolourable sets in higher dimensional space from corresponding sets in lower dimension modification of cabello estebaranz and garcia alcaine s method by re examination of cabello estebaranz and garcia alcaine s method ceg for constructing a ray set which gives a proof of kochen specker theorem in a higher dimension from an already known set in a lower dimension a more refined method is derived in the construction of ray sets of higher dimension we need fewer rays than in ceg by using the method an analytical proof of the ks noncolourability of ray sets in real hilbert spaces is also given whose ks noncolourability was found by ceg by computer calculation

the veldkamp space of multiple qubits we introduce a point line incidence geometry in which the commutation relations of the real pauli group of multiple qubits are fully encoded its points are pairs of pauli operators differing in sign and each line contains three pairwise commuting operators any of which is the product of the other two up to sign we study the properties of its veldkamp space enabling us to identify subsets of operators which are distinguished from the geometric point of view these are geometric hyperplanes and pairwise intersections among the geometric hyperplanes one can find the set of self dual operators with respect to the wootters spin flip operation well known from studies concerning multiqubit entanglement measures in the two and three qubit cases a class of hyperplanes gives rise to mermin squares and other generalized quadrangles in the three qubit case the hyperplane with points corresponding to the 27 wootters self dual operators is just the underlying geometry of the e6 6 symmetric entropy formula describing black holes and strings in five dimensions

an algorithmic test for checking stability of feedback spectral systems abstract given a certain class of regular spectral systems an algorithm is presented that is designed to test the stability properties of the feedback interconnection of such a system and either a bounded state feedback operator or a finite dimensional linear time invariant controller the applicability of this test is independent of the method used to design the feedback controller and is designed to provide a separate independent method for verifying whether or not the plant controller interconnection is exponentially stable the test is particularly well suited to problems involving certain partial differential equations pde with spatially varying coefficients or complicated boundary shapes

orthogonal array based latin hypercubes abstract in this article we use orthogonal arrays oa s to construct latin hypercubes besides preserving the univariate stratification properties of latin hypercubes these strength r oa based latin hypercubes also stratify each r dimensional margin therefore such oa based latin hypercubes provide more suitable designs for computer experiments and numerical integration than do general latin hypercubes we prove that when used for integration the sampling scheme with oa based latin hypercubes offers a substantial improvement over latin hypercube sampling

nonlocal games and quantum permutation groups we present a strong connection between quantum information and quantum permutation groups specifically we define a notion of quantum isomorphisms of graphs based on quantum automorphisms from the theory of quantum groups and then show that this is equivalent to the previously defined notion of quantum isomorphism corresponding to perfect quantum strategies to the isomorphism game moreover we show that two connected graphs x and y are quantum isomorphic if and only if there exists x v x and y v y that are in the same orbit of the quantum automorphism group of the disjoint union of x and y this connection links quantum groups to the more concrete notion of nonlocal games and physically observable quantum behaviours we exploit this link by using ideas and results from quantum information in order to prove new results about quantum automorphism groups and about quantum permutation groups more generally in particular we show that asymptotically almost surely all graphs have trivial quantum automorphism group furthermore we use examples of quantum isomorphic graphs from previous work to construct an infinite family of graphs which are quantum vertex transitive but fail to be vertex transitive answering a question from the quantum group literature our main tool for proving these results is the introduction of orbits and orbitals orbits on ordered pairs of quantum permutation groups we show that the orbitals of a quantum permutation group form a coherent configuration algebra a notion from the field of algebraic graph theory we then prove that the elements of this quantum orbital algebra are exactly the matrices that commute with the magic unitary defining the quantum group we furthermore show that quantum isomorphic graphs admit an isomorphism of their quantum orbital algebras which maps the adjacency matrix of one graph to that of the other

necessary and sufficient condition for quantum state independent contextuality we solve the problem of whether a set of quantum tests reveals state independent contextuality and use this result to identify the simplest set of the minimal dimension we also show that identifying state independent contextuality graphs r ramanathan and p horodecki phys rev lett 112 040404 2014 is not sufficient for revealing state independent contextuality

family of bell like inequalities as device independent witnesses for entanglement depth we present a simple family of bell inequalities applicable to a scenario involving arbitrarily many parties each of which performs two binary outcome measurements we show that these inequalities are members of the complete set of full correlation bell inequalities discovered by werner wolf ifmmode dot z else z fi ukowski brukner for scenarios involving a small number of parties we further verify that these inequalities are facet defining for the convex set of bell local correlations moreover we show that the amount of quantum violation of these inequalities naturally manifests the extent to which the underlying system is genuinely many body entangled in other words our bell inequalities when supplemented with the appropriate quantum bounds naturally serve as device independent witnesses for entanglement depth allowing one to certify genuine k partite entanglement in an arbitrary n ensuremath ge k partite scenario without relying on any assumption about the measurements being performed or the dimension of the underlying physical system a brief comparison is made between our witnesses and those based on some other bell inequalities as well as quantum fisher information a family of witnesses for genuine k partite nonlocality applicable to an arbitrary n ensuremath ge k partite scenario based on our bell inequalities is also presented

bellʼs inequality and extremal non local box from hardyʼs test for non locality bell showed 50 years ago that quantum theory is non local via his celebrated inequalities turning the issue of quantum non locality from a matter of taste into a matter of test years later hardy proposed a test for non locality without inequality which is a kind of something versus nothing argument hardy s test for n particles induces an n partite bell s inequality with two dichotomic local measurements for each observer which has been shown to be violated by all entangled pure states our first result is to show that the bell hardy inequality arising form hardy s non locality test is tight for an arbitrary number of parties i e it defines a facet of the bell polytope in the given scenario on the other hand quantum theory is not that non local since it forbids signaling and even not as non local as allowed by non signaling conditions i e quantum mechanical predictions form a strict subset of the so called non signaling polytope in the scenario of each observer measuring two dichotomic observables fritz established a duality between the bell polytope and the non signaling polytope tight bell s inequalities the facets of the bell polytope are in a one to one correspondence with extremal non signaling boxes the vertices of the non signaling polytope our second result is to provide an alternative and more direct formula for this duality as an example the tight bell hardy inequality gives rise to an extremal non signaling box that serves as a natural multipartite generalization of popescu rohrlich box this article is part of a special issue of journal of physics a mathematical and theoretical devoted to 50 years of bell s theorem

the morita theory of quantum graph isomorphisms we classify instances of quantum pseudo telepathy in the graph isomorphism game exploiting the recently discovered connection between quantum information and the theory of quantum automorphism groups specifically we show that graphs quantum isomorphic to a given graph are in bijective correspondence with morita equivalence classes of certain frobenius algebras in the category of finite dimensional representations of the quantum automorphism algebra of that graph we show that such a frobenius algebra may be constructed from a central type subgroup of the classical automorphism group whose action on the graph has coisotropic vertex stabilisers in particular if the original graph has no quantum symmetries quantum isomorphic graphs are classified by such subgroups we show that all quantum isomorphic graph pairs corresponding to a well known family of binary constraint systems arise from this group theoretical construction we use our classification to show that of the small order vertex transitive graphs with no quantum symmetry none is quantum isomorphic to a non isomorphic graph we show that this is in fact asymptotically almost surely true of all graphs

a hidden variables versus quantum mechanics experiment in the light of the bell kochen specker theorem we examine a feasible experimental test in order to discriminate between non contextual hidden variables and some probabilistic predictions of quantum mechanics

optimal classical simulation of state independent quantum contextuality simulating quantum contextuality with classical systems requires memory a fundamental yet open question is what is the minimum memory needed and therefore the precise sense in which quantum systems outperform classical ones here we make rigorous the notion of classically simulating quantum state independent contextuality qsic in the case of a single quantum system submitted to an infinite sequence of measurements randomly chosen from a finite qsic set we obtain the minimum memory needed to simulate arbitrary qsic sets via classical systems under the assumption that the simulation should not contain any oracular information in particular we show that while classically simulating two qubits tested with the peres mermin set requires log 2 24 4 585 bits simulating a single qutrit tested with the yu oh set requires at least 5 740 bits

stabilization of a coupled transport diffusion system with boundary input we consider the problem of stabilizing a coupled transport diffusion system with boundary input the system is described by two linear transport diffusion equations and is not asymptotically stable in order to stabilize the system with boundary input sensor influence functions are assumed to be located at interior of the domain first we formulate the system as an evolution equation with unbounded output operators in a hilbert space using variable transformation next we derive a reduced order model with a finite dimensional state variable for the infinite dimensional system then a stabilizing controller is constructed for the reduced order model under an additional assumption it is shown that the finite dimensional controller together with a residual mode filter plays a role of a finite dimensional stabilizing controller for the original infinite dimensional system if the order of the residual mode filter is chosen sufficiently large finally the validity of the design method is demonstrated through a numerical simulation