entropy of random quantum states the authors use a simple generating function to calculate exactly the entropy of random quantum states for finite dimensional hilbert spaces over real complex and quaternionic scalars this allows them to extend their previous formula for the quantum correlation information of a state determination apparatus to include real and quaternionic von neumann analysers

comments on hastings additivity counterexamples hastings 12 recently provided a proof of the existence of channels which violate the additivity conjecture for minimal output entropy in this paper we present an expanded version of hastings proof in addition to a careful elucidation of the details of the proof we also present bounds for the minimal dimensions needed to obtain a counterexample

a priori probabilities of separable quantum states zyczkowski horodecki sanpera and lewenstein zhsl recently proposed a natural measure on the n dimensional quantum systems but expressed surprise when it led them to conclude that for n 2 2 disentangled separable systems are more probable 0 632 0 002 in nature than entangled ones we contend however that zhsl s rejected intuition has in fact a sound theoretical basis and that the a priori probability of disentangled 2 2 systems should more properly be viewed as considerably less than 0 5 we arrive at this conclusion in two quite distinct ways the first based on classical and the second quantum considerations both approaches however replace in whole or part the zhsl product measure by ones based on the volume elements of monotone metrics which in the classical case amounts to adopting the jeffreys prior of bayesian theory only the quantum theoretic analysis which yields the smallest probabilities of disentanglement uses the minimum number of parameters possible that is n2 1 as opposed to n2 n 1 although this over parametrization as recently indicated by byrd should be avoidable however despite substantial computation we are not able to obtain precise estimates of these probabilities and the need for additional possibly supercomputer analyses is indicated particularly so for higher dimensional quantum systems such as the 2 3 ones which we also study here

completeness and geometry of schrodinger minimum uncertainty states the symmetry geometry and completeness properties of schrodinger minimum uncertainty states smus are considered smus are equivalent to the coherent states with maximal symmetry related to the semidirect product g hw su 1 1 hw being the heizenberg weyl group the invariant measures on g and on the homogeneous space g k are constructed as well as noninvariant resolution unity measures the fiber bundle and the symplectic kaehler structures of smus are elucidated with the implications to their stable evolution

decomposition of hilbert space in sets of coherent states within the generalized definition of coherent states as group orbits we study the orbit spaces and the orbit manifolds in the projective spaces constructed from linear representations invariant functions are suggested for arbitrary groups the group su 2 is studied in particular and the orbit spaces of its j 1 2 and 1 representations completely determined the orbits of su 2 in cpn can be either two or three dimensional the former being either isomorphic to s2 or to rp2 and the latter being isomorphic to quotient spaces of rp3 we end with a look from the same perspective to the quantum mechanical space of states in particle mechanics

canonical coherent states for the relativistic harmonic oscillator in this paper there are constructed manifestly covariant relativistic coherent states on the entire complex plane which reproduce others previously introduced on a given sl 2 r representation once a change of variables z c zd unit disk is performed also introduced are higher order relativistic creation and annihilation operators a a with canonical commutation relation a a 1 rather than the covariant one z z energy and naturally associated with the sl 2 r group the canonical relativistic coherent states are then defined as eigenstates of a finally a canonical minimal representation is constructed in configuration space by means of eigenstates of a canonical position operator

noise dressing of financial correlation matrices we show that results from the theory of random matrices are potentially of great interest to understand the statistical structure of the empirical correlation matrices appearing in the study of multivariate time series the central result of the present study which focuses on the case of financial price fluctuations is the remarkable agreement between the theoretical prediction based on the assumption that the correlation matrix is random and empirical data concerning the density of eigenvalues associated to the time series of the different stocks of the s 500 or other major markets in particular the present study raises serious doubts on the blind use of empirical correlation matrices for risk management

exact evaluation of the collapse phase boundary for two dimensional directed polymers the phase boundary of the collapsed phase for a directed polymer on a square lattice in the presence of an attractive wall and monomer monomer interactions is calculated exactly using transfer matrix techniques the position of the multicritical point is also identified

distributions of singular values for some random matrices the singular value decomposition is a matrix decomposition technique widely used in the analysis of multivariate data such as complex space time images obtained in both physical and biological systems in this paper we examine the distribution of singular values of low rank matrices corrupted by additive noise past studies have been limited to uniform uncorrelated noise using diagrammatic and saddle point integration techniques we extend these results to heterogeneous and correlated noise sources we also provide perturbative estimates of error bars on the reconstructed low rank matrix obtained by truncating a singular value decomposition 1999 the american physical society

realigning random states we study how the realignment criterion also called computable cross norm criterion succeeds asymptotically in detecting whether random states are separable or entangled we consider random states on cd cd obtained by partial tracing a haar distributed random pure state on cd cd cs over an ancilla space cs we show that for large d typically the realignment criterion is successful in detecting entanglement if and only if s 83 2d2 in this sense the realignment criterion is asymptotically weaker than the partial transposition criterion

uncertainty for spin systems a modified definition of quantum mechanical uncertainty for spin systems which is invariant under the action of su 2 is suggested its range is shown to be 2j 2j j 1 within any irreducible representation j of su 2 and its mean value in hilbert space computed using the fubini study metric is determined to be mean 2j j 1 2 the most used sets of coherent states in spin systems coincide with the set of minimum uncertainty states

on the reduction criterion for random quantum states in this paper we study the reduction criterion for detecting entanglement of large dimensional bipartite quantum systems we first obtain an explicit formula for the moments of a random quantum state to which the reduction criterion has been applied we show that the empirical eigenvalue distribution of this random matrix converges strongly to a limit that we compute in three different asymptotic regimes we then employ tools from free probability theory to study the asymptotic positivity of the reduction operators finally we compare the reduction criterion with other entanglement criteria via thresholds

global entangling properties of the coupled kicked tops we study global entangling properties of the system of coupled kicked tops testing various hypotheses and predictions concerning entanglement in quantum chaotic systems in order to analyze the averaged initial entanglement production rate and the averaged asymptotic entanglement various ensembles of initial product states are evolved two different ensembles with natural probability distribution are considered product states of independent spin coherent states and product states of random states it appears that the choice of either of these ensembles results in significantly different averaged entanglement behavior we investigate also a relation between the averaged asymptotic entanglement and the mean entanglement of eigenvectors of the evolution operator lower bound on the averaged asymptotic entanglement is derived expressed in terms of the eigenvector entanglement

barut girardello coherent states for and and their macroscopic superpositions the barut girardello bg coherent states cs representation is extended to the noncompact algebras and in reducible quadratic boson realizations the bg cs take the form of multimode ordinary schr dinger cat states macroscopic superpositions of cs canonical cs n 1 2 are pointed out which are overcomplete in the n mode hilbert space and the relation between the canonical cs and the bg type cs representations is established the sets of and bg cs and their discrete superpositions contain many states studied in quantum optics even and odd n mode cs pair cs and provide an approach to quadrature squeezing alternative to that of intelligent states new subsets of weakly and strongly nonclassical states are pointed out and their statistical properties first and second order squeezing photon number distributions are discussed for specific values of the angle parameters and small amplitude of the canonical cs components these states approach multimode fock states with one two or three bosons photons it is shown that eigenstates of a squared non hermitian operator generalized cat states can exhibit squeezing of the quadratures of a

generalized coherent and squeezed states based on the h 1 su 2 algebra states which minimize the schrodinger robertson uncertainty relation are constructed as eigenstates of an operator which is an element of the h 1 su 2 algebra the relations with supercoherent and supersqueezed states of the supersymmetric harmonic oscillator are given moreover we are able to compute general hamiltonians which behave like the harmonic oscillator hamiltonian or are related to the jaynes cummings hamiltonian

analytic representations based on su 1 1 coherent states and their applications we consider two analytic representations of the su 1 1 lie group the representation in the unit disc based on the su 1 1 perelomov coherent states and the barut girardello representation based on the eigenstates of the su 1 1 lowering generator we show that these representations are related through a laplace transform a weak resolution of the identity in terms of the perelomov su 1 1 coherent states is presented which is valid even when the bargmann index k is smaller than various applications of these results in the context of the two photon realization of su 1 1 in quantum optics are also discussed

statistical mechanics of multipartite entanglement we characterize the multipartite entanglement of a system of n qubits in terms of the distribution function of the bipartite purity over all balanced bipartitions we search for those maximally multipartite entangled states whose purity is minimum for all bipartitions and recast this optimization problem into a problem of statistical mechanics

recursion for the smallest eigenvalue density of β wishart laguerre ensemble the statistics of the smallest eigenvalue of wishart laguerre ensemble is important from several perspectives the smallest eigenvalue density is typically expressible in terms of determinants or pfaffians these results are of utmost significance in understanding the spectral behavior of wishart laguerre ensembles and among other things unveil the underlying universality aspects in the asymptotic limits however obtaining exact and explicit expressions by expanding determinants or pfaffians becomes impractical if large dimension matrices are involved for the real matrices beta 1 edelman has provided an efficient recurrence scheme to work out exact and explicit results for the smallest eigenvalue density which does not involve determinants or matrices very recently an analogous recurrence scheme has been obtained for the complex matrices beta 2 in the present work we extend this to beta wishart laguerre ensembles for the case when exponent alpha in the associated laguerre weight function lambda alpha e beta lambda 2 is a non negative integer while beta is positive real this also gives access to the smallest eigenvalue density of fixed trace beta wishart laguerre ensemble as well as moments for both cases moreover comparison with earlier results for the smallest eigenvalue density in terms of certain hypergeometric function of matrix argument results in an effective way of evaluating these explicitly exact evaluations for large values of n the matrix dimension and alpha also enable us to compare with tracy widom density and large deviation results of katzav and castillo we also use our result to obtain the density of the largest of the proper delay times which are eigenvalues of the wigner smith matrix and are relevant to the problem of quantum chaotic scattering

characteristic uncertainty relations new uncertainty relations for n observables are established the relations take the invariant form of inequalities between the characteristic coefficients of order r rd 1 2 n of the uncertainty matrix and the matrix of mean commutators of the observables it is shown that the second and third order characteristic inequalities for the three generators of su 1 1 and su 2 are minimized in the corresponding group related coherent states with maximal symmetry

a numerical scheme for the solution of the space charge problem on a multiply connected region in this paper we extend the work of budd and wheeler proc r soc london a 417 389 1988 who described a new numerical scheme for the solution of the space charge equation on a simple connected domain to multiply connected regions the space charge equation 0 is a third order nonlinear partial differential equation for the electric potential which models the electric field in the vicinity of a coronating conductor budd and wheeler described a new way of analysing this equation by constructing an orthogonal coordinate system and recasting the equation in terms of x y and as functions of this transformation is singular on multiply connected regions and in this paper we show how this may be overcome to provide an efficient numerical scheme for the solution of the space charge equation this scheme also provides a new method for the solution of laplaces equation and the calculation of orthogonal meshes on multiply connected regions

a system of partial differential equations arising in electrophotography abstract we consider the process which takes place in the photocopy machine as soon as the document to be photocopied is exposed to light this process is modeled by a coupled system of one elliptic equation for the voltage v and one parabolic equation for the charge density p with small diffusion e the leading coefficient in the equation for v has some discontinuities with jump whose size is a nonlinear functional with memory of p and v we prove that there exists a unique global solution and then study the vector field v and the charge density p as ee 0

asymptotic spectral analysis of growing regular graphs we propose the quantum probabilistic techniques to obtain the asymptotic spectral distribution of the adjacency matrix of a growing regular graph we prove the quantum central limit theorem for the adjacency matrix of a growing regular graph in the vacuum and deformed vacuum states the condition for the growth is described in terms of simple statistics arising from the stratification of the graph the asymptotic spectral distribution of the adjacency matrix is obtained from the classical reduction

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

the space change problem a space charge problem arising in modelling steady electric field in a neighborhood of an ionising conductor is considered mathematically the problem reduces to a system consisting of one elliptic equation and one nonlinear hyperbolic equation the existence of a weak solution is proved and its properties are studied in part rigorously and in part heuristically and numerically

induced measures in the space of mixed quantum states we analyse several product measures in the space of mixed quantum states in particular we study measures induced by the operation of partial tracing the natural rotationally invariant measure on the set of all pure states of a n k composite system induces a unique measure in the space of n n mixed states or in the space of k k mixed states if the reduction takes place with respect to the first subsystem for k n the induced measure is equal to the hilbert schmidt measure which is shown to coincide with the measure induced by singular values of non hermitian random gaussian matrices pertaining to the ginibre ensemble we compute several averages with respect to this measure and show that the mean entanglement of n n pure states behaves as lnn 1 2

measuring dynamical randomness of quantum chaos by statistics of schmidt eigenvalues we study statistics of entanglement generated by quantum chaotic dynamics using an ensemble of the very large number 10 7 of quantum states obtained from the temporally evolving coupled kicked tops we verify that the estimated one body distribution of the squared schmidt eigenvalues for the quantum chaotic dynamics can agree surprisingly well with the analytical one for the universality class of the random matrices described by the fixed trace ensemble fte in order to quantify this agreement we introduce the l 1 norm of the difference between the one body distributions for the quantum chaos and fte and use it as an indicator of the dynamical randomness as we increase the scaled coupling constant the l 1 difference decreases when the effective planck constant is not small enough the decrease saturates which implies quantum suppression of dynamical randomness on the other hand when the effective planck constant is small enough the decrease of the l 1 difference continues until it is masked by statistical fluctuation due to finiteness of the ensemble furthermore we carry out two statistical analyses the 2 goodness of fit test and an autocorrelation analysis on the difference between the distributions to seek for dynamical remnants buried under the statistical fluctuation we observe that almost all fluctuating deviations are statistical however even for well developed quantum chaos unexpectedly we find a slight nonstatistical deviation near the largest schmidt eigenvalue in this way the statistics of schmidt eigenvalues enables us to measure dynamical randomness of quantum chaos with reference to the random matrix theory of fte

gibbs state on a distance regular graph and its application to a scaling limit of the spectral distributions of discrete laplacians on the adjacency algebra of a distance regular graph we introduce an analogue of the gibbs state depending on a parameter related to temperature of the graph we discuss a scaling limit of the spectral distribution of the laplacian on the graph with respect to the gibbs state in the manner of central limit theorem in algebraic probability where the volume of the graph goes to while the temperature tends to 0 in the model we discuss here the laplacian on the johnson graph the resulting limit distributions form a one parameter family beginning with an exponential distribution which corresponds to the case of the vacuum state and consisting of its deformations by a bessel function

generalized intelligent states and squeezing the robertson schrodinger uncertainty relation for two observables a and b is shown to be minimized in the eigenstates of the operator a ib being a complex number such states called generalized intelligent states gis can exhibit arbitrarily strong squeezing of a or b the time evolution of gis is stable for hamiltonians which admit linear in a and b invariants systems of gis for the su 1 1 and su 2 groups are constructed and discussed it is shown that su 1 1 gis contain all the perelomov coherent states cs and the barut and girardello cs while the spin cs are a subset of su 2 gis cs for an arbitrary semisimple lie group can be considered as a gis for the quadratures of the weyl generators

random matrix ensembles with an effective extensive external charge recent theoretical studies of chaotic scattering have encountered ensembles of random matrices in which the eigenvalue probability density function contains a one body factor with an exponent proportional to the number of eigenvalues two such ensembles have been encountered an ensemble of unitary matrices specified by the so called poisson kernel and the laguerre ensemble of positive definite matrices here we consider various properties of these ensembles jack polynomial theory is used to prove a reproducing property of the poisson kernel and a certain unimodular mapping is used to demonstrate that the variance of a linear statistic is the same as in the dyson circular ensemble for the laguerre ensemble the scaled global density is calculated exactly for all even values of the parameter while for random matrices with unitary symmetry the neighbourhood of the smallest eigenvalue is shown to be in the soft edge universality class

classical statistical mechanics approach to multipartite entanglement we characterize the multipartite entanglement of a system of n qubits in terms of the distribution function of the bipartite purity over balanced bipartitions we search for maximally multipartite entangled states whose average purity is minimal and recast this optimization problem into a problem of statistical mechanics by introducing a cost function a fictitious temperature and a partition function by investigating the high temperature expansion we obtain the first three moments of the distribution we find that the problem exhibits frustration

universal and nonuniversal properties of cross correlations in financial time series we use methods of random matrix theory to analyze the cross correlation matrix c of stock price changes of the largest 1000 u s companies for the 2 year period 1994 1995 we find that the statistics of most of the eigenvalues in the spectrum of c agree with the predictions of random matrix theory but there are deviations for a few of the largest eigenvalues we find that c has the universal properties of the gaussian orthogonal ensemble of random matrices furthermore we analyze the eigenvectors of c through their inverse participation ratio and find eigenvectors with large ratios at both edges of the eigenvalue spectrum a situation reminiscent of localization theory results

random bistochastic matrices ensembles of random stochastic and bistochastic matrices are investigated while all columns of a random stochastic matrix can be chosen independently the rows and columns of a bistochastic matrix have to be correlated we evaluate the probability measure induced into the birkhoff polytope of bistochastic matrices by applying the sinkhorn algorithm to a given ensemble of random stochastic matrices for matrices of order n 2 we derive explicit formulae for the probability distributions induced by random stochastic matrices with columns distributed according to the dirichlet distribution for arbitrary n we construct an initial ensemble of stochastic matrices which allows one to generate random bistochastic matrices according to a distribution locally flat at the center of the birkhoff polytope the value of the probability density at this point enables us to obtain an estimation of the volume of the birkhoff polytope consistent with recent asymptotic results

representations and properties of generalized ar statistics coherent states and robertson uncertainty relations the generalization of ar statistics including bosonic and fermionic sectors is performed by means of the so called jacobson generators the corresponding fock spaces are constructed the bargmann representations are also considered for the bosonic ar statistics two inequivalent bargmann realizations are developed the first resp second realization induces in a natural way coherent states recognized as gazeau klauder resp klauder perelomov ones in the fermionic case the bargamnn realization leads to the klauder perelomov coherent states for each considered realization the inner product of two analytic functions is defined with respect to a measure explicitly computed the jacobson generators are realized as differential operators it is shown that the obtained coherent states minimize the robertson schr dinger uncertainty relation

robust and efficient generator of almost maximal multipartite entanglement quantum chaotic maps can efficiently generate pseudorandom states carrying almost maximal multipartite entanglement as characterized by the probability distribution of bipartite entanglement between all possible bipartitions of the system we show that such multipartite entanglement is robust in the sense that when realistic noise is considered distillable entanglement of bipartitions remains almost maximal up to a noise strength that drops only polynomially with the number of qubits

robertson intelligent states the diagonalization of the uncertainty matrix and the minimization of robertson inequality for n observables are considered it is proved that for even n this relation is minimized in states which are eigenstates of n 2 independent complex linear combinations of the observables in the case of canonical observables this eigenvalue condition is also necessary such minimizing states are called robertson intelligent states ris the group related coherent states cs with maximal symmetry for semisimple lie groups are a particular case of ris for the quadratures of weyl generators explicit constructions of ris are considered for operators of su 1 1 su 2 and sp n r algebras unlike the group related cs ris can exhibit strong squeezing of group generators multimode squared amplitude squeezed states are naturally introduced as sp n r ris it is shown that the uncertainty matrices for quadratures of q deformed boson operators q 0 and of any k power of are positive definite and can be diagonalized by symplectic linear transformations

a new approach to the space charge problem in this paper we consider a model for the electric potential phi arising from the field due to a coronating electrode this results in the third order nonlinear partial differential equation nabla cdot delta phi nabla phi 0 which is of mixed type and we study here in two spatial dimensions we describe a new way of analysing this equation by constructing an orthogonal coordinate system phi psi and recasting the equation in terms of x y and delta phi as functions of phi psi it may be regarded as a synthesis of the method of characteristics for a hyperbolic equation and a hodograph method for laplace s equation this results in an effective algorithm for a numerical solution with finite differences

propagation of cracks in elastic media throughout this paper the normal n denotes the interior normal direction i e n f x1 1 p 1 jf x1 j when x approaches from above denoted by and n f x1 1 p 1 jf x1 j from below denoted by in a recent paper 2 the present authors studied the asymptotic behavior of any solution of 1 2 1 4 in a neighborhood of the tip x t taking for simplicity t 0 and assuming that

a dynamical uncertainty principle in von neumann algebras by operator monotone functions suppose that a1 an are observables selfadjoint matrices and is a state density matrix in this case the standard uncertainty principle proved by robertson gives a bound for the quantum generalized variance namely for det cov aj ak using the commutators aj ak this bound is trivial when n is odd recently a dierent inequality of robertson type has been proved by the authors with the help of the theory of operator monotone functions in this case the bound makes use of the commutators a j and is non trivial for any n in the present paper we generalize this new result to the von neumann algebra case nevertheless the proof appears to simplify all the existing ones

generalized robertson intelligent states and squeezing for supersymmetric and shape invariant systems an algebraic construction we obtain the robertson schrodinger uncertainty relation for shape invariant systems and construct generalized robertson intelligent states for these systems using an algebraic approach based on the supersymmetric quantum mechanics using the variances of generalized quadrature operators we study the coherency and squeezing properties evaluating their dependence on different kinds of generalizations for shape invariant systems with potential parameters related by a translation poschl teller potential and by a scaling self similar potential

generalized coherent and intelligent states for exact solvable quantum systems the so called gazeau klauder and perelomov coherent states are introduced for an arbitrary quantum system we give also the general framework to construct the generalized intelligent states which minimize the robertson schrodinger uncertainty relation as illustration the poschl teller potentials of trigonometric type will be chosen we show the advantage of the analytical representations of gazeau klauder and perelomov coherent states in obtaining the generalized intelligent states in analytical way

characterization of su 1 1 coherent states in terms of affine group wavelets the perelomov coherent states of su 1 1 are labelled by elements of the quotient of su 1 1 by the compact subgroup taking advantage of the fact that this quotient is isomorphic to the affine group of the real line we are able to parametrize the coherent states by elements of that group or equivalently by points in the half plane such a formulation permits to find new properties of the su 1 1 coherent states and to relate them to affine wavelets

su 1 1 intelligent states analytic representation in the unit disk intelligent states of the su 1 1 lie group are investigated using the analytic representation in the unit disk of the su 1 1 coherent state basis by developing this representation we study a special class of states which are both intelligent and coherent these states can be created using hamiltonians for which su 1 1 is the dynamical symmetry group

spectral statistics for the difference of two wishart matrices in this work we consider the weighted difference of two independent complex wishart matrices and derive the joint probability density function of the corresponding eigenvalues in a finite dimension scenario using two distinct approaches the first derivation involves the use of unitary group integral while the second one relies on applying the derivative principle the latter relates the joint probability density of eigenvalues of a matrix drawn from a unitarily invariant ensemble to the joint probability density of its diagonal elements exact closed form expressions for an arbitrary order correlation function are also obtained and spectral densities are contrasted with monte carlo simulation results analytical results for moments as well as probabilities quantifying positivity aspects of the spectrum are also derived additionally we provide a large dimension asymptotic result for the spectral density using the stieltjes transform approach for algebraic random matrices finally we point out the relationship of these results with the corresponding results for difference of two random density matrices and obtain some explicit and closed form expressions for the spectral density and absolute mean

state extended uncertainty relations a scheme for construction of uncertainty relations for n observables and m states is presented several lowest order inequalities are displayed and briefly discussed for two states and and canonical observables the entangled extension of the heisenberg relation reads p 2 q 2 p 2 q 2

area law for random graph states random pure states of multi partite quantum systems associated with arbitrary graphs are investigated each vertex of the graph represents a generic interaction between subsystems described by a random unitary matrix distributed according to the haar measure while each edge of the graph represents a bipartite maximally entangled state for any splitting of the graph into two parts we consider the corresponding partition of the quantum system and compute the average entropy of entanglement first in the special case where the partition does not cross any vertex of the graph we show that the area law is satisfied exactly in the general case we show that the entropy of entanglement obeys an area law on average this time with a correction term that depends on the topologies of the graph and of the partition the results obtained are applied to the problem of distribution of quantum entanglement in a quantum network with prescribed topology

uncertainty relations in deformation quantization robertson and hadamard robertson theorems on non negative definite hermitian forms are generalized to an arbitrary ordered field these results are then applied to the case of formal power series fields and the heisenberg robertson robertson schrodinger and trace uncertainty relations in deformation quantization are found some conditions under which the uncertainty relations are minimized are also given

central limit theorem for the adjacency operators on the infinite symmetric group an adjacency operator on a group is a formal sum of left regular representations over a conjugacy class for such adjacency operators on the infinite symmetric group which are parametrized by the young diagrams we discuss the correlation of their powers with respect to the vacuum vector state we compute exactly the correlation function under suitable normalization and through the infinite volume limit this approach is viewed as a central limit theorem in quantum probability where the operators are interpreted as random variables via spectral decomposition in k kerov showed the corresponding result for one row young diagrams our formula provides an extension of kerov s theorem to the case of arbitrary young diagrams

composed ensembles of random unitary matrices composed ensembles of random unitary matrices are defined via products of matrices each pertaining to a given canonical circular ensemble of dyson we investigate statistical properties of spectra of some composed ensembles and demonstrate their physical relevance we also discuss the methods of generating random matrices distributed according to invariant haar measure on the orthogonal and unitary group

factorization of analytic representations in the unit disc and number phase statistics of a quantum harmonic oscillator the inner outer part factorization of analytic representations in the unit disc is used for an effective characterization of the number phase statistical properties of a quantum harmonic oscillator it is shown that the factorization is intimately connected with the number phase weyl semigroup and its properties in the barut girardello analytic representation the factorization is implemented as a convolution several examples are given which demonstrate the physical significance of the factorization and its role for quantum statistics in particular we study the effect of phase space interference on the factorization properties of a superposition state

hall normalization constants for the bures volumes of the n state quantum systems we report the results of certain integrations of quantum theoretic interest relying in this regard upon recently developed parametrizations of boya et al 1998 preprint quant ph 9810084 of the n n density matrices in terms of squared components of the unit n 1 sphere and the n n unitary matrices firstly we express the normalized volume elements of the bures minimal monotone metric for n 2 and 3 thereby obtaining bures prior probability distributions over the two and three state systems then as a first step in extending these results to n 3 we determine that the hall normalization constant cn for the marginal bures prior probablity distribution over the n 1 dimensional simplex of the n eigenvalues of the n n density matrices is for n 4 equal to 71 680 2 since we also find that c3 35 it follows that c4 is simply equal to 211c3 c2 itself is known to equal 2 the constant c5 is also found it too is associated with a remarkably simple decomposition involving the product of the eight consecutive prime numbers from 3 to 23 we also preliminarily investigate several cases n 5 with the use of quasi monte carlo integration we hope that the various analyses reported will prove useful in deriving a general formula which evidence suggests will involve the bernoulli numbers for the hall normalization constant for arbitrary n this would have diverse applications including quantum inference and universal quantum coding

the ppt square conjecture holds generically for some classes of independent states let be a random pure state on where is a random unit vector uniformly distributed on the sphere in let be a random induced state whose distribution is and let be a random induced state following the same distribution independent of let be a random state induced by the entanglement swapping of and we show that the empirical spectrum of converges almost surely to the marcenko pastur law with parameter c 2 as and as an application we prove that the state is separable generically if are ppt entangled

geometries of quantum states the quantum analog of the fisher information metric of a probability simplex is searched and several riemannian metrics on the set of positive definite density matrices are studied some of them appeared in the literature in connection with cramer rao type inequalities or the generalization of the berry phase to mixed states they are shown to be stochastically monotone here all stochastically monotone riemannian metrics are characterized by means of operator monotone functions and it is proven that there exist a maximal and a minimal among them a class of metrics can be extended to pure states and a constant multiple of the fubini study metric appears in the extension

bures volume of the set of mixed quantum states we compute the volume of the n2 1 dimensional set n of density matrices of size n with respect to the bures measure and show that it is equal to that of an n2 1 dimensional hyper hemisphere of radius 1 2 for n 2 we obtain the volume of the uhlmann hemisphere s3 4 we find also the area of the boundary of the set n and obtain analogous results for the smaller set of all real density matrices an explicit formula for the bures hall normalization constants is derived for an arbitrary n

feynman graphs and the large dimensional limit of multipartite entanglement in this paper we extend the analysis of multipartite entanglement based on techniques from classical statistical mechanics to a system composed of n d level parties qudits we introduce a suitable partition function at a fictitious temperature with the average local purity of the system as hamiltonian in particular we analyze the high temperature expansion of this partition function prove the convergence of the series and study its asymptotic behavior as d we make use of a diagrammatic technique classify the graphs and study their degeneracy we are thus able to evaluate their contributions and estimate the moments of the distribution of the local purity

a robertson type uncertainty principle and quantum fisher information let a1 an be complex self adjoint matrices and let be a density matrix the robertson uncertainty principle det cov ah aj det i 2 tr a h aj gives a bound for the quantum generalized variance in terms of the commutators ah aj the right side matrix is antisymmetric and therefore the bound is trivial equal to zero in the odd case n 2m 1 let f be an arbitrary normalized symmetric operator monotone function and let h i f be the associated quantum fisher information we have conjectured the inequality det cov ah aj det f 0 hi a h i a j i f

analytic representations in quantum mechanics various euclidean hyperbolic and elliptic analytic representations are introduced and relations among them are discussed the bargmann analytic representation in the complex plane is considered and its relation to other phase space methods for the harmonic oscillator is reviewed the general theory that relates the growth of analytic functions with the density of their zeros is applied to bargmann functions and it leads to theorems on the completeness of sequences of glauber coherent states two hyperbolic analytic representations in the unit disc based on su 1 1 coherent states and also on phase states are introduced a third analytic representation in the complex plane based on barut girardello states is also considered and transformations which relate it to the other ones are studied in the case of systems with finite dimensional hilbert space an elliptic analytic representation in the extended complex plane and also another analytic representation based on theta functions are introduced the berezin formalism in the euclidean hyperbolic and elliptic cases is discussed contour analytic representations in these three cases are also presented

application of nonlinear deformation algebra to a physical system with poschl teller potential nonlinear deformation algebra are realized in a physical system with p schl teller potential the raising and lowering operators satisfying this algebra are constructed from which the eigenproblem of the system can be exactly solved by the operator method the physical meaning of two deforming functions involved in this algebra is also found in addition algebra is obtained naturally and discussions on the coherent state are also made

central limit theorems for large graphs method of quantum decomposition a new method is proposed for investigating spectral distribution of the combinatorial laplacian adjacency matrix of a large regular graph on the basis of quantum decomposition and quantum central limit theorem general results are proved for cayley graphs of discrete groups and for distance regular graphs the coxeter groups and the johnson graphs are discussed in detail by way of illustration in particular the limit distributions obtained from the johnson graphs are characterized by the meixner polynomials which form a one parameter deformation of the laguerre polynomials

analytic representations based on su 3 coherent states and robertson intelligent states robertson intelligent states which minimize the schrodinger robertson uncertainty relation are constructed as eigenstates of a linear combination of weyl generators of the su 3 algebra the construction is based on the analytic representations of su 3 coherent states new classes of coherent and squeezed states are explicitly derived

engineering transient spectrum for a two level system interacting with two mode intelligent states abstract the problem of a single two level atom in its excited state placed in a bimodal cavity in which an arbitrary form of the intensity dependent atom field coupling is present is solved exactly expressions for the energy eigenvalues and eigenvectors are derived and an exact representation for the time dependent unitary evolution operator of the system is given by means of which we analyze the analytic form of the fluorescence spectrum using the transitions among the dressed states of the system the influence of parameter misfits on the quantum system is discussed an interesting relation between the fluorescence spectrum and the dynamical evolution is found when the initial field states are prepared in properly intelligent states by comparison with exact numerical results we demonstrate that features of the fluorescence spectrum are influenced significantly by the different kinds of the nonlinearity of the intensity dependent atom field coupling we provide numerous examples to illustrate this correspondence and provide evidence of its usefulness the present work considerably extends earlier results for two level systems

generalized deflated block elimination a stable algorithm is presented to solve a nonsingular bordered system of the form left begin array 20 c a b c t d end array right left begin array 20 c x y end array right left begin array 20 c f g end array right where b and c are n by m matrices and the n by n matrix a could be nearly singular with at most mu small singular values the algorithm needs only a solver for a and the solution to an m mu by m mu dense linear system it is thus well suited for problems for which a has easily exploitable structures and m mu ll n such as in continuation methods bifurcation problems and constrained optimization

the monge metric on the sphere and geometry of quantum states topological and geometrical properties of the set of mixed quantum states in the n dimensional hilbert space are analysed assuming that the corresponding classical dynamics takes place on the sphere we use the vector su 2 coherent states and the generalized husimi distributions to define the monge distance between two arbitrary density matrices the monge metric has a simple semiclassical interpretation and induces a non trivial geometry among all pure states the distance from the maximally mixed state proportional to the identity matrix admits the largest value for the coherent states while the delocalized chaotic states are close to this contrasts the geometry induced by the standard trace hilbert schmidt or bures metrics for which the distance from is the same for all pure states we discuss possible physical consequences including unitary time evolution and the process of decoherence we introduce also a simplified monge metric defined in the space of pure quantum states and more suitable for numerical computation

diagonal quantum discord quantum discord measures quantum correlation by comparing the quantum mutual information with the maximal amount of mutual information accessible to a quantum measurement this paper analyzes the properties of diagonal discord a simplified version of discord that compares quantum mutual information with the mutual information revealed by a measurement that correspond to the eigenstates of the local density matrices in contrast to the optimized discord diagonal discord is easily computable it also finds connections to thermodynamics and resource theory here we further show that for the generic case of non degenerate local density matrices diagonal discord exhibits desirable properties as a preferable discord measure we employ the theory of resource destroying maps liu z w et al 2017 phys rev lett 118 060502 to prove that diagonal discord is monotonically nonincreasing under the operation of local discord nongenerating qudit channels d 2 and provide numerical evidence that such monotonicity holds for qubit channels as well we also show that it is continuous and derive a fannes like continuity bound our results hold for a variety of simple discord measures generalized from diagonal discord

exact solutions for the general nonstationary oscillator with a singular perturbation three linearly independent hermitian invariants for the nonstationary generalized singular oscillator so are constructed and their complex linear combination is diagonalized the constructed family of eigenstates contains as subsets all previously obtained solutions for the so and includes all robertson and schrodinger intelligent states for the three invariants it is shown that the constructed analogues of the su 1 1 group related coherent states for the so minimize the robertson and schrodinger uncertainty relations for the three invariants and for every pair of them simultaneously the squeezing properties of the new states are briefly discussed