bell type inequalities for nonlocal resources we present bipartite bell type inequalities which allow the two partners to use some nonlocal resource such inequalities can only be violated if the parties use a resource which is more nonlocal than the one permitted by the inequality we introduce a family of n input nonlocal machines which are generalizations of the well known pr popescu rohrlich box then we construct bell type inequalities that cannot be violated by strategies that use one of these new machines finally we discuss implications for the simulation of quantum states

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

likelihood methods for mpsk modulation classification new algorithms based on the likelihood functional lf and approximations thereof are proposed for the problem of classifying mpsk modulations in additive white gaussian noise previously introduced classifiers for this problem are theoretically interpreted as simplified versions of the ones in here the performance of a single term approximation to the optimal lf classifier is evaluated analytically and is shown to be very close to that of the optimal furthermore recursive algorithms for the implementation of this new quasi log likelihood ratio qllr classifier are derived which imply no significant increase in classifier complexity the present method of generating classification algorithms can be generalized to arbitrary two dimensional signal constellations

lifting and separation procedures for the cut polytope the max cut problem and the associated cut polytope on complete graphs have been extensively studied over the last 25 years however in comparison only little research has been conducted for the cut polytope on arbitrary graphs in particular separation algorithms have received only little attention in this study we describe new separation and lifting procedures for the cut polytope on general graphs these procedures exploit algorithmic and structural results known for the cut polytope on complete graphs to generate valid and sometimes facet defining inequalities for the cut polytope on arbitrary graphs in a cutting plane framework we report computational results on a set of well established benchmark problems

a comparison of snr estimation techniques for the awgn channel the performances of several signal to noise ratio snr estimation techniques reported in the literature are compared to identify the best estimator the snr estimators are investigated by the computer simulation of baseband binary phase shift keying psk signals in real additive white gaussian noise awgn and baseband 8 psk signals in complex awgn the mean square error is used as a measure of performance in addition to comparing the relative performances the absolute levels of performance are also established the simulated performances are compared to a published cramer rao bound crb for real awgn and a crb for complex awgn that is derived here some known estimator structures are modified to perform better on the channel of interest estimator structures for both real and complex channels are examined

entropic nonsignaling correlations we introduce the concept of entropic nonsignaling correlations i e entropies arising from probabilistic theories that are compatible with the fact that we cannot transmit information instantaneously we characterize and show the relevance of these entropic correlations in a variety of different scenarios ranging from typical bell experiments to more refined descriptions such as bilocality and information causality in particular we apply the framework to derive the first entropic inequality testing genuine tripartite nonlocality in quantum systems of arbitrary dimension and also prove the first known monogamy relation for entropic bell inequalities further within the context of complex bell networks we show that entropic nonlocal correlations can be activated

ramanujan s theories of elliptic functions to alternative bases in his famous paper 3 10 pp 23 39 ramanujan offers several beautiful series representations for 1 pi he first states three formulas one of which is frac 4 pi sum limits mathbf n 0 infty frac left 6 mathbf n 1 right left frac 1 2 right 3 n left mathbf n right 3 4 n where a o 1 and for each positive integer n left mathbf a right n mathbf a left mathbf a 1 right left mathbf a 2 right left mathbf a mathbf n 1 right

the extension problem for partial boolean structures in quantum mechanics alternative partial boolean structures implicit in the discussion of classical representability of sets of quantum mechanical predictions are characterized with definite general conclusions on the equivalence of the approaches going back to bell and kochen specker an algebraic approach is presented allowing for a discussion of partial classical extension amounting to reduction of the number of contexts classical representability arising as a special case as a result known techniques are generalized and some of the associated computational difficulties overcome the implications on the discussion of boole bell inequalities are indicated

cramer rao bounds for snr estimation of oversampled linearly modulated signals most signal to noise ratio snr estimators use the receiver matched filter output sampled at the symbol rate an approach which does not preserve all information in the analog waveform due to aliasing thus it is relevant to ask whether avoiding aliasing could improve snr estimation to this end we compute the corresponding data aided da and nondata aided nda cramer rao bounds crbs we adopt a novel dual filter framework which is shown to be information preserving under suitable conditions and considerably simplifies the analysis it is shown that the crb can be substantially reduced by exploiting any available excess bandwidth depending on the modulation scheme the snr range and the estimator type da or nda

looking for symmetric bell inequalities finding all bell inequalities for a given number of parties measurement settings and measurement outcomes is in general a computationally hard task we show that all bell inequalities which are symmetric under the exchange of parties can be found by examining a symmetrized polytope which is simpler than the full bell polytope as an illustration of our method we generate 238 885 new bell inequalities and 1085 new svetlichny inequalities we find in particular facet inequalities for bell experiments involving two parties and two measurement settings that are not of the collins gisin linden massar popescu type

generalized elliptic integrals and the legendre m function abstract we study monotonicity and convexity properties of functions arising in the theory of elliptic integrals and in particular in the case of a schwarz christoffel conformal mapping from a half plane to a trapezoid we obtain sharp monotonicity and convexity results for combinations of these functions as well as functional inequalities and a linearization property

a relevant two qubit bell inequality inequivalent to the chsh inequality we computationally investigate the complete polytope of bell inequalities for two particles with small numbers of possible measurements and outcomes our approach is limited by pitowsky s connection of this problem to the computationally hard np problem despite this we find that there are very few relevant inequivalent inequalities for small numbers for example in the case with three possible 2 outcome measurements on each particle there is just one new inequality we describe mixed 2 qubit states which violate this inequality but not the chsh the new inequality also illustrates a sharing of bi partite non locality between three qubits something not seen using the chsh inequality it also inspires us to discover a class of bell inequalities with m possible n outcome measurements on each particle

quasi bell inequalities from symmetrized products of noncommuting qubit observables noncommuting observables cannot be simultaneously measured however under local hidden variable models they must simultaneously hold premeasurement values implying the existence of a joint probability distribution we study the joint distributions of noncommuting observables on qubits with possible criteria of positivity and the frechet bounds limiting the joint probabilities concluding that the latter may be negative we use symmetrization justified heuristically and then more carefully via the moyal characteristic function to find the quantum operator corresponding to the product of noncommuting observables this is then used to construct quasi bell inequalities bell inequalities containing products of noncommuting observables on two qubits these inequalities place limits on the local hidden variable models that define joint probabilities for noncommuting observables we find that the quasi bell inequalities have a quantum to classical violation as high as 32 on two qubit higher than conventi

lifting bell inequalities a bell inequality defined for a specific experimental configuration can always be extended to a situation involving more observers measurement settings or measurement outcomes in this article such liftings of bell inequalities are studied it is shown that if the original inequality defines a facet of the polytope of local joint outcome probabilities then the lifted one also defines a facet of the more complex polytope

correlation polytopes their geometry and complexity a family of polytopes correlation polytopes which arise naturally in the theory of probability and propositional logic is defined these polytopes are tightly connected to combinatorial problems in the foundations of quantum mechanics and to the ising spin model correlation polytopes exhibit a great deal of symmetry exponential size symmetry groups which leave the polytope invariant and act transitively on its vertices are defined using the symmetries a large family of facets is determined a conjecture concerning the full facet structure of correlation polytopes is formulated the conjecture however implies that np co np various complexity results are proved it is shown that deciding membership in a correlation polytope is an np complete problem and deciding facets is probably not even in np the relations between the polytope symmetries and its complexity are indicated

correlation inequalities and hidden variables a counterexample is given to a recent suggestion that if the inequalities of clauser and horne hold then there exists a hidden variable model for a spin textonehalf correlation experiment of the einstein podolsky rosen type

bell inequalities from variable elimination methods tight bell inequalities are facets of pitowsky s correlation polytope and are usually obtained from its extreme points by solving the hull problem here we present an alternative method based on a combination of algebraic results on extensions of measures and variable elimination methods e g the fourier motzkin method our method is shown to overcome some of the computational difficulties associated with the hull problem in some non trivial cases moreover it provides an explanation for the arising of only a finite number of families of bell inequalities in measurement scenarios where one experimenter can choose between an arbitrary number of different measurements

on the inequivalence of the ch and chsh inequalities due to finite statistics different variants of a bell inequality such as chsh and ch are known to be equivalent when evaluated on nonsignaling outcome probability distributions however in experimental setups the outcome probability distributions are estimated using a finite number of samples therefore the nonsignaling conditions are only approximately satisfied and the robustness of the violation depends on the chosen inequality variant we explain that phenomenon using the decomposition of the space of outcome probability distributions under the action of the symmetry group of the scenario and propose a method to optimize the statistical robustness of a bell inequality in the process we describe the finite group composed of relabeling of parties measurement settings and outcomes and identify correspondences between the irreducible representations of this group and properties of outcome probability distributions such as normalization signaling or having uniform marginals

multigraph approach to quantum non locality non contextuality nc and bell inequalities can be expressed as bounds for positive linear combinations s of probabilities of events exclusive events in s can be represented as adjacent vertices of a graph called the exclusivity graph of s in the case that events correspond to the outcomes of quantum projective measurements quantum probabilities are intimately related to the grotschel lovasz schrijver theta body of the exclusivity graph then one can easily compute an upper bound to the maximum quantum violation of any nc or bell inequality by optimizing s over the theta body and calculating the lovasz number of the corresponding exclusivity graph in some cases this upper bound is tight and gives the exact maximum quantum violation however in general this is not the case the reason is that the exclusivity graph does not distinguish among the different ways exclusivity can occur in bell inequality and similar scenarios an interesting question is whether there is a graph theoretical concept which accounts for this problem here we show that for any given n partite bell inequality an edge coloured multigraph composed of n single colour graphs can be used to encode the relationships of exclusivity between each party s parts of the events then the maximum quantum violation of the bell inequality is exactly given by a refinement of the lovasz number that applies to these edge coloured multigraphs we show how to calculate upper bounds for this number using a hierarchy of semi definite programs and calculate upper bounds for i3 i3322 and the three bipartite bell inequalities whose exclusivity graph is a pentagon the multigraph theoretical approach introduced here may remove some obstacles in the program of explaining quantum correlations from first principles this article is part of a special issue of journal of physics a mathematical and theoretical devoted to 50 years of bell s theorem

functional inequalities for the ratio of complete p elliptic integrals abstract in this paper we show monotonicity and convexity properties of a function involving the ratio of complete p elliptic integrals which reduces to the modulus of the grotzsch ring as applications we obtain several sharp functional inequalities

snr estimation for multilevel constellations using higher order moments the performance of existing moments based non data aided nda estimators of signal to noise ratio snr in digital communication systems substantially degrades with multilevel constellations we propose a novel moments based approach that is amenable to practical implementation and significantly improves on previous estimators of this class this approach is based on a linear combination of ratios of certain even order moments which allow the derivation of nda snr estimators without requiring memory costly lookup tables the weights of the linear combination can be tuned according to the constellation and the snr operation range as particular case we develop an eighth order statistics eos based estimator showing in detail the statistical analysis that leads to the weight optimization procedure the eos based estimators yield improved performance for multilevel constellations especially for those with two and three amplitude levels monte carlo simulations validate the new approach in a wide snr range

solution to a conjecture on the legendre m function with an application to the generalized modulus abstract in this note we give a solution to a conjecture on the legendre m function proposed by heikkala linden vamanamurthy and vuorinen in the paper heikkala et al 2008 5 as an application of this result we obtain a functional inequality of the generalized modulus

designing bell inequalities from a tsirelson bound we present a simple analytic bound on the quantum value of general correlation type bell inequalities similar to tsirelson s bound it is based on the maximal singular value of the coefficient matrix associated with the inequality we provide a criterion for tightness of the bound and show that the class of inequalities where our bound is tight covers many famous examples from the literature we describe how this bound helps to construct bell inequalities in particular inequalities that witness the dimension of the measured observables

snr estimation for nonconstant modulus constellations we propose a new technique to estimate the signal to noise ratio snr over the flat fading channel this is a nondata aided envelope based estimator that can be applied to nonconstant modulus constellations which is a feature not found in existing approaches we also analyze the performance of our estimators for both phase shift keying psk and non psk constellations by deriving their asymptotic variances and comparing with the crame spl acute r rao bounds crbs moreover we discuss how the snr estimates can be used to approximate the bit error rate ber and how the accuracy of the snr estimate is related to that of the ber estimate which justifies the necessity for the accurate estimation of snr the analytical performance is shown for both psk and non psk constellations such as 8 quadrature amplitude modulation qam and 16 qam monte carlo simulation results corroborate our analysis

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

loopholes in bell inequality tests of local realism bell inequalities are intended to show that local realist theories cannot describe the world a local realist theory is one where physical properties are defined prior to and independent of measurement and no physical influence can propagate faster than the speed of light quantum mechanical predictions for certain experiments violate the bell inequality while a local realist theory cannot and this shows that a local realist theory cannot give those quantum mechanical predictions however because of unexpected circumstances or loopholes in available experiment tests local realist theories can reproduce the data from these experiments this paper reviews such loopholes what effect they have on bell inequality tests and how to avoid them in experiment avoiding all these simultaneously in one experiment usually called a loophole free or definitive bell test remains an open task but is very important for technological tasks such as device independent security of quantum cryptography and ultimately for our understanding of the world this article is part of a special issue of journal of physics a mathematical and theoretical devoted to 50 years of bell s theorem

a geometric comparison of entanglement and quantum nonlocality in discrete systems we compare entanglement with quantum nonlocality employing a geometric structure of the state space of bipartite qudits the central object is a regular simplex spanned by generalized bell states the collins gisin linden massar popescu bell inequality is used to reveal states of this set that cannot be described by local realistic theories optimal measurement settings necessary to ascertain nonlocality are determined by means of a recently proposed parameterization of the unitary group combined with robust numerical methods the main results of this paper are descriptive geometric illustrations of the state space that emphasize the difference between entanglement and quantum nonlocality namely it is found that the shape of the boundaries of separability and bell inequality violation are essentially different moreover it is also shown that for mixtures of states sharing the same amount of entanglement bell inequality violations and entanglement measures are non monotonically related

on the relationship between convex bodies related to correlation experiments with dichotomic observables in this paper we explore further the connections between convex bodies related to quantum correlation experiments with dichotomic variables and related bodies studied in combinatorial optimization especially cut polyhedra such a relationship was established in avis et al 2005 j phys a math gen 38 10971 87 with respect to bell inequalities we show that several well known bodies related to cut polyhedra are equivalent to bodies such as those defined by tsirelson 1993 hadronic j suppl 8 329 45 to represent hidden deterministic behaviours quantum behaviours and no signalling behaviours among other things our results allow a unique representation of these bodies give a necessary condition for vertices of the no signalling polytope and give a method for bounding the quantum violation of bell inequalities by means of a body that contains the set of quantum behaviours optimization over this latter body may be performed efficiently by semidefinite programming in the second part of the paper we apply these results to the study of classical correlation functions we provide a complete list of tight inequalities for the two party case with m n dichotomic observables when m 4 n 4 and when min m n 3 and give a new general family of correlation inequalities

maximum likelihood snr estimation of linearly modulated signals over time varying flat fading simo channels in this paper we tackle for the first time the problem of maximum likelihood ml estimation of the signal to noise ratio snr parameter over time varying single input multiple output simo channels both the data aided da and the non data aided nda schemes are investigated unlike classical techniques where the channel is assumed to be slowly time varying and therefore considered as constant over the entire observation period we address the more challenging problem of instantaneous i e short term or local snr estimation over fast time varying channels the channel variations are tracked locally using a polynomial in time expansion first we derive in closed form expressions the da ml estimator and its bias the latter is subsequently subtracted in order to obtain a unbiased da estimator whose variance and the corresponding cramer rao lower bound crlb are also derived in closed form due to the extreme nonlinearity of the log likelihood function llf in the nda case we resort to the expectation maximization em technique to iteratively obtain the exact nda ml snr estimates within very few iterations most remarkably the new em based nda estimator is applicable to any linearly modulated signal and provides sufficiently accurate soft estimates i e soft detection for the unknown transmitted symbols therefore hard detection can be easily embedded in the iteration loop in order to improve its performance at low snr levels we show by extensive computer simulations that the new estimators are able to accurately estimate the instantaneous per antenna snrs as they coincide with the da crlb over a wide range of practical snrs

on hypergeometric functions and generalizations of legendre s relation we prove some convexity properties for a sum of hypergeometric functions and obtain a generalization of legendre s relation for complete elliptic integrals we apply these results to prove some inequalities for hypergeometric functions incomplete beta functions and legendre functions

classifying 50 years of bell inequalities since john s bell demonstrated the interest of studying linear combinations of probabilities in relation with the epr paradox in 1964 bell inequalities have lead to numerous developments unfortunately the description of bell inequalities is subject to several degeneracies which make any exchange of information about them unnecessarily hard here we analyze these degeneracies and propose a decomposition for bell like inequalities based on a set of reference expressions which is not affected by them these reference expressions set a common ground for comparing bell inequalities we provide algorithms based on finite group theory to compute this decomposition implementing these algorithms allows us to set up a compendium of reference bell like inequalities available online at www faacets com this website constitutes a platform where registered bell like inequalities can be explored new inequalities can be compared to previously known ones and relevant information on bell inequalities can be added in a collaborative manner this article is part of a special issue of journal of physics a mathematical and theoretical devoted to 50 years of bell s theorem

geometry of the set of synchronous quantum correlations we provide a complete geometric description of the set of synchronous quantum correlations for the three experiment two outcome scenario we show that these correlations form a closed set moreover every correlation in this set can be realized using projection valued measures on a hilbert space of dimension no more than 16

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

generating facets for the cut polytope of a graph by triangular elimination the cut polytope of a graph arises in many fields although much is known about facets of the cut polytope of the complete graph very little is known for general graphs the study of bell inequalities in quantum information science requires knowledge of the facets of the cut polytope of the complete bipartite graph or more generally the complete k partite graph lifting is a central tool to prove certain inequalities are facet inducing for the cut polytope in this paper we introduce a lifting operation named triangular elimination applicable to the cut polytope of a wide range of graphs triangular elimination is a specific combination of zero lifting and fourier motzkin elimination using the triangle inequality we prove sufficient conditions for the triangular elimination of facet inducing inequalities to be facet inducing the proof is based on a variation of the lifting lemma adapted to general graphs the result can be used to derive facet inducing inequalities of the cut polytope of various graphs from those of the complete graph we also investigate the symmetry of facet inducing inequalities of the cut polytope of the complete bipartite graph derived by triangular elimination

snr estimation in time varying fading channels signal to noise ratio snr estimation is considered for phase shift keying communication systems in time varying fading channels both data aided da estimation and nondata aided nda estimation are addressed the time varying fading channel is modeled as a polynomial in time inherent estimation accuracy limitations are examined via the cramer rao lower bound where it is shown that the effect of the channel s time variation on snr estimation is negligible a novel maximum likelihood ml snr estimator is derived for the time varying channel model in da scenarios where the estimator has a simple closed form solution the exact performance is evaluated both with correct and incorrect i e mismatched polynomial order in nda estimation the unknown data symbols are modeled as random and the marginal likelihood is used the expectation maximization algorithm is proposed to iteratively maximize this likelihood function simulation results show that the resulting estimator offers statistical efficiency over a wider range of scenarios than previously published methods

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

on the extension complexity of combinatorial polytopes in this paper we extend recent results of fiorini et al on the extension complexity of the cut polytope and related polyhedra we first describe a lifting argument to show exponential extension complexity for a number of np complete problems including subset sum and three dimensional matching we then obtain a relationship between the extension complexity of the cut polytope of a graph and that of its graph minors using this we are able to show exponential extension complexity for the cut polytope of a large number of graphs including those used in quantum information and suspensions of cubic planar graphs

visualizing two qubits the notions of entanglement witnesses and separable and entangled states for a two qubit system can be visualized in three dimensions using the slocc equivalence classes this visualization preserves the duality relations between the various sets and allows us to give proof by inspection of a nonelementary result of horodecki et al phys lett a 223 1 8 1996 that for two qubits peres ppt positive partial transpose test for separability is iff we then show that the chsh bell inequalities can be visualized as circles and cylinders in the same diagram this allows us to give a geometric proof of yet another result of horodecki et al phys lett a 200 340 344 1995 which optimizes the violation of the chsh bell inequality finally we give numerical evidence that remarkably allowing alice and bob to use three rather than two measurements each does not help them to distinguish any new entangled slocc equivalence class beyond the chsh class

blind signal to noise ratio estimation of real sinusoid in additive noise we consider the problem of estimation of signal to noise ratio snr with a real deterministic sinusoid with unknown frequency phase and amplitude in additive gaussian noise of unknown variance the method of moments a general method to derive estimators based on high order moments is used to derive a blind snr estimator that does not require the knowledge of the instantaneous frequency of the sinusoid through separate estimation of signal and noise power cramer rao lower bounds crlbs are also derived for estimators of signal and noise power and then for snr estimators we show through numerical simulations the statistical performances of the estimators that we compare to the corresponding crlbs and discuss their use in practical applications

two party bell inequalities derived from combinatorics via triangular elimination we establish a relation between the two party bell inequalities for two valued measurements and a high dimensional convex polytope called the cut polytope in polyhedral combinatorics using this relation we propose a method triangular elimination to derive tight bell inequalities from facets of the cut polytope this method gives two hundred million inequivalent tight bell inequalities from currently known results on the cut polytope in addition this method gives general formulae which represent families of infinitely many bell inequalities these results can be used to examine general properties of bell inequalities

local hidden variable models for entangled quantum states while entanglement and violation of bell inequalities were initially thought to be equivalent quantum phenomena we now have different examples of entangled states whose correlations can be described by local hidden variable models and therefore do not violate any of the bell inequalities we provide an up to date overview of the existing literature regarding local hidden variable models for entangled quantum states in both the bipartite and multipartite cases and discuss some of the most relevant open questions in this context our review covers twenty five years of this line of research beginning with the seminal work by werner 1989 phys rev a 40 8 which provided the first example of an entangled state with a local model werner s work in turn appeared twenty five years after the seminal work by bell 1964 physics 1 195 about the impossibility of recovering the predictions of quantum mechanics using a local hidden variable theory this article is part of a special issue of journal of physics a mathematical and theoretical devoted to 50 years of bell s theorem

bell inequalities for arbitrarily high dimensional systems we develop a novel approach to bell inequalities based on a constraint that the correlations exhibited by local variable theories must satisfy this is used to construct a family of bell inequalities for bipartite quantum systems of arbitrarily high dimensionality which are strongly resistant to noise in particular our work gives an analytic description of previous numerical results and generalizes them to arbitrarily high dimensionality

multipartite bell type inequalities for arbitrary numbers of settings and outcomes per site we introduce a single general representation incorporating in a unique manner all bell type inequalities for a multipartite correlation scenario with an arbitrary number of settings and any spectral type of outcomes at each site specifying this general representation for correlation functions we prove that the form of any correlation bell type inequality does not depend on spectral types of outcomes in particular on their numbers at different sites and is determined only by extremal values of outcomes at each site we also specify the general form of bounds in bell type inequalities on joint probabilities our approach to the derivation of bell type inequalities is universal concise and can be applied to a multipartite correlation experiment with outcomes of any spectral type discrete or continuous we in particular prove that for an n partite quantum state possibly infinite dimensional admitting the setting lhv description the mermin klyshko inequality holds for any two bounded quantum observables per site not necessarily dichotomic

all clauser horne shimony holt polytopes the correlations that admit a local hidden variable model are described by a family of polytopes whose facets are the bell inequalities the clauser horne shimony holt chsh inequality is the simplest such bell inequality and is a facet of every bell polytope we investigate for which bell polytopes the chsh inequality is also the unique non trivial facet we prove that the chsh inequality is the unique facet for all bipartite polytopes where at least one party has a binary choice of dichotomic measurements irrespective of the number of measurement settings and outcomes for the other party based on numerical results we conjecture that it is also the unique facet for all bipartite polytopes involving two measurements per party where at least one measurement is dichotomic finally we remark that these two situations can be the only ones for which the chsh inequality is the unique facet i e any polytope that does not correspond to one of these two cases necessarily has facets that are not of the chsh form as a byproduct of our approach we derive a new family of facet inequalities this article is part of a special issue of journal of physics a mathematical and theoretical devoted to 50 years of bell s theorem

cramer rao lower bound and em algorithm for envelope based snr estimation of nonconstant modulus constellations signal to noise ratio snr estimation for linearly modulated signals is addressed in this letter focusing on envelope based estimators which are robust to carrier offsets and phase jitter and on the challenging case of nonconstant modulus constellations for comparison purposes the true cramer rao lower bound is numerically evaluated obtaining an analytical expression in closed form for the asymptotic case of high snr values which quantifies the performance loss with respect to coherent estimation as the maximum likelihood algorithm is too complex for practical implementation an expectation maximization em approach is proposed achieving a good tradeoff between complexity and performance for medium to high snrs finally a hybrid scheme based on em and moments based estimates is suggested which performs close to the theoretical limit over a wide snr range

a new device independent dimension witness and its experimental implementation a dimension witness is a criterion that sets a lower bound on the dimension needed to reproduce the observed data three types of dimension witnesses can be found in the literature device dependent ones in which the bound is obtained assuming some knowledge on the state and the measurements device independent prepare and measure ones that can be applied to any system including classical ones and device independent bell based ones that certify the minimal dimension of some entangled systems here we consider the collins gisin linden massar popescu bell type inequality for four outcomes we show that a sufficiently high violation of this inequality witnesses d 4 and present a proof of principle experimental observation of such a violation this presents a first experimental violation of the third type of dimension witness beyond qutrits

remarks on generalized elliptic integrals we study the monotonicity for certain combinations of generalized elliptic integrals thus generalizing analogous well known results for classical complete elliptic integrals and prove a conjecture put forward by heikkala vamanamurthy and vuorinen

hidden variables joint probability and the bell inequalities it is shown that the following statements about a quantum correlation experiment are mutually equivalent 1 there is a deterministic hidden variables model for the experiment 2 there is a factorizable stochastic model 3 there is one joint distribution for all observables of the experiment returning the experimental probabilities 4 there are well defined compatible joint distributions for all pairs and triples of commuting and noncommuting observables 5 the bell inequalities hold