arithmetic properties of mirror map and quantum coupling we study some arithmetic properties of the mirror maps and the quantum yukawa couplings for some 1 parameter deformations of calabi yau manifolds first we use the schwarzian differential equation which we derived previously to characterize the mirror map in each case for algebraic k3 surfaces we solve the equation in terms of thej function by deriving explicit modular relations we prove that some k3 mirror maps are algebraic over the genus zero function fieldq j this leads to a uniform proof that those mirror maps have integral fourier coefficients regarding the maps as riemann mappings we prove that they are genus zero functions by virtue of the conway norton conjecture proved by borcherds using frenkel lepowsky meurman s moonshine module we find that these maps are actually the reciprocals of the thompson series for certain conjugacy classes in the griess fischer group this also gives as an immediate consequence a second proof that those mirror maps are integral we thus conjecture a surprising connection between k3 mirror maps and the thompson series for threefolds we construct a formal nonlinear ode for the quantum coupling reduced modp under the mirror hypothesis and an integrality assumption we derive modp congurences for the fourier coefficients for the quintics we deduce at least for 5 d that the degreed instanton numbersnd are divisible by 53 a fact first conjectured by clemens

typical local measurements in generalized probabilistic theories emergence of quantum bipartite correlations what singles out quantum mechanics as the fundamental theory of nature here we study local measurements in generalized probabilistic theories gpts and investigate how observational limitations affect the production of correlations we find that if only a subset of typical local measurements can be made then all the bipartite correlations produced in a gpt can be simulated to a high degree of accuracy by quantum mechanics our result makes use of a generalization of dvoretzky s theorem for gpts the tripartite correlations can go beyond those exhibited by quantum mechanics however

nonadditive conditional entropy and its significance for local realism based on the form invariance of the structures given by khinchin s axiomatic foundations of information theory and the pseudoadditivity of the tsallis entropy indexed by q the concept of conditional entropy is generalized to the case of nonadditive nonextensive composite systems the proposed nonadditive conditional entropy is classically nonnegative but can be negative in the quantum context indicating its utility for characterizing quantum entanglement a criterion deduced from it for separability of density matrices for validity of local realism is examined in detail by employing a bipartite spin 1 2 system it is found that the strongest criterion is obtained in the limit q

fitting and testing conditional multinormal partial credit models a multinormal partial credit model for factor analysis of polytomously scored items with ordered response categories is derived using an extension of the dutch identity holland in psychometrika 55 5 18 1990 in the model latent variables are assumed to have a multivariate normal distribution conditional on unweighted sums of item scores which are sufficient statistics attention is paid to maximum likelihood estimation of item parameters multivariate moments of latent variables and person parameters it is shown that the maximum likelihood estimates can be found without the use of numerical integration techniques more general models are discussed which can be used for testing the model and it is shown how models with different numbers of latent variables can be tested against each other in addition multi group extensions are proposed which can be used for testing both measurement invariance and latent population differences models and procedures discussed are demonstrated in an empirical data example

gaussian quantum marginal problem the quantum marginal problem asks what local spectra are consistent with a given spectrum of a joint state of a composite quantum system this setting also referred to as the question of the compatibility of local spectra has several applications in quantum information theory here we introduce the analogue of this statement for gaussian states for any number of modes and solve it in generality for pure and mixed states both concerning necessary and sufficient conditions formally our result can be viewed as an analogue of the sing thompson theorem respectively horn s lemma characterizing the relationship between main diagonal elements and singular values of a complex matrix we find necessary and sufficient conditions for vectors d1 dn and c1 cn to be the symplectic eigenvalues and symplectic main diagonal elements of a strictly positive real matrix respectively more physically speaking this result determines what local temperatures or entropies are consistent with a pure or mixed gaussian state of several modes we find that this result implies a solution to the problem of sharing of entanglement in pure gaussian states and allows for estimating the global entropy of non gaussian states based on local measurements implications to the actual preparation of multi mode continuous variable entangled states are discussed we compare the findings with the marginal problem for qubits the solution of which for pure states has a strikingly similar and in fact simple form

characterizing the manifest probabilities of latent trait models the problem of characterizing the manifest probabilities of a latent trait model is considered the item characteristic curve is transformed to the item passing odds curve and a corresponding transformation is made on the distribution of ability this results in a useful expression for the manifest probabilities of any latent trait model the result is then applied to give a characterization of the rasch model as a log linear model for a 2 j contingency table partial results are also obtained for other models the question of the identifiability of guessing parameters is also discussed

further results on entropy and separability let be a bi stochastic quantum operation we obtain that s s for any quantum state if and only if there exists a unitary operator u such that u u that is is a unitary operation it is well known that a bipartite quantum state ab is separable if and only if it can be written as ab i i i i i i where i i 1 i and i are the normalized pure states of the subsystems and respectively which may not be orthogonal in general in this paper we also present some necessary and sufficient conditions for which the sets i are orthonormal vectors

a class of inequalities inducing new separability criteria for bipartite quantum systems inspired by the realignment or computable cross norm criterion we present a new result about the characterization of quantum entanglement precisely an interesting class of inequalities satisfied by all separable states of a bipartite quantum system is derived these inequalities induce new separability criteria that generalize the realignment criterion

a criterion for the integrality of the taylor coefficients of mirror maps in several variables we give a necessary and sufficient condition for the integrality of the taylor coefficients at the origin of formal power series qi z ziexp gi z f z with z z1 zd and where f z and gi z log zi f z i 1 d are particular solutions of certain a systems of differential equations this criterion is based on the analytical properties of landau s function which is classically associated with sequences of factorial ratios and it generalizes the criterion in the case of one variable presented in e delaygue critere pour l integralite des coefficients de taylor des applications miroir j reine angew math 662 2012 205 252 one of the techniques used to prove this criterion is a generalization of a version of a theorem of dwork on formal congruences between formal series proved by krattenthaler and rivoal in c krattenthaler t rivoal multivariate p adic formal congruences and integrality of taylor coefficients of mirror maps in l di vizio t rivoal eds theories galoisiennes et arithmetiques des equations differentielles in seminaire et congres vol 27 soc math france paris 2011 pp 279 307

generalized hypergeometric functions and rational curves on calabi yau complete intersections in toric varieties we formulate general conjectures about the relationship between the a model connection on the cohomology of ad dimensional calabi yau complete intersectionv ofr hypersurfacesv1 vr in a toric varietyp and the system of differential operators annihilating the special generalized hypergeometric series 0 constructed from the fan using this generalized hypergeometric series we propose conjectural mirrorsv ofv and the canonicalq coordinates on the moduli spaces of calabi yau manifolds

local random quantum circuits are approximate polynomial designs we prove that local random quantum circuits acting on n qubits composed of o t10n2 many nearest neighbor two qubit gates form an approximate unitary t design previously it was unknown whether random quantum circuits were a t design for any t 3 the proof is based on an interplay of techniques from quantum many body theory representation theory and the theory of markov chains in particular we employ a result of nachtergaele for lower bounding the spectral gap of frustration free quantum local hamiltonians a quasi orthogonality property of permutation matrices a result of oliveira which extends to the unitary group the path coupling method for bounding the mixing time of random walks and a result of bourgain and gamburd showing that dense subgroups of the special unitary group composed of elements with algebraic entries are copy tensor product expanders we also consider pseudo randomness properties of local random quantum circuits of small depth and prove that circuits of depth o t10n constitute a quantum t copy tensor product expander the proof also rests on techniques from quantum many body theory in particular on the detectability lemma of aharonov arad landau and vazirani we give applications of the results to cryptography equilibration of closed quantum dynamics and the generation of topological order in particular we show the following pseudo randomness property of generic quantum circuits almost every circuit u of size o nk on n qubits cannot be distinguished from a haar uniform unitary by circuits of size o n k 9 11 that are given oracle access to u

are random pure states useful for quantum computation we show the following a randomly chosen pure state as a resource for measurement based quantum computation is with overwhelming probability of no greater help to a polynomially bounded classical control computer than a string of random bits thus unlike the familiar cluster states the computing power of a classical control device is not increased from p to bqp bounded error quantum polynomial time but only to bpp bounded error probabilistic polynomial time the same holds if the task is to sample from a distribution rather than to perform a bounded error computation furthermore we show that our results can be extended to states with significantly less entanglement than random states

corrections to second order asymptotics for source coding dense coding and pure state entanglement conversions in this correspondence we correct a few errors in the proofs of intermediate results in 1 that were encountered during the preparation of the phd thesis of the second author we address these errors in their order of appearance equation numbers preceded by a c refer to equations in this correspondence all other equation numbers as well as theorem numbers refer to the corresponding equations and theorems in the paper 1

optimal entanglement criterion for mixed quantum states we develop a strong and computationally simple entanglement criterion the criterion is based on an elementary positive map phi which operates on state spaces with even dimension n or 4 it is shown that phi detects many entangled states with a positive partial transposition ppt and that it leads to a class of optimal entanglement witnesses this implies that there are no other witnesses which can detect more entangled ppt states the map phi yields a systematic method for the explicit construction of high dimensional manifolds of bound entangled states

generic emergence of objectivity of observables in infinite dimensions quantum darwinism posits that information becomes objective whenever multiple observers indirectly probe a quantum system by each measuring a fraction of the environment it was recently shown that objectivity of observables emerges generically from the mathematical structure of quantum mechanics whenever the system of interest has finite dimensions and the number of environment fragments is large f g s l brandao m piani and p horodecki nat commun 6 7908 2015 ncaobw2041 172310 1038 ncomms8908 despite the importance of this result it necessarily excludes many practical systems of interest that are infinite dimensional including harmonic oscillators extending the study of quantum darwinism to infinite dimensions is a nontrivial task we tackle it here by using a modified diamond norm suitable to quantify the distinguishability of channels in infinite dimensions we prove two theorems that bound the emergence of objectivity first for finite mean energy systems and then for systems that can only be prepared in states with an exponential energy cutoff we show that the latter class includes any bounded energy subset of single mode gaussian states

large deviation analysis for quantum security via smoothing of renyi entropy of order 2 it is known that the security evaluation can be done by smoothing of renyi entropy of order 2 in the classical and quantum settings when we apply universal 2 hash functions using the smoothing of renyi entropy of order 2 we derive security bounds for l 1 distinguishability and modified mutual information criterion under the classical and quantum setting and have derived these exponential decreasing rates these results are extended to the case when we apply e almost dual universal 2 hash functions furthermore we apply this analysis to the secret key generation with error correction

classical randomness in quantum measurements similarly to quantum states also quantum measurements can be mixed corresponding to a random choice within an ensemble of measuring apparatuses such mixing is equivalent to a sort of hidden variable which produces a noise of purely classical nature it is then natural to ask which apparatuses are indecomposable i e do not correspond to any random choice of apparatuses this problem is interesting not only for foundations but also for applications since most optimization strategies give optimal apparatuses that are indecomposable mathematically the problem is posed describing each measuring apparatus by a positive operator valued measure povm which gives the statistics of the outcomes for any input state the povms form a convex set and in this language the indecomposable apparatuses are represented by extremal points the analogous of pure states in the convex set of states differently from the case of states however indecomposable povms are not necessarily rank one e g von neumann measurements in this paper we give a complete classification of indecomposable apparatuses for discrete spectrum by providing different necessary and sufficient conditions for extremality of povms along with a simple general algorithm for the decomposition of a povm into extremals as an interesting application informationally complete measurements are analysed in this respect the convex set of povms is fully characterized by determining its border in terms of simple algebraic properties of the corresponding povms

picard fuchs uniformization and modularity of the mirror map arithmetic properties of mirror symmetry type iia iib string duality are studied we give criteria for the mirror map q series of certain families of calabi yau manifolds to be automorphic functions for families of elliptic curves and lattice polarized k3 surfaces with surjective period mappings global torelli theorems allow one to present these criteria in terms of the ramification behavior of natural algebraic invariants the functional and generalized functional invariants respectively in particular when applied to one parameter families of rank 19 lattice polarized k3 surfaces our criterion demystifies the mirror moonshine phenomenon of lian and yau and highlights its non monstrous nature the lack of global torelli theorems and presence of instanton corrections makes calabi yau threefold families more complicated via the constraints of special geometry the picard fuchs equations for one parameter families of calabi yau threefolds imply a differential equation criterion for automorphicity of the mirror map in terms of the yukawa coupling in the absence of instanton corrections the projective periods map to a twisted cubic space curve a hierarchy of algebraic instanton corrections correlated with the differential galois group of the picard fuchs equation is proposed

separability and entanglement of quantum states based on covariance matrices we investigate the separability of quantum states based on covariance matrices separability criteria are presented for multipartite states the lower bound of concurrence proposed in vicente 2007 phys rev a 75 052320 is improved by optimizing the local orthonormal observables

detecting quantum entanglement we review the criteria for separability and quantum entanglement both in a bipartite as well as a multipartite setting we discuss bell inequalities entanglement witnesses entropic inequalities bound entanglement and several features of multipartite entanglement we indicate how these criteria bear on the experimental detection of quantum entanglement

the off diagonal block of a ppt matrix abstract we give an operator inequality involving the off diagonal block of a positive partial transpose matrix and the geometric mean of its diagonal blocks some new eigenvalue inequalities are derived nicely completing the existing ones

quantify entanglement by concurrence hierarchy we define the concurrence hierarchy as d 1i ndependent invariants under local unitary transformations in d level quantum system the first one is the original concurrence defined by wootters 1998 phys rev lett 80 2245 and hill and wootters 1997 phys rev l ett 78 5022 in a two level quantum system and generalized to the d level pure quantum state case we propose to use this concurrence hierarchy as a measurement of entanglement this measurement does not increase under local quantum operations and classical communication

generalized disorder measures and the detection of quantum entanglement abstract we discuss the main properties of general non additive entropic forms based on arbitrary concave functions and their relation with the theory of majorization as application we examine the generalized entropic criterion for separability of mixed states of composite quantum systems where non additive disorder measures play a fundamental role these features are then analyzed in two qubit and two qudit systems where it is seen that the von neumann based criterion is especially weak for detecting entanglement in contrast with those based on the tsallis and other non additive disorder measures

a rasch model for partial credit scoring a unidimensional latent trait model for responses scored in two or more ordered categories is developed this partial credit model is a member of the family of latent trait models which share the property of parameter separability and so permit specifically objective comparisons of persons and items the model can be viewed as an extension of andrich s rating scale model to situations in which ordered response alternatives are free to vary in number and structure from item to item the difference between the parameters in this model and the category boundaries in samejima s graded response model is demonstrated an unconditional maximum likelihood procedure for estimating the model parameters is developed

mcmc estimation and some model fit analysis of multidimensional irt models a bayesian procedure to estimate the three parameter normal ogive model and a generalization of the procedure to a model with multidimensional ability parameters are presented the procedure is a generalization of a procedure by albert 1992 for estimating the two parameter normal ogive model the procedure supports analyzing data from multiple populations and incomplete designs it is shown that restrictions can be imposed on the factor matrix for testing specific hypotheses about the ability structure the technique is illustrated using simulated and real data

majorization criterion for distillability of a bipartite quantum state bipartite quantum states are classified into three categories separable states bound entangled states and free entangled states it is of great importance to characterize these families of states for the development of quantum information science in this letter i show that the separable states and the bound entangled states have a common spectral property more precisely i prove that for undis tillable separable and bound entangled states the eigenvalue vector of the global system is majorized by that of the local system this result constitutes a new sufficient condition for distillability of bipartite quantum states this is achieved by proving that if a bipartite quantum state satisfies the reduction criterion for distillability then it satisfies the majorization criterion for separability

majorization properties of generalized thermal distributions abstract we examine the majorization properties of general thermal like mixed states depending on a set of parameters sufficient conditions which ensure the increase in mixedness and hence of any associated entropic form when these parameters are varied are identified we then discuss those exhibiting a power law distribution showing that they can be characterized by two distinct mixing parameters one associated with temperature and the other with the non extensivity index q illustrative numerical results are also provided

all teleportation and dense coding schemes we establish a one to one correspondence between 1 quantum teleportation schemes 2 dense coding schemes 3 orthonormal bases of maximally entangled vectors 4 orthonormal bases of unitary operators with respect to the hilbert schmidt scalar product and 5 depolarizing operations whose kraus operators can be chosen to be unitary the teleportation and dense coding schemes are assumed to be tight in the sense that all hilbert spaces involved have the same finite dimension d and the classical channel involved distinguishes d 2 signals a general construction procedure for orthonormal bases of unitaries involving latin squares and complex hadamard matrices is also presented

large deviation bounds for k designs we present a technique for de randomizing large deviation bounds of functions on the unitary group we replace the haar measure with a pseudo random distribution a k design k designs have the first k moments equal to those of the haar measure the advantage of this is that approximate k designs can be implemented efficiently whereas haar random unitaries cannot we find large deviation bounds for unitaries chosen from a k design and then illustrate this general technique with three applications we first show that the von neumann entropy of a pseudo random state is almost maximal then we show that if the dynamics of the universe produces a k design then suitably sized subsystems will be in the canonical state as predicted by statistical mechanics finally we show that pseudo random states are useless for measurement based quantum computation

optimal sequence of quantum measurements in the sense of stein s lemma in quantum hypothesis testing we derive a necessary and sufficient condition for a sequence of quantum measurements to achieve the optimal performance in quantum hypothesis testing we discuss what quantum measurement we should perform in order to attain the optimal exponent of the second error probability under the condition that the first error probability goes to 0 as an asymptotically optimal measurement we propose a projection measurement characterized by the irreducible representation theory of the special linear group sl especially in the spin 1 2 system it is realized by the simultaneous measurement of the total momentum and a momentum of a specified direction as a by product we obtain another proof of quantum stein s lemma in addition an asymptotically optimal measurement is constructed in the quantum gaussian case and it is physically meaningful

approximating the set of separable states using the positive partial transpose test the positive partial transpose test is one of the main criteria for detecting entanglement and the set of states with positive partial transpose is considered as an approximation of the set of separable states however we do not know to what extent this criterion as well as the approximation is efficient in this paper we show that the positive partial transpose test gives no bound on the distance of a density matrix from separable states more precisely we prove that as the dimension of the space tends to infinity the maximum trace distance of a positive partial transpose state from separable states tends to 1 using similar techniques we show that the same result holds for other well known separability criteria such as reduction criterion majorization criterion and symmetric extension criterion we also bring in evidence that the sets of positive partial transpose states and separable states have totally different shapes

sampling based approaches to calculating marginal densities abstract stochastic substitution the gibbs sampler and the sampling importance resampling algorithm can be viewed as three alternative sampling or monte carlo based approaches to the calculation of numerical estimates of marginal probability distributions the three approaches will be reviewed compared and contrasted in relation to various joint probability structures frequently encountered in applications in particular the relevance of the approaches to calculating bayesian posterior densities for a variety of structured models will be discussed and illustrated

metrics of quantum states in this work we study metrics of quantum states which are natural generalizations of the usual trace metric and bures metric some useful properties of the metrics are proved such as the joint convexity and contractivity under quantum operations our result has a potential application in studying the geometry of quantum states as well as the entanglement detection

inclusion relations among separability criteria we revisit the application of different separability criteria by recourse to an exhaustive monte carlo exploration involving the pertinent state space of pure and mixed states the corresponding chain of implications of different criteria is in such a way numerically elucidated we also quantify for a bipartite system of arbitrary dimension the proportion of states that can be distilled according to a definite criterion our work can be regarded as a complement to the recent review paper by terhal b 2002 theor comput sci 287 313 some questions posed there receive an answer here

correlative capacity of composite quantum states we characterize the optimal correlative capacity of entangled separable and classically correlated states introducing the notions of the infimum and supremum within majorization theory we construct the least disordered separable state compatible with a set of marginals the maximum separable correlation information supportable by the marginals of a multiqubit pure state is shown to be a local operations and classical communication monotone the least disordered composite of a pair of qubits is found for the above classes with classically correlated states defined as diagonal in the product of marginal bases

on the integrality of the taylor coefficients of mirror maps we continue our study begun in on the integrality of the taylor coefficients of mirror maps duke math j to appear of the fine integrality properties of the taylor coefficients of the series q z z exp g z f z where f z and g z log z f z are specific solutions of certain hypergeometric differential equations with maximal unipotent monodromy at z 0 more precisely we address the question of finding the largest integer v such that the taylor coefficients of z 1q z 1 v are still integers in particular we determine the dwork kontsevich sequence un n 1 where un is the largest integer such that qn z n is a series with integer coefficients where qn z exp gn z fn z fn z m 0 nm z m and gn z m 1 hnm hm nm z m with hn denoting the n th harmonic number conditional on the conjecture that there are no prime number p and integer n such that the p adic valuation of hn 1 is strictly greater than 3

on information gain by quantum measurements of continuous observables a generalization of shannon s amount of information into quantum measurements of continuous observables is introduced a necessary and sufficient condition for measuring processes to have a non negative amount of information is obtained this resolves groenewold s conjecture completely including the case of measurements of continuous observables as an application the approximate position measuring process considered by von neumann and later by davies is shown to have a non negative amount of information

the dutch identity a new tool for the study of item response models the dutch identity is a useful way to reexpress the basic equations of item response models that relate the manifest probabilities to the item response functions irfs and the latent trait distribution the identity may be exploited in several ways for example a to suggest how item response models behave for large numbers of items they are approximate submodels of second order loglinear models for 2 j tables b to suggest new ways to assess the dimensionality of the latent trait principle components analysis of matrices composed of second order interactions from loglinear models c to give insight into the structure of latent class models and d to illuminate the problem of identifying the irfs and the latent trait distribution from sample data

symmetry constraints on temporal order in measurement based quantum computation we discuss the interdependence of resource state measurement setting and temporal order in measurement based quantum computation the possible temporal orders of measurement events are constrained by the principle that the randomness inherent in quantum measurement should not affect the outcome of the computation we provide a classification for all temporal relations among measurement events compatible with a given initial stabilizer state and measurement setting in terms of a matroid conversely we show that classical processing relations necessary for turning the local measurement outcomes into computational output determine the resource state and measurement setting up to local equivalence further we find a symmetry transformation related to local complementation that leaves the temporal relations invariant

approximate transformations of bipartite pure state entanglement from the majorization lattice abstract we study the problem of deterministic transformations of an initial pure entangled quantum state into a target pure entangled quantum state by using local operations and classical communication locc a celebrated result of nielsen 1999 gives the necessary and sufficient condition that makes this entanglement transformation process possible indeed this process can be achieved if and only if the majorization relation holds where and are probability vectors obtained by taking the squares of the schmidt coefficients of the initial and target states respectively in general this condition is not fulfilled however one can look for an approximate entanglement transformation vidal et al 2000 have proposed a deterministic transformation using locc in order to obtain a target state opt most approximate to in terms of maximal fidelity between them here we show a strategy to deal with approximate entanglement transformations based on the properties of the majorization lattice more precisely we propose as approximate target state one whose schmidt coefficients are given by the supremum between and our proposal is inspired on the observation that fidelity does not respect the majorization relation in general remarkably enough we find that for some particular interesting cases like two qubit pure states or the entanglement concentration protocol both proposals are coincident

bayesian analysis of binary and polychotomous response data abstract a vast literature in statistics biometrics and econometrics is concerned with the analysis of binary and polychotomous response data the classical approach fits a categorical response regression model using maximum likelihood and inferences about the model are based on the associated asymptotic theory the accuracy of classical confidence statements is questionable for small sample sizes in this article exact bayesian methods for modeling categorical response data are developed using the idea of data augmentation the general approach can be summarized as follows the probit regression model for binary outcomes is seen to have an underlying normal regression structure on latent continuous data values of the latent data can be simulated from suitable truncated normal distributions if the latent data are known then the posterior distribution of the parameters can be computed using standard results for normal linear models draws from this posterior are used to sample new latent data and t

mirror symmetry and rational curves on quintic threefolds a guide for mathematicians we give a mathematical account of a recent string theory calcula tion which predicts the number of rational curves on the generic quintic three fold our account involves the interpretation of yukawa couplings in terms of variations of hodge structure a new q expansion principle for functions on the moduli space of calabi yau manifolds and the mirror symmetry phe nomenon recently observed by string theorists department of mathematics duke university durham north carolina 27706 e mail address drm math duke edu this content downloaded from 157 55 39 224 on wed 14 dec 2016 04 59 36 utc all use subject to http about jstor org terms

bayesian estimation of a multilevel irt model using gibbs sampling in this article a two level regression model is imposed on the ability parameters in an item response theory irt model the advantage of using latent rather than observed scores as dependent variables of a multilevel model is that it offers the possibility of separating the influence of item difficulty and ability level and modeling response variation and measurement error another advantage is that contrary to observed scores latent scores are test independent which offers the possibility of using results from different tests in one analysis where the parameters of the irt model and the multilevel model can be concurrently estimated the two parameter normal ogive model is used for the irt measurement model it will be shown that the parameters of the two parameter normal ogive model and the multilevel model can be estimated in a bayesian framework using gibbs sampling examples using simulated and real data are given

some properties of renyi entropy and renyi entropy rate in this paper we define the conditional renyi entropy and show that the so called chain rule holds for the renyi entropy then we introduce a relation for the rate of renyi entropy and use it to derive the rate of the renyi entropy for an irreducible aperiodic markov chain we also show that the bound for the renyi entropy rate is simply the shannon entropy rate

a bound on the mutual information and properties of entropy reduction for quantum channels with inefficient measurements the holevo bound is a bound on the mutual information for a given quantum encoding in 1996 schumacher westmoreland and wootters phys rev lett 76 3452 1996 derived a bound that reduces to the holevo bound for complete measurements but that is tighter for incomplete measurements the most general quantum operations may be both incomplete and inefficient here we show that the bound derived by sww can be further extended to obtain one that is yet again tighter for inefficient measurements this allows us in addition to obtain a generalization of a bound derived by hall and to show that the average reduction in the von neumann entropy during a quantum operation is concave in the initial state for all quantum operations this is a quantum version of the concavity of the mutual information we also show that both this average entropy reduction and the mutual information for pure state ensembles are schur concave for unitarily covariant measurements that is for these measurements information

integral quantum fluctuation theorems under measurement and feedback control we derive integral quantum fluctuation theorems and quantum jarzynski equalities for a feedback controlled system and a memory which registers outcomes of the measurement the obtained equalities involve the information content which reflects the information exchange between the system and the memory and take into account the back action of a general measurement contrary to the classical case the generalized second law of thermodynamics under measurement and feedback control is reproduced from these equalities

spin swapping operator as an entanglement witness for quantum heisenberg spin s systems using the su n representation of the group theory we derive the general form of the spin swapping operator for the quantum heisenberg spin s systems we further prove that such a spin swapping operator is equal to the spin singlet pairing operator under the partial transposition for su 2 invariant states it is shown that the expectation value of the spin swapping operator and its generalizations the permutations can be used as an entanglement witness especially for the formulation of observable conditions of entanglement

topos logic in measurement based quantum computation we report first steps towards elucidating the relationship between contextuality measurement based quantum computation mbqc and the non classical logic of a topos associated with the computation we show that in a class of mbqc classical universality requires non classical logic which is consumed during the course of the computation thereby pinpointing another potential quantum computational resource

ising n fold integrals as diagonals of rational functions and integrality of series expansions we show that the n fold integrals n of the magnetic susceptibility of the ising model as well as various other n fold integrals of the ising class or n fold integrals from enumerative combinatorics like lattice green functions correspond to a distinguished class of functions generalizing algebraic functions they are actually diagonals of rational functions as a consequence the power series expansions of the analytic at x 0 solutions of these linear differential equations derived from geometry are globally bounded which means that after just one rescaling of the expansion variable they can be cast into series expansions with integer coefficients we also give several results showing that the unique analytical solution of calabi yau odes and more generally picard fuchs linear odes with solutions of maximal weights are always diagonals of rational functions besides in a more enumerative combinatorics context generating functions whose coefficients are expressed in terms of nested sums of products of binomial terms can also be shown to be diagonals of rational functions we finally address the question of the relations between the notion of integrality series with integer coefficients or more generally globally bounded series and the modularity of odes

entropy reduction of quantum measurements it is shown that the entropy reduction the information gain in the initial terminology of an efficient ideal or pure quantum measurement coincides with the generalized quantum mutual information of a quantum classical channel mapping an a priori state to the corresponding posteriori probability distribution of the outcomes of the measurement as a result the entropy reduction is defined for arbitrary a priori states not only for states with finite von neumann entropy and its analytical properties is studied in detail by using general properties of the quantum mutual information by using this approach it is shown that the entropy reduction of an efficient quantum measurement is a nonnegative lower semicontinuous concave function on the set of all a priori states having continuous restrictions to subsets on which the von neumann entropy is continuous monotonicity and subadditivity of the entropy reduction are also easily proved by this method a simple continuity condition for the entropy reduction

a limit of the quantum renyi divergence recently an interesting quantity called the quantum renyi divergence or sandwiched renyi relative entropy was defined for pairs of positive semi definite operators and it depends on a parameter and acts as a parent quantity for other relative entropies which have important operational significance in quantum information theory the quantum relative entropy and the min and max relative entropies there is however another relative entropy called the 0 relative renyi entropy which plays a key role in the analysis of various quantum information processing tasks in the one shot setting we prove that the 0 relative renyi entropy is obtainable from the quantum renyi divergence only if and have equal supports this along with existing results in the literature suggests that it suffices to consider two essential parent quantities from which operationally relevant entropic quantities can be derived the quantum renyi divergence with parameter 1 2 and the relative renyi entropy with 0 1

conditional q entropies and quantum separability a numerical exploration we revisit the relationship between quantum separability and the sign of the relative q entropies of composite quantum systems the q entropies depend on the density matrix eigenvalues pi through the quantity q ipqi renyi s and tsallis measures constitute particular instances of these entropies we perform a systematic numerical survey of the space of mixed states of two qubit systems in order to determine as a function of the degree of mixture and for different values of the entropic parameter q the volume in state space occupied by those states characterized by positive values of the relative entropy similar calculations are performed for qubit qutrit systems and for composite systems described by hilbert spaces of larger dimensionality we pay particular attention to the limit case q our numerical results indicate that as the dimensionalities of both subsystems increase typical mixed states of composite quantum systems tend as far as their relative q entropies are concerned to behave in a classical way

general non additive entropic forms and the inference of quantum density operators abstract we discuss a general formalism for the inference of quantum density operators from incomplete information based on the maximization of general non additive entropic forms and its application to the reconstruction of mixed states of composite quantum systems from generalized bell measurements the method provides a direct way to infer least biased densities with minimum entanglement for any data determined by bell constraints in two qubit systems in contrast with the conventional scheme based on the von neumann entropy in particular it is shown that in this case fake entanglement is always avoided for large q when the tsallis entropy is employed

second order asymptotics for source coding dense coding and pure state entanglement conversions we introduce two variants of the information spectrum relative entropy defined by tomamichel and hayashi which have the particular advantage of satisfying the data processing inequality i e monotonicity under quantum operations this property allows us to obtain one shot bounds for various information processing tasks in terms of these quantities moreover these relative entropies have a second order asymptotic expansion which in turn yields tight second order asymptotics for optimal rates of these tasks in the independent and identically distributed setting the tasks studied in this paper are fixed length quantum source coding noisy dense coding entanglement concentration pure state entanglement dilution and transmission of information through a classical quantum channel in the latter case we retrieve the second order asymptotics obtained by tomamichel and tan our results also yield the known second order asymptotics of fixed length classical source coding derived by hayashi the second order asymptotics of entanglement concentration and dilution provide a refinement of the inefficiency of these protocols a quantity which in the case of entanglement dilution was studied by harrow and lo we prove how the discrepancy between the optimal rates of these two processes in the second order implies the irreversibility of entanglement concentration established by kumagai and hayashi in addition the spectral divergence rates of the information spectrum approach isa can be retrieved from our relative entropies in the asymptotic limit this enables us to directly obtain the more general results of the isa from our one shot bounds

further results on entanglement detection and quantification from the correlation matrix criterion the correlation matrix cm criterion is a recently derived powerful sufficient condition for the presence of entanglement in bipartite quantum states of arbitrary dimensions it has been shown that it can be stronger than the positive partial transpose ppt criterion as well as the computable cross norm or realignment ccnr criterion in different situations however it remained as an open question whether there existed sets of states for which the cm criterion could be stronger than both criteria simultaneously here we give an affirmative answer to this question by providing examples of entangled states that scape detection by both the ppt and ccnr criteria whose entanglement is revealed by the cm condition we also show that the cm can be used to measure the entanglement of pure states and obtain lower bounds for the entanglement measure known as tangle for general mixed states

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

conditional entropies and their relation to entanglement criteria we discuss conditional renyi and tsallis entropies for bipartite quantum systems of finite dimension we investigate the relation between the positivity of conditional entropies and entanglement properties it is in particular shown that any state having a negative conditional entropy with respect to any value of the entropic parameter is distillable since it violates the reduction criterion moreover we show that the entanglement of werner states in odd dimensions can neither be detected by entropic criteria nor by any other spectral criterion

quantum entanglement and geometry of determinantal varieties quantum entanglement was first recognized as a feature of quantum mechanics in the famous paper of einstein podolsky and rosen recently it has been realized that quantum entanglement is a key ingredient in quantum computation quantum communication and quantum cryptography in this paper we introduce algebraic sets which are determinantal varieties in the complex projective spaces or the products of complex projective spaces for the mixed states on bipartite or multipartite quantum systems as their invariants under local unitary transformations these invariants are naturally arised from the physical consideration of measuring mixed states by separable pure states our construction has applications in the following important topics in quantum information theory 1 separability criterion it is proved that the algebraic sets must be a union of the linear subspaces if the mixed states are separable 2 simulation of hamiltonians it is proved that the simulation of semipositive hamiltonians of the same rank implies the projective isomorphisms of the corresponding algebraic sets 3 construction of bound entangled mixed states examples of the entangled mixed states which are invariant under partial transpositions thus ppt bound entanglement are constructed systematically from our new separability criterion

majorization relations and disorder in generalized statistics abstract the theory of majorization is applied to examine the disorder properties of generalized thermal distributions arising in non extensive statistics we show that they share with the boltzmann gibbs thermal state the property of becoming more mixed as the temperature increases implying the increase of any associated disorder measure we also show that power law distributions exhibit a second mixing parameter associated with the non extensivity index as application we examine the thermal response of quantum entanglement in a spin system for different statistics

quantumness of bipartite states in terms of conditional entropies quantum discord as defined by olliver and zurek 2002 phys rev lett 88 017901 as the difference of two natural quantum extensions of the classical mutual information plays an interesting role in characterizing quantumness of correlations inspired by this idea we will study quantumness of bipartite states arising from different quantum analogs of the classical conditional entropy our approach is intrinsic in contrast to the olliver zurek method that involves extrinsic local measurements for this purpose we introduce two alternative variants of quantum conditional entropies via conditional density operators which in turn are intuitive quantum extensions of equivalent classical expressions for the conditional probability the significance of these quantum conditional entropies in characterizing quantumness of bipartite states is illustrated through several examples

state space structure and entanglement of rotationally invariant spin systems we investigate the structure of so 3 invariant quantum systems which are composed of two particles with spins j1 and j2 the states of the composite spin system are represented by means of two complete sets of rotationally invariant operators namely by the projections pj onto the eigenspaces of the total angular momentum j and by certain invariant operators qk which are built out of spherical tensor operators of rank k it is shown that these representations are connected by an orthogonal matrix whose elements are expressible in terms of wigner s 6 j symbols the operation of the partial time reversal of the combined spin system is demonstrated to be diagonal in the qk representation these results are employed to obtain a complete characterization of spin systems with j1 1 and arbitrary j2 1 we prove that the peres horodecki criterion of positive partial transposition ppt is necessary and sufficient for separability if j2 is an integer while for half integer spins j2 there always exist entangled ppt states bound entanglement we construct an optimal entanglement witness for the case of half integer spins and design a protocol for the detection of entangled ppt states through measurements of the total angular momentum

the structure of renyi entropic inequalities we investigate the universal inequalities relating the rnyi entropies of the marginals of a multi partite quantum state this is in analogy to the same question for the shannon and von neumann ent

bipartite quantum systems on the realignment criterion and beyond inspired by the computable cross norm or realignment criterion we propose a new point of view about the characterization of the states of bipartite quantum systems we consider a schmidt decomposition of a bipartite density operator the corresponding schmidt coefficients or the associated symmetric polynomials are regarded as quantities that can be used to characterize bipartite quantum states in particular starting from the realignment criterion a family of necessary conditions for the separability of bipartite quantum states are derived we conjecture that these conditions which are weaker than the parent criterion can be strengthened in such a way to obtain a new family of criteria that are independent of the original one this conjecture is supported by numerical examples for the low dimensional cases these ideas can be applied to the study of quantum channels leading to a relation between the rate of contraction of a map and its ability to preserve entanglement

separable states are more disordered globally than locally a remarkable feature of quantum entanglement is that an entangled state of two parties alice a and bob b may be more disordered locally than globally that is s a s a b where s is the von neumann entropy it is known that satisfaction of this inequality implies that a state is nonseparable in this paper we prove the stronger result that for separable states the vector of eigenvalues of the density matrix of system ab is majorized by the vector of eigenvalues of the density matrix of system a alone this gives a strong sense in which a separable state is more disordered globally than locally and a new necessary condition for separability of bipartite states in arbitrary dimensions

the origin of separable states and separability criteria from entanglement breaking channels in this paper we show that an arbitrary separable state can be the output of a certain entanglement breaking channel corresponding exactly to the input of a maximally entangled state a necessary and sufficient separability criterion and some sufficient separability criteria from entanglement breaking channels are given

monodromy for the hypergeometric function nfn 1 la fonction hypergeometrique le groupe hypergeometrique la forme hermitienne invariante le cas imprimitif theorie de galois differentielle fonctions hypergeometriques algebriques

a gibbs sampler for the extended marginal rasch model in their seminal work on characterizing the manifest probabilities of latent trait models cressie and holland give a theoretically important characterization of the marginal rasch model because their representation of the marginal rasch model does not involve any latent trait nor any specific distribution of a latent trait it opens up the possibility for constructing a markov chain monte carlo method for bayesian inference for the marginal rasch model that does not rely on data augmentation such an approach would be highly efficient as its computational cost does not depend on the number of respondents which makes it suitable for large scale educational measurement in this paper such an approach will be developed and its operating characteristics illustrated with simulated data

identifying the information gain of a quantum measurement we show that quantum to classical channels i e quantum measurements can be asymptotically simulated by an amount of classical communication equal to the quantum mutual information of the measurement if sufficient shared randomness is available this result generalizes winter s measurement compression theorem for fixed independent and identically distributed inputs to arbitrary inputs and more importantly it identifies the quantum mutual information of a measurement as the information gained by performing it independent of the input state on which it is performed our result is a generalization of the classical reverse shannon theorem to quantum to classical channels in this sense it can be seen as a quantum reverse shannon theorem for quantum to classical channels but with the entanglement assistance and quantum communication replaced by shared randomness and classical communication respectively the proof is based on a novel one shot state merging protocol for classically coherent states as well as the postselection technique for quantum channels and it uses techniques developed for the quantum reverse shannon theorem

separability criteria and bounds for entanglement measures employing a recently proposed separability criterion we develop analytical lower bounds for the concurrence and for the entanglement of formation of bipartite quantum systems the separability criterion is based on a nondecomposable positive map which operates on state spaces with even dimension n 4 and leads to a class of nondecomposable optimal entanglement witnesses it is shown that the bounds derived here complement and improve the existing bounds obtained from the criterion of positive partial transposition and from the realignment criterion

a class of positive atomic maps we construct a new class of positive indecomposable maps in the algebra of d d complex matrices these maps are characterized by the weakest positivity property and for this reason they are called atomic this class provides a new rich family of atomic entanglement witnesses which define an important tool for investigating quantum entanglement it turns out that they are able to detect states with the weakest quantum entanglement

a mcmc method for models with continuous latent responses this paper introduces a new technique for estimating the parameters of models with continuous latent data using the rasch model as an example it is shown that existing bayesian techniques for parameter estimation such as the gibbs sampler are not always easy to implement then a new sampling based bayesian technique called the da t gibbs sampler is introduced the da t gibbs sampler relies on the particular latent data structure of latent response models to simplify the computations involved in parameter estimation

the ising model from elliptic curves to modular forms and calabi yau equations we show that almost all the linear differential operators factors obtained in the analysis of the n particle contributions s of the susceptibility of the ising model for n 6 are linear differential operators associated with elliptic curves beyond the simplest differential operators factors which are homomorphic to symmetric powers of the second order operator associated with the complete elliptic integral e the second and third order differential operators z2 f2 f3 can actually be interpreted as modular forms of the elliptic curve of the ising model a last order 4 globally nilpotent linear differential operator is not reducible to this elliptic curve modular form scheme this operator is shown to actually correspond to a natural generalization of this elliptic curve modular form scheme with the emergence of a calabi yau equation corresponding to a selected 4f3 hypergeometric function this hypergeometric function can also be seen as a hadamard product of the complete elliptic integral k with a remarkably simple algebraic pull back square root extension the corresponding calabi yau fourth order differential operator having a symplectic differential galois group the mirror maps and higher order schwarzian odes associated with this calabi yau ode present all the nice physical and mathematical ingredients we had with elliptic curves and modular forms in particular an exact isogenies representation of the generators of the renormalization group extending the modular group to a symmetry group