local channels preserving the states without measurement induced nonlocality measurement induced nonlocality is a measure of nonlocality introduced recently by luo and fu we present here sufficient and necessary conditions for a quantum state for which this quantity is equal to zero furthermore it is shown that for such a state ab with any local channel acting on ha cannot create measurement induced nonlocality if and only if either it is a completely contractive channel or it is a nontrivial isotropic channel for the qubit case this property is an additional characteristic of the completely contractive channel or the commutativity preserving unital channel

quantum discord for qubit qudit systems we present two formulae to calculate quantum discord a kind of quantum correlation between a qubit and a second party of arbitrary dimension d the first formula is the original entropic definition and the second is a recently proposed geometric distance measure which leads to an analytical formulation the tracing over the qubit in the entropic calculation is reduced to a very simple prescription and when the d dimensional system is a so calledx state the density matrix having non zero elements only along the diagonal and anti diagonal the entropic calculation can also be carried out analytically such states of the full bipartite qubit qudit system may be named extended x states whose density matrix is built of four block matrices each visually appearing as an x the optimization involved in the entropic calculation is generally over two parameters reducing to one for many cases and avoided altogether for an overwhelmingly large set of density matrices as our numerical investigations demonstrate in the case of n 2 extended x states encompass the entire 15 dimensional parameter space that is they represent the full qubit qubit system

distinguishing classical correlations from quantum correlations the aim of this paper is to distinguish classical correlations from quantum ones first a new characterization of a classical correlated cc state is established corresponding results for the left and right classical correlations are also obtained second a sufficient and necessary condition for a convex combination of two cc states to be cc is given it is proved that the set cc ha hb of all cc states on ha hb is a perfect nowhere dense and compact subset of the metric space d ha hb of all states density operators on ha hb based on our new characterization of cc states a quantity q is associated with a state it is shown that a state is cc if and only if q 0 in particular we prove that the werner state w in a two qubit system with a single real parameter is cc if and only if 0 25

entanglement optimizing mixtures of two qubit states entanglement in incoherent mixtures of pure states of two qubits is considered via the concurrence measure a set of pure states is optimal if the concurrence for any mixture of them is the weighted sum of the concurrences of the generating states when two or three pure real states are mixed it is shown that 28 5 or 5 12 of the cases respectively are optimal conditions that are obeyed by the pure states generating such optimally entangled mixtures are derived for four or more pure states it is shown that there are no such sets of real states the implication of these on the superposition of two or more dimerized states is discussed a corollary of these results also show in how many cases rebit concurrence can be the same as that of qubit concurrence

hamiltonians on discrete structures jumps of the integrated density of states and uniform convergence we study equivariant families of discrete hamiltonians on amenable geometries and their integrated density of states ids we prove that the eigenspace of a fixed energy is spanned by eigenfunctions with compact support the size of a jump of the ids is consequently given by the equivariant dimension of the subspace spanned by such eigenfunctions from this we deduce uniform convergence w r t the spectral parameter of the finite volume approximants of the ids our framework includes quasiperiodic operators on delone sets periodic and random operators on quasi transitive graphs and operators on percolation graphs

stress relaxation of near critical gels the time dependent stress relaxation for a rouse model of a cross linked polymer melt is completely determined by the spectrum of eigenvalues of the connectivity matrix the latter has been computed analytically for a mean field distribution of cross links it shows a lifshitz tail for small eigenvalues and all concentrations below the percolation threshold giving rise to a stretched exponential decay of the stress relaxation function in the sol phase at the critical point the density of states is finite for small eigenvalues resulting in a logarithmic divergence of the viscosity and an algebraic decay of the stress relaxation function numerical diagonalization of the connectivity matrix supports the analytical findings and has furthermore been applied to cluster statistics corresponding to random bond percolation in two and three dimensions

long time tails in the parabolic anderson model with bounded potential we consider the parabolic anderson problem t u u u on 0 z d with random i i d potential z z zd and the initial condition u 0 1 our main assumption is that esssup 0 0 depending on the thickness of the distribution prob 0 close to its essential supremum we identify both the asymptotics of the moments of u t 0 and the almost sure asymptotics of u t 0 as t in terms of variational problems as a by product we establish lifshitz tails for the random schrodinger operator at the bottom of its spectrum in our class of distributions the lifshitz exponent ranges from d 2 to the power law is typically accompanied by lower order corrections

quantum correlations and distinguishability of quantum states a survey of various concepts in quantum information is given with a main emphasis on the distinguishability of quantum states and quantum correlations covered topics include generalized and least square measurements state discrimination quantum relative entropies the bures distance on the set of quantum states the quantum fisher information the quantum chernoff bound bipartite entanglement the quantum discord and geometrical measures of quantum correlations the article is intended both for physicists interested not only by collections of results but also by the mathematical methods justifying them and for mathematicians looking for an up to date introductory course on these subjects which are mainly developed in the physics literature

enlargement of obstacles for the simple random walk we consider a continuous time simple random walk moving among obstacles which are sites resp bonds of the lattice z d we derive in this context a version of the technique of enlargement of obstacles developed by sznitman in the brownian case this method gives controls on exponential moments of certain death times as well as good lower bounds for certain principal eigenvalues we give an application to recover an asymptotic result of donsker and varadhan on the number of sites visited by the random walk and another application to the number of bonds visited by the random walk

a class of separable quantum states we present a sufficient condition for a bipartite state to be separable via the strong positive partial transposition structure introduced in chru ci ski et al 2008 phys rev a 77 022113 from which we obtain a class of separable states in particular we prove that any classical quantum state is a state of our class but not vice versa both finite and infinite dimensional systems are considered

unified entropic measures of quantum correlations induced by local measurements we introduce quantum correlation measures based on the minimal change in unified entropies induced by local rank one projective measurements divided by a factor that depends on the generalized purity of the system in the case of nonadditive entropies in this way we overcome the issue of the artificial increasing of the value of quantum correlation measures based on nonadditive entropies when an uncorrelated ancilla is appended to the system without changing the computability of our entropic correlation measures with respect to the previous ones moreover we recover as limiting cases the quantum correlation measures based on von neumann and renyi entropies i e additive entropies for which the adjustment factor becomes trivial in addition we distinguish between total and semiquantum correlations and obtain some inequalities between them finally we obtain analytical expressions of the entropic correlation measures for typical quantum bipartite systems

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

correlation function and mutual information correlation function and mutual information are two powerful tools to characterize the correlations in a quantum state of a composite system widely used in many body physics and in quantum information science respectively we find that these two tools may give different conclusions about the order of the degrees of correlation in two specific two qubit states this result implies that the orderings of bipartite quantum states according to the degrees of correlation depend on which correlation measure we adopt

the geometric approach to quantum correlations computability versus reliability we propose a modified metric based on the hilbert schmidt norm and adopt it to define a rescaled version of the geometric measure of quantum discord such a measure is found not to suffer from pathological dependence on state purity although the employed metric is still non contractive under quantum operations we show that the resulting indicator of quantum correlations is in agreement with other bona fide discord measures in a number of physical examples we present a critical assessment of the requirements of reliability versus computability when approaching the task of quantifying or measuring general quantum correlations in a bipartite state

semicontinuity problems in the calculus of variations soit f r 3 r une fonction deux fois continument differentiable et pour u w 1 1 a b f u a b a b f x u x u x dx si f r n r m r nm r satisfait 1 f est mesurable en x continue en cs et 2 0 f x s a x c s p p ou p 1 a est une fonction localement sommable non negative et c une constante non negative alors la fonctionnelle f u a b est sequentiellement faiblement semi continue inferieurement sur w 1 p r m si et seulement si f x s est quasi convexe pour chaque s et presque chaque x

quantum game players can have advantage without discord the last two decades have witnessed a rapid development of quantum information processing a new paradigm which studies the power and limit of quantum advantages in various information processing tasks problems such as when quantum advantage exists and if existing how much it could be are at a central position of these studies in a broad class of scenarios there are implicitly or explicitly at least two parties involved who share a state and the correlation in this shared state is the key factor to the efficiency under concern in these scenarios the shared entanglement or discord is usually what accounts for quantum advantage in this paper we examine a fundamental problem of this nature from the perspective of game theory a branch of applied mathematics studying selfish behaviors of two or more players we exhibit a natural zero sum game in which the chance for any player to win the game depends only on the ending correlation we show that in a certain classical equilibrium a situation in which no player can further increase her payoff by any local classical operation whoever first uses a quantum computer has a big advantage over its classical opponent the equilibrium is fair to both players and as a shared correlation it does not contain any discord yet a quantum advantage still exists this indicates that at least in game theory the previous notion of discord as a measure of non classical correlation needs to be reexamined when there are two players with different objectives

some remarks concerning quasiconvexity and strong convergence we show that the weak convergence of a sequence of functions in a sobolev space plus the convergence of appropriately quasiconvex energies imply in fact strong convergence this assertion makes rigorous for example the heuristic principle that quasiconvexity damps out oscillations in the gradients of minimising sequences in the calculus of variations

characterizing nonclassical correlations via local quantum uncertainty quantum mechanics predicts that measurements of incompatible observables carry a minimum uncertainty which is independent of technical deficiencies of the measurement apparatus or incomplete knowledge of the state of the system nothing yet seems to prevent a single physical quantity such as one spin component from being measured with arbitrary precision here we show that an intrinsic quantum uncertainty on a single observable is ineludible in a number of physical situations when revealed on local observables of a bipartite system such uncertainty defines an entire class of bona fide measures of nonclassical correlations for the case of 2 ifmmode times else texttimes fi d systems we find that a unique measure is defined which we evaluate in closed form we then discuss the role that these correlations which are of the discord type can play in the context of quantum metrology we show in particular that the amount of discord present in a bipartite mixed probe state guarantees a minimum precision as quantified by the quantum fisher information in the optimal phase estimation protocol

renyi squashed entanglement discord and relative entropy differences the squashed entanglement quantifies the amount of entanglement in a bipartite quantum state and it satisfies all of the axioms desired for an entanglement measure the quantum discord is a measure of quantum correlations that are different from those due to entanglement what these two measures have in common is that they are both based upon the conditional quantum mutual information in berta et al 2015 j math phys 56 022205 we recently proposed renyi generalizations of the conditional quantum mutual information of a tripartite state on abc with c being the conditioning system which were shown to satisfy some properties that hold for the original quantity such as non negativity duality and monotonicity with respect to local operations on the system b with it being left open to show that the renyi quantity is monotone with respect to local operations on system a here we define a renyi squashed entanglement and a renyi quantum discord based on a renyi conditional quantum mutual information and investigate these quantities in detail taking as a conjecture that the renyi conditional quantum mutual information is monotone with respect to local operations on both systems a and b we prove that the renyi squashed entanglement and the renyi quantum discord satisfy many of the properties of the respective original von neumann entropy based quantities in our prior work berta et al 2015 phys rev a 91 022333 we also detailed a procedure to obtain renyi generalizations of any quantum information measure that is equal to a linear combination of von neumann entropies with coefficients chosen from the set 1 0 1 here we extend this procedure to include differences of relative entropies using the extended procedure and a conjectured monotonicity of the renyi generalizations in the renyi parameter we discuss potential remainder terms for well known inequalities such as monotonicity of the relative entropy joint convexity of the relative entropy and the holevo bound

spectral analysis of percolation hamiltonians we study the family of hamiltonians which corresponds to the adjacency operators on a percolation graph we characterise the set of energies which are almost surely eigenvalues with finitely supported eigenfunctions this set of energies is a dense subset of the algebraic integers the integrated density of states has discontinuities precisely at this set of energies we show that the convergence of the integrated densities of states of finite box hamiltonians to the one on the whole space holds even at the points of discontinuity for this we use an equicontinuity from the right argument the same statements hold for the restriction of the hamiltonian to the infinite cluster in this case we prove that the integrated density of states can be constructed using local data only finally we study some mixed anderson quantum percolation models and establish results in the spirit of wegner and delyon and souillard

conditional decoupling of quantum information insights from quantum information theory show that correlation measures based on quantum entropy are fundamental tools that reveal the entanglement structure of multipartite states in that spirit groisman popescu and winter phys rev a 72 032317 2005 showed that the quantum mutual information i a b quantifies the minimal rate of noise needed to erase the correlations in a bipartite state of quantum systems ab here we investigate correlations in tripartite systems abe in particular we are interested in the minimal rate of noise needed to apply to the systems ae in order to erase the correlations between a and b given the information in system e in such a way that there is only negligible disturbance on the marginal be we present two such models of conditional decoupling called deconstruction and conditional erasure cost of tripartite states abe our main result is that both are equal to the conditional quantum mutual information i a b e establishing it as an operational measure for tripartite quantum correlations

the role of coherence entropy of physical twin observables in entanglement the concept of physical twin observables pto for bipartite quantum states introduced and proved relevant for quantum information theory in recent work is substantially simplified the relation of observable and state is studied in detail from the point of view of coherence entropy properties of this quantity are further explored it is shown that besides for pure states also for a class of mixed states quantum discord measure of entanglement can be expressed through the coherence entropy of a pto complete in relation to the state

numerical approximation of non homogeneous non convex vector variational problems in this paper we study a numerical scheme for non convex vector variational problems allowing for microstructure based on the approximation of gradient young measures we present a convergence result and some numerical experiments

discord of response the presence of quantum correlations in a quantum state is related to the state s response to local unitary perturbations such a response is quantified by the distance between the unperturbed and perturbed states minimized with respect to suitably identified sets of local unitary operations in order to be a bona fide measure of quantum correlations the distance function must be chosen among those that are contractive under completely positive and trace preserving cptp maps the most relevant instances of such physically well behaved metrics include the trace the bures and the hellinger distance to each of these metrics one can associate the corresponding discord of response namely the trace or hellinger or bures minimum distance from the set of unitarily perturbed states all these three discords of response satisfy the basic axioms for a proper measure of quantum correlations in the present work we focus in particular on the bures distance which enjoys the unique property of being both riemannian and contractive under cptp maps and admits important operational interpretations in terms of state distinguishability we compute analytically the bures discord of response for two qubit states with maximally mixed marginals and we compare it with the corresponding bures geometric discord namely the geometric measure of quantum correlations defined as the bures distance from the set of classical quantum states finally we investigate and identify the maximally quantum correlated two qubit states according to the bures discord of response these states exhibit a remarkable nonlinear dependence on the global state purity

spectral properties of the laplacian on bond percolation graphs bond percolation graphs are random subgraphs of the d dimensional integer lattice generated by a standard bond percolation process the associated graph laplacians subject to dirichlet or neumann conditions at cluster boundaries represent bounded self adjoint ergodic random operators with off diagonal disorder they possess almost surely the non random spectrum 0 4d and a self averaging integrated density of states the integrated density of states is shown to exhibit lifshits tails at both spectral edges in the non percolating phase while the characteristic exponent of the lifshits tail for the dirichlet neumann laplacian at the lower upper spectral edge equals d 2 and thus depends on the spatial dimension this is not the case at the upper lower spectral edge where the exponent equals 1 2

new features of quantum discord uncovered by q entropies the notion of quantum discord introduced by ollivier and zurek phys rev lett 88 2001 017901 see also henderson and vedral j phys a 34 2001 6899 has attracted increasing attention in recent years as an entropic quantifier of non classical features pertaining to the correlations exhibited by bipartite quantum systems here we generalize the notion so as to encompass power law q entropies that reduce to the standard shannon entropy in the limit q 1 and study the concomitant consequences the ensuing new discord like measures we advance describe aspects of non classicality that are different from those associated with the standard quantum discord a particular manifestation of this difference concerns a feature related to order let d1 stand for the standard shannon based discord measure and dq for the q 1 one if two quantum states a b are such that d1 a d1 b this order relation does not remain invariant under a change from d1 to dq

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

generalized conditional entropy in bipartite quantum systems we analyze for a general concave entropic form the associated conditional entropy of a quantum system a b obtained as a result of a local measurement on one of the systems b this quantity is a measure of the average mixedness of a after such measurement and its minimum over all local measurements is shown to be the associated entanglement of formation between a and a purifying third system c in the case of the von neumann entropy this minimum determines also the quantum discord for classically correlated states and mixtures of a pure state with the maximally mixed state we show that the minimizing measurement can be determined analytically and is universal i e the same for all concave forms while these properties no longer hold for general states we also show that in the special case of the linear entropy an explicit expression for the associated conditional entropy can be obtained whose minimum among projective measurements in a general qudit qubit state can be determined analytically in terms of the largest eigenvalue of a simple 3 3 correlation matrix such minimum determines the maximum conditional purity of a and the associated minimizing measurement is shown to be also universal in the vicinity of maximal mixedness results for x states including typical reduced states of spin pairs in xy chains at weak and strong transverse fields are also provided and indicate that the measurements minimizing the von neumann and linear conditional entropies are typically coincident in these states being determined essentially by the main correlation they can differ however substantially from that minimizing the geometric discord

local minimizers and the schmid law in corner shaped domains this paper focuses on the mathematical analysis of biaxial loading experiments in martensite more particularly on how hysteresis relates to metastability these experiments were carried out by chu and james and their mathematical treatment was initiated by ball chu and james experimentally it is observed that a homogeneous deformation y 1 is the stable state for small loads while y 2 is stable for large loads a model was proposed by ball chu and james which for a certain intermediate range of loads predicts crucially that y 1 remains metastable that is a local as opposed to global minimiser of the energy this result explains convincingly the hysteresis that is observed experimentally it is easy to get an upper bound on the load at which metastability finishes however it was also noticed that this bound the schmid law may not be sharp though this required some geometric conditions on the sample in this research we rigorously justify the ball chu james model by means of de giorgi s convergence establish some properties of local minimisers of the limiting energy and prove the metastability result mentioned above an important part of the paper is then devoted to establishing which geometric conditions are necessary and sufficient for the counter example to the schmid law to apply namely the presence of sharp corners in the sample

monogamy of measurement induced nonlocality measurement induced nonlocality was introduced by luo and fu 2011 phys rev lett 106 120401 as a measure of nonlocality in a bipartite state in this paper we will discuss the monogamy property of measurement induced nonlocality for some three and four qubit classes of states unlike discord we find quite surprising results in this situation both the ghz and w states satisfy monogamy relations in the three qubit case however in general there are violations of monogamy relations in both the ghz class and w class states in the case of the four qubit system monogamy holds for most of the states in the generic class the four qubit ghz state does not satisfy the monogamy relation but the w state does we provide several numerical results including counterexamples regarding the monogamy nature of measurement induced nonlocality we will also extend our results of the generalized w class to n qubit systems

shared information in classical mean field models universal scaling of entanglement estimators of critical quantum systems has drawn a lot of attention in the past recent studies indicate that similar universal properties can be found for bipartite information estimators of classical systems near phase transition opening a new direction in the study of critical phenomena we explore this subject by studying the information estimators of classical spin chains with general mean field interactions in our explicit analysis of two different bipartite information estimators in the canonical ensemble we find that away from criticality both the estimators remain finite in the thermodynamic limit on the other hand along the critical line there is a logarithmic divergence with increasing system size the coefficient of the logarithm is fully determined by the mean field interaction and it is the same for the class of models we consider the scaling function however depends on the details of each model in addition we study the information estimators in the micro canonical ensemble where they are shown to exhibit a different universal behavior we verify our results using numerical calculation for two specific cases of the general hamiltonian

critical dynamics of gelation shear relaxation and dynamic density fluctuations are studied within a rouse model generalized to include the effects of permanent random crosslinks we derive an exact correspondence between the static shear viscosity and the resistance of a random resistor network this relation allows us to compute the static shear viscosity exactly for uncorrelated crosslinks for more general percolation models which are amenable to a scaling description it yields the scaling relation k straight phi beta for the critical exponent of the shear viscosity here beta is the thermal exponent for the gel fraction and straight phi is the crossover exponent of the resistor network the results on the shear viscosity are also used in deriving upper and lower bounds on the incoherent scattering function in the long time limit thereby corroborating previous results

quantum discord a measure of the quantumness of correlations two classically identical expressions for the mutual information generally differ when the systems involved are quantum this difference defines the quantum discord it can be used as a measure of the quantumness of correlations separability of the density matrix describing a pair of systems does not guarantee vanishing of the discord thus showing that absence of entanglement does not imply classicality we relate this to the quantum superposition principle and consider the vanishing of discord as a criterion for the preferred effectively classical states of a system i e the pointer states

unifying approach to the quantification of bipartite correlations by bures distance the notion of distance defined on the set of states of a composite quantum system can be used to quantify total quantum and classical correlations in a unifying way we provide new closed formulae for classical and total correlations of two qubit bell diagonal states by considering the bures distance complementing the known corresponding expressions for entanglement and more general quantum correlations we thus complete the quantitative hierarchy of bures correlations for bell diagonal states we then explicitly calculate bures correlations for two relevant families of states werner states and rank 2 bell diagonal states highlighting the subadditivity which holds for total correlations with respect to the sum of classical and quantum ones when using bures distance finally we analyse a dynamical model of two independent qubits locally exposed to non dissipative decoherence channels where both quantum and classical correlations measured by bures distance exhibit freezing phenomena in analogy with other known quantifiers of correlations

quantum discord discord between the whole and its constituent quantum discord a measure of quantum correlation beyond entanglement is initially defined as the discord between two classically equivalent while quantum discordant definitions of mutual information in this paper we report some new interpretations of discord which rely on the differences between measurement induced effects on the local measured system and the whole system specifically with proper quantitative definitions introduced in buscemi et al 2008 phys rev lett 100 210504 we find that quantum discord can be interpreted as the differences of measurement induced disturbance or information gain on the local measured system and on the whole system combined with previous similar results based on measurement induced entanglement and decoherence our results provide a unified view on quantum discord

geometry of two qubit states with negative conditional entropy we review the geometric features of negative conditional entropy and the properties of the conditional amplitude operator proposed by cerf and adami for two qubit states in comparison with entanglement and nonlocality of the states we identify the region of negative conditional entropy in the tetrahedron of locally maximally mixed two qubit states within this set of states negative conditional entropy implies nonlocality and entanglement but not vice versa and we show that the cerf adami conditional amplitude operator provides an entanglement witness equivalent to the peres horodecki criterion outside of the tetrahedron this equivalence is generally not true

assisted work distillation we study the process of assisted work distillation this scenario arises when two parties share a bipartite quantum state ab and their task is to locally distill the optimal amount of work when one party is restricted to thermal operations whereas the other can perform general quantum operations and they are allowed to communicate classically we demonstrate that this question is intimately related to the distillation of classical and quantum correlations in particular we show that the advantage of one party performing global measurements over many copies of ab is related to the nonadditivity of the entanglement of formation we also show that there may exist work bound in the quantum correlations of the state that is only extractable under the wider class of local gibbs preserving operations

multipartite generalization of quantum discord a generalization of quantum discord to multipartite systems is proposed a key feature of our formulation is its consistency with the conventional definition of discord in bipartite systems it is by construction zero only for systems with classically correlated subsystems and is a non negative quantity giving a measure of the total nonclassical correlations in the multipartite system with respect to a fixed measurement ordering for the tripartite case we show that the discord can be decomposed into contributions resulting from changes induced by nonclassical correlation breaking measurements in the conditional mutual information and tripartite mutual information the former gives a measure of the bipartite nonclassical correlations and is a non negative quantity while the latter is related to the monogamy of the nonclassical correlations

uniform existence of the integrated density of states for random schrodinger operators on metric graphs over zd abstract we consider ergodic random schrodinger operators on the metric graph z d with random potentials and random boundary conditions taking values in a finite set we show that normalized finite volume eigenvalue counting functions converge to a limit uniformly in the energy variable this limit the integrated density of states can be expressed by a closed shubin pastur type trace formula it supports the spectrum and its points of discontinuity are characterized by existence of compactly supported eigenfunctions among other examples we discuss random magnetic fields and percolation models

peculiarities of quantum discord s geometric measure some properties of the quantum discord based on the geometric measure advanced by dakic et al 2010 phys rev lett 105 190502 are discussed here by recourse to a systematic survey of the two qubit state space with emphasis on werner and mem states we explore the dependence of quantum discord on the degree of mixedness of the bipartite states and also its connection with non locality as measured by the maximum violation of a bell inequality within the chsh scenario some considerations regarding the xy model are also made

on the spectrum of lamplighter groups and percolation clusters let mathfrak g be a finitely generated group and x its cayley graph with respect to a finite symmetric generating set s furthermore let mathfrak h be a finite group and mathfrak h wr mathfrak g the lamplighter group wreath product over mathfrak g with group of lamps mathfrak h we show that the spectral measure plancherel measure of any symmetric switch walk switch random walk on mathfrak h wr mathfrak g coincides with the expected spectral measure integrated density of states of the random walk with absorbing boundary on the cluster of the group identity for bernoulli site percolation on x with parameter mathsf p 1 mathfrak h the return probabilities of the lamplighter random walk coincide with the expected annealed return probabilities on the percolation cluster in particular if the clusters of percolation with parameter mathsf p are almost surely finite then the spectrum of the lamplighter group is pure point this generalizes results of grigorchuk and uk resp dicks and schick regarding the case when mathfrak g is infinite cyclic analogous results relate bond percolation with another lamplighter random walk in general the integrated density of states of site or bond percolation with arbitrary parameter mathsf p is always related with the plancherel measure of a convolution operator by a signed measure on mathfrak h wr mathfrak g where mathfrak h mathbb z or another suitable group

multipartite quantum correlations and local recoverability characterizing genuine multipartite quantum correlations in quantum physical systems has historically been a challenging problem in quantum information theory more recently however the total correlation or multipartite information measure has been helpful in accomplishing this goal especially with the multipartite symmetric quantum msq discord piani et al 2008 phys rev lett 100 090502 doi 10 1103 physrevlett 100 090502 1 and the conditional entanglement of multipartite information cemi yang et al 2008 phys rev lett 101 140501 doi 10 1103 physrevlett 101 140501 2 here we apply a recent and significant improvement of strong subadditivity of quantum entropy fawzi renner 2014 in order to develop these quantities further in particular we prove that the msq discord is nearly equal to zero if and only if the multipartite state for which it is evaluated is approximately locally recoverable after performing measurements on each of its systems furthermore we prove that the cemi is a faithful entanglement measure i e it vanishes if and only if the multipartite state for which it is evaluated is a fully separable state along the way we provide an operational interpretation of the msq discord in terms of the partial state distribution protocol which in turn as a special case gives an interpretation for the original discord quantity finally we prove an inequality that could potentially improve upon the fawzi renner inequality in the multipartite context but it remains an open question to determine whether this is so 1 http dx doi org 10 1103 physrevlett 100 090502 2 http dx doi org 10 1103 physrevlett 101 140501

unified view of quantum and classical correlations we discuss the problem of the separation of total correlations in a given quantum state into entanglement dissonance and classical correlations using the concept of relative entropy as a distance measure of correlations this allows us to put all correlations on an equal footing entanglement and dissonance whose definition is introduced here jointly belong to what is known as quantum discord our methods are completely applicable for multipartite systems of arbitrary dimensions we investigate additivity relations between different correlations and show that dissonance may be present in pure multipartite states

hellinger distance as a measure of gaussian discord especially investigated in recent years the gaussian discord can tentatively be quantified by a distance between a given two mode gaussian state gs and the set of all the zero discord two mode gss however as this set consists only of product states such a distance captures all the correlations quantum and classical between modes therefore it is merely an upper bound for the geometric discord no matter which is the employed distance in this work we choose for this purpose the hellinger metric that is known to have many beneficial properties recommending it as a good measure of quantum behaviour in general this metric is determined by affinity a relative of the uhlmann fidelity with which it shares many important features as a first step of our work the affinity of a pair of n mode gss is written then in the two mode case we succeeded in determining exactly the closest gaussian product state and computed the gaussian discord accordingly the obtained general formula is remarkably simple and becomes still friendlier in the significant case of symmetric two mode gss we then analyse in detail two special classes of two mode gss of theoretical and experimental interest as well the squeezed thermal states and the mode mixed thermal ones the former are separable under a well known threshold of squeezing while the latter are always separable it is worth stressing that for symmetric states belonging to either of these classes we find consistency between their geometric hellinger discord and the originally defined discord in the gaussian approach at the same time the gaussian hellinger discord of such a state turns out to be a reliable measure of the total amount of its cross correlations

non uniqueness of minimizers for strictly polyconvex functionals in this note we solve a problem posed by ball in philos trans r soc lond ser a 306 1496 557 611 1982 about the uniqueness of smooth equilibrium solutions to boundary value problems for strictly polyconvex functionals mathcal f u int omega f nabla u x rm d x quad rm and quad u vert partial omega u 0 where is homeomorphic to a ball

entanglement as the symmetric portion of correlated coherence we show that the symmetric portion of correlated coherence is always a valid quantifier of entanglement and that this property is independent of the particular choice of coherence measure this leads to an infinitely large class of coherence based entanglement monotones which is always computable for pure states if the coherence measure is also computable it is already known that every entanglement measure can be constructed as a coherence measure the results presented here show that the converse is also true the constructions that are presented can also be extended to include more general notions of nonclassical correlations leading to quantifiers that are related to quantum discord thus providing an avenue for unifying all such notions of quantum correlations under a single framework

coherence distribution in multipartite systems this paper examines the coherence in multipartite systems we first discuss the distribution of total coherence in a given multipartite quantum state into discord between subsystems and coherent dissonance in each individual subsystem using the relative entropy as a distance measure then we give some trade off relations between various types of coherence and discord within a bipartite system 13 and extend these results to the multipartite setting finally the change of coherence in entanglement distribution is studied

superadditivity of wigner yanase dyson information revisited the wigner yanase dyson information is an important variant of quantum fisher information two fundamental requirements concerning this notion of information content originally postulated by wigner and yanase are convexity and superadditivity the former was fully established by lieb in 1973 and led to the first proof of the strong subadditivity of quantum entropy the latter although widely believed to be true was quite recently disproved by hansen nevertheless superadditivity has also been established in two extreme cases i e when the states are pure or classical in this paper we first review a scheme to classify bipartite states into a hierarchy of classical semi quantum and quantum states which are arranged in the order of increasing quantumness we then prove the superadditivity of the wigner yanase dyson information for all semi quantum states the convexity of the wigner yanase dyson information plays a crucial role here

completely positive maps and classical correlations we expand the set of initial states of a system and its environment that are known to guarantee completely positive reduced dynamics for the system when the combined state evolves unitarily we characterize the correlations in the initial state in terms of its quantum discord 1 we prove that initial states that have only classical correlations lead to completely positive reduced dynamics the induced maps can be not completely positive when quantum correlations including but not limited to entanglement are present

optimal design and relaxation of variational problems iii abstract this paper has attempted a synthesis of three subjects that have developed separately optimal design homogenization and relaxation in the calculus of variations the underlying theme is that of oscillations they occur with certain definite patterns in minimizing sequences for the variational problem the same patterns recur in nearly optimal designs and in the coefficients of the equation being homogenized each problem is resolved by determining the structure of those oscillations and above all their macroscopic averages it is those averages that solve the relaxed problem they also determine the optimal design and the solution of the homogenized equation we emphasize also the role of optimization the homogenized equations and composite materials of interest here come not from arbitrary mixtures but from those that are extremal since they correspond to minimizing sequences for the variational problem the effective properties of these composites attain the optimal bounds for given materials in fixed proportions

a weak strong convergence property and symmetry of minimizers of constrained variational problems in mathbb r n we prove a weak strong convergence result for functionals of the form rnj x u du dx on w1 p along equiintegrable sequences we will then use it to study cases of equality in the extended polya szego inequality and discuss applications of such a result to prove the symmetry of minimizers of a class of variational problems including nonlocal terms under multiple constraints

direct scheme for measuring the geometric quantum discord we propose a scheme to directly measure the exact value of the geometric quantum discord of an arbitrary two qubit state we need only to perform the projective measurement in all the anti symmetric subspace and our scheme is parametrically efficient in contrast to the widely adopted quantum state tomography scheme in the sense of less parameter estimations and projectors moreover the present scheme can be easily realized with the current experimental techniques

a quantum measure of coherence and incompatibility the well known two slit interference is understood as a special relation between an observable localization at the slits and a state being on both slits the relation between an observable and a quantum state is investigated in the general case it is assumed that the amount of coherence equals that of the incompatibility between an observable and a state on these grounds an argument is presented that leads to a natural quantum measure of coherence called coherence or incompatibility information its properties are studied in detail making use of the mixing property of relative entropy derived in this paper a precise relation between the measure of coherence of an observable and that of its coarsening is obtained and discussed from the intuitive point of view convexity of the measure is proved and thus the fact that it is an information entity is established a few more detailed properties of the coherence information are derived with a view to investigating the final state entanglement in general repeatable measurement and more importantly general bipartite entanglement in follow ups of this study

generalizations of quantum discord the original definition of quantum discord of bipartite states was defined over projective measurements in this paper we discuss some generalizations of it these generalizations are defined over general measurements rank 1 general measurements or neumark extension measurements we investigate the non negativity zero discord sets of all these quantum discords and some properties of them

stationary twists and energy minimizers on a space of measure preserving maps abstract let r n be a bounded lipschitz domain f r n n r a suitably quasiconvex integrand and consider the energy functional f u f u over the space of measure preserving maps a p u w 1 p r n u x det u 1 a e in in this paper we discuss the question of existence of multiple strong local minimizers for f over a p moreover motivated by their significance in topology and the study of mapping class groups we consider a class of maps referred to as twists and examine them in connection with the corresponding euler lagrange equations and investigate various qualitative properties of the resulting solutions the stationary twists particular attention is paid to the special case of the so called p dirichlet energy i e when f p 1 p

local minimizers and quasiconvexity the impact of topology the aim of this paper is to discuss the question of existence and multiplicity of strong local minimizers for a relatively large class of functionals open image in new window open image in new window from a purely topological point of view the basic assumptions on open image in new window are sequential lower semicontinuity with respect to w1 p weak convergence and w1 p weak coercivity and the target is a multiplicity bound on the number of such minimizers in terms of convenient topological invariants of the manifolds open image in new window and open image in new window

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

critical behaviour of the rouse model for gelling polymers it is shown that the traditionally accepted rouse values for the critical exponents at the gelation transition do not arise from the rouse model for gelling polymers the true critical behaviour of the rouse model for gelling polymers is obtained from spectral properties of the connectivity matrix of the fractal clusters that are formed by the molecules the required spectral properties are related to the return probability of a blind ant random walk on the critical percolating cluster the resulting scaling relations express the critical exponents of the shear stress relaxation function and hence those of the shear viscosity and of the first normal stress coefficient in terms of the spectral dimension ds of the critical percolating cluster and the exponents and of the cluster size distribution

a meshing strategy for a quadratic iso parametric fem in cavitation computation in nonlinear elasticity abstract the approximation properties of a quadratic iso parametric finite element method for a typical cavitation problem in nonlinear elasticity in two dimensions are analyzed more precisely 1 the finite element interpolation errors are established in terms of the mesh parameters 2 a mesh distribution strategy based on an error equi distribution principle is given 3 the convergence of finite element cavity solutions is proved numerical experiments show that in fact the optimal convergence rate can be achieved by the numerical cavity solutions

on conjectures of classical and quantum correlations in bipartite states in this paper two conjectures which were proposed in luo et al 2010 phys rev a http dx doi org 10 1103 physreva 82 052122 on the correlations in a bipartite state ab are studied if the mutual information i ab between two quantum systems a and b before any measurement is considered as the total amount of correlations in the state ab then it can be separated into two parts classical correlations and quantum correlations the so called classical correlations c ab in the state ab are defined by the maximizing mutual information between two quantum systems a and b after von neumann measurements on system b we show that it is upper bounded by the von neumann entropies of both subsystems a and b which answered the conjecture on the classical correlation if the quantum correlations q ab in the state ab are defined by q ab i ab c ab we also show that it is upper bounded by the von neumann entropy of subsystem b it is also found that q ab is upper bounded by the von neumann entropy of subsystem a for a class of states

can quantum correlations be completely quantum deficit of information zero way was proposed in horodecki 2005 phys rev a 71 062307 as one of the possible measures of quantumness of correlations numerical calculations suggested that there exist such states for which this quantity is almost equal to mutual information in this paper we present a family of states for which we have equality between the above measure of quantumness of correlations and the measure of total correlations mutual information this means that whole correlations in these states have in some sense quantum character and that quantum correlations do not necessarily imply classical correlations we prove this intriguing feature for a subclass of 2 2 separable states we also present numerical results suggesting that this interesting situation might also happen for 2 2 entangled states

the extended bloch representation of quantum mechanics explaining superposition interference and entanglement an extended bloch representation of quantum mechanics was recently derived to offer a possible hidden measurements solution to the measurement problem in this article we use this representation to investigate the geometry of superposition and entangled states explaining interference effects and entanglement correlations in terms of the different orientations a state vector can take within the generalized bloch sphere we also introduce a tensorial determination of the generators of su n which we show to be particularly suitable for the description of multipartite systems from the viewpoint of the sub entities we then use it to show that non product states admit a general description where sub entities can remain in well defined states even when entangled this means that the completed version of quantum mechanics provided by the extended bloch representation where density operators are also considered to be representative of genuine states providing a complete description not only offers a pl

lifschitz tails for the anderson model we present in an expository way an elementary rigorous proof patterned after an argument of kirsch martinelli that the anderson model has lifschitz tails in very great generality

quasiconvexity and partial regularity in the calculus of variations we prove partial regularity of minimizers of certain functionals in the calculus of variations under the principal assumption that the integrands be uniformly strictly quasiconvex this is of interest since quasiconvexity is known in many circumstances to be necessary and sufficient for the weak sequential lower semicontinuity of these functionals on appropriate sobolev spaces examples covered by the regularity theory include functionals with integrands which are convex in the determinants of various submatrices of the gradient matrix

robustness of quantum correlations against linear noise relative robustness of quantum correlations rroqc of a bipartite state is firstly introduced relative to a classically correlated state robustness of quantum correlations roqc of a bipartite state is then defined as the minimum of rroqc of the state relative to all classically correlated ones it is proved that as a function on quantum states roqc is nonnegative lower semi continuous and neither convex nor concave especially it is zero if and only if the state is classically correlated thus roqc not only quantifies the endurance of quantum correlations of a state against linear noise but also can be used to distinguish between quantum and classically correlated states furthermore the effects of local quantum channels on the robustness are explored and characterized

distillability and ppt entanglement of low rank quantum states the bipartite quantum states with rank strictly smaller than the maximum of the ranks of the reduced states a and b are distillable by local operations and classical communication horodecki p smolin j a terhal b m and thapliyal a v 2003 theor comput sci 292 589 96 1999 arxiv quant ph 9910122 our first main result is that this is also true for npt states with rank equal to this maximum a state is ppt if the partial transpose of its density matrix is positive semidefinite and otherwise it is npt this was conjectured first in 1999 in the special case when the ranks of a and b are equal see horodecki p smolin j a terhal b m and thapliyal a v 2003 theor comput sci 292 589 96 1999 arxiv quant ph 9910122 our second main result provides a complete solution of the separability problem for bipartite states of rank 4 namely we show that such a state is separable if and only if it is ppt and its range contains at least one product state we also prove that the so called checkerboard states are distillable if and only if they are npt

eigenvalue distribution of large weighted random graphs we study eigenvalue distribution of the adjacency matrix a n p of weighted random graphs n p we assume that the graphs have n vertices and the average number of edges attached to one vertex is p to each edge of the graph eij we assign a weight given by a random variable aij with zero mathematical expectation and all moments finite in the first part of the paper we consider the moments of normalized eigenvalue counting function n p of a n p assuming all moments of a finite we obtain recurrent relations that determine the moments of the limiting measure p limn n p the method developed is applied to the laplace operator closely related with a n p using the recurrent relations we analyze the form of p for the both of random matrix families in the second part of the paper we consider the resolvents g a z of a n p and of n p and study the functions fn a z u 1 n k 1n exp ugkk a z in the limit n we derive closed equations that uniquely determine the limiting functio

on the density of state for the quantum percolation problem for the site dilution model on the hypercubic lattice zd d or 2 the authors examine the density of states for the tight binding hamiltonian projected onto the infinite cluster it is shown that with probability one the corresponding integrated density of states is discontinuous on a set of energies which is dense in the band this result is proved by constructing states supported on finite regions of the infinite cluster analogous to the kirkpatrick and eggarter zero energy molecular state

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