growth and decay of shock and acceleration waves in a traffic flow model with relaxation abstract the usual ficken based constitutive relation for traffic flux is replaced with one based on the maxwell cattaneo model the resulting flux law which now takes into account the reaction time of driver and vehicle results in a second order hyperbolic generalization of burgers equation as the pde governing the traffic density an analytical study of this equation is presented with an emphasis on shock and related kinematic wave phenomena specifically the exact traveling wave solution tws is derived and it is shown that shock formation is possible only if the diffusivity is non vanishing using singular surface theory exact amplitude expressions for both shock and acceleration waves are obtained and their temporal evolution determined the exact upper bound of the reaction time parameter is established and connections between singular surface and tws results are noted

all maximally entangled four qubit states we find an operational interpretation for the 4 tangle as a type of residual entanglement somewhat similar to the interpretation of the 3 tangle using this remarkable interpretation we are able to find the class of maximally entangled four qubits states which is characterized by four real parameters the states in the class are maximally entangled in the sense that their average bipartite entanglement with respect to all possible bipartite cuts is maximal we show that while all the states in the class maximize the average tangle there are only a few states in the class that maximize the average tsillas or renyi entropy of entanglement quite remarkably we find that up to local unitaries there exists two unique states one maximizing the average tsallis entropy of entanglement for all 2 while the other maximizing it for all 0 2 including the von neumann case of 1 furthermore among the maximally entangled four qubits states there are only three maximally entangled states that have the property that for two out of the three bipartite cuts consisting of two qubits verses two qubits the entanglement is 2 ebits and for the remaining bipartite cut the entanglement between the two groups of two qubits is 1 ebit the unique three maximally entangled states are the three cluster states that are related by a swap operator we also show that the cluster states are the only states up to local unitaries that maximize the average renyi entropy of entanglement for all 2

entangled three qubit states without concurrence and three tangle we provide a complete analysis of mixed three qubit states composed of a greenberger horne zeilinger state and a w state orthogonal to the former we present optimal decompositions and convex roofs for the three tangle further we provide an analytical method to decide whether or not an arbitrary rank 2 state of three qubits has vanishing three tangle these results highlight intriguing differences compared to the properties of two qubit mixed states and may serve as a quantitative reference for future studies of entanglement in multipartite mixed states by studying the coffman kundu wootters inequality we find that while the amounts of inequivalent entanglement types strictly add up for pure states this monogamy can be lifted for mixed states by virtue of vanishing tangle measures

bounds on general entropy measures we show how to determine the maximum and minimum possible values of one measure of entropy for a given value of another measure of entropy these maximum and minimum values are obtained for two standard forms of probability distribution or quantum state independent of the entropy measures provided the entropy measures satisfy a concavity convexity relation these results may be applied to entropies for classical probability distributions entropies of mixed quantum states and measures of entanglement for pure states

generalized reynolds ideals and derived equivalences for algebras of dihedral and semidihedral type abstract generalized reynolds ideals are ideals of the center of a symmetric algebra over a field of positive characteristic they have been shown by the second author to be invariant under derived equivalences in this paper we determine the generalized reynolds ideals of algebras of dihedral and semidihedral type as defined by erdmann in characteristic 2 in this way we solve some open problems about scalars occurring in the derived equivalence classification of these algebras

additive bounds of minimum output entropies for unital channels and an exact qubit formula we find an upper bound for the minimum output entropy of a unital quantum channel and obtain an exact formula for general qubit channels our techniques incorporate the renyi entropies particularly with renyi parameter alpha 2 moreover since our upper bound is additive under tensor product we get as a corollary an upper bound for the classical capacity of unital quantum channels interestingly our upper bound for the classical capacity depends only on the operator norm of matrix representations of channels on the space of traceless hermitian operators and is tight in the sense that it gives the precise quantity of classical capacity of the werner holevo channel as an example we study quantum channels with operator sum representation that is made of the discrete weyl operators generalized pauli operators and explain how our formula works in this case finally we find new examples for which the minimum output renyi 2 entropy is additive

reducible correlations in dicke states we apply a simple observation to show that the generalized dicke states can be determined from their reduced subsystems in this framework it is sufficient to calculate the expression for only the diagonal elements of the reduced density matrices in terms of the state coefficients we prove that the correlation in generalized dicke states gd l n can be reduced to 2l partite level application to the quantum marginal problem is also discussed

quantifying entanglement resources we present an overview of the quantitative theory of single copy entanglement in finite dimensional quantum systems in particular we emphasize the point of view that different entanglement measures quantify different types of resources which leads to a natural interdependence of entanglement classification and quantification apart from the theoretical basis we outline various methods for obtaining quantitative results on arbitrary mixed states this article is part of a special issue of journal of physics a mathematical and theoretical devoted to 50 years of bell s theorem

on maximal entanglement between two pairs in four qubit pure states we show that the state with the highest known average two particle von neumann entanglement entropy proposed by sudbery and one of the authors gives a local maximum of this entropy we also show that this is not the case for an alternative highly entangled state proposed by brown et al

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

generalized reynolds ideals for non symmetric algebras abstract we show how to extend the theory of generalized reynolds ideals as introduced by b kulshammer from symmetric algebras to arbitrary finite dimensional algebras over fields with positive characteristic this provides new invariants of the derived module categories of finite dimensional algebras extending recent results of the third author for symmetric algebras

unified entropy entanglement measures and monogamy of multi party entanglement we show that restricted shareability of multi qubit entanglement can be fully characterized by unified q s entropy we provide a two parameter class of bipartite entanglement measures namely unified q s entanglement with its analytic formula in two qubit systems for q 1 0 s 1 and qs 3 using unified q s entanglement we establish a broad class of the monogamy inequalities of multi qubit entanglement for q 2 0 s 1 and qs 3

concurrence vectors in arbitrary multipartite quantum systems for a given pure state of a multipartite system the concurrence vector is defined by employing the defining representation of generators of the corresponding rotation groups the norm of a concurrence vector is considered as a measure of entanglement for the multipartite pure state the concurrence vector is regarded as the direct sum of concurrence subvectors in the sense that each subvector is associated with a pair of particles it is proposed to use the norm of each subvector as the contribution of the corresponding pair in entanglement of the system

slocc invariants for multipartite mixed states we construct a nontrivial set of invariants for any multipartite mixed states under the stochastic local operations and classical communication symmetry these invariants are given by hyperdeterminants and independent of basis change in particular a family of d2 invariants for arbitrary d dimensional even partite mixed states are explicitly given

front propagation into unstable states universal algebraic convergence towards uniformly translating pulled fronts fronts that start from a local perturbation and propagate into a linearly unstable state come in two classes pulled fronts and pushed fronts the term pulled front expresses that these fronts are pulled along by the spreading of linear perturbations about the unstable state accordingly their asymptotic speedv equals the spreading speed of perturbations whose dynamics is governed by the equations linearized about the unstable state the central result of this paper is the analysis of the convergence of asymptotically uniformly traveling pulled fronts towardsv we show that when such fronts evolve from sufficiently steep initial conditions which initially decay faster than e x forx 1 t hey have auniversal relaxation behavioras timet 1 the velocity of a pulled front always relaxes algebraically like v t d v 3 2t c 3 p d d 2 t 3 2 c o 1 t 2 the parametersv and d are determined through a saddle point analysis from the equation of motion linearized about the unstable invaded state this front velocity is independent of the precise value of the front amplitude which one tracks to measure the front position the interior of the front is essentially slaved to the leading edge and develops universally as x t d8v t x rt dt 0 v t 0 c o 1 t 2 where8v x vt is a uniformly translating front solution with velocity v v our result which can be viewed as a general center manifold result for pulled front propagation is derived in detail for the well known nonlinear diffusion equation of type t d 2 x c 3 where the invaded unstable state is d 0 even for this simple case the subdominant t 3 2 term extends an earlier result of bramson our analysis is then generalized to more general sets of partial differential equations with higher spatial or temporal derivatives to pdes with memory kernels and also to difference equations such as those that occur in numerical finite difference codes our universal result for pulled fronts thus implies independence i of the level curve which is used to track the front position ii of the precise nonlinearities iii of the precise form of the linear operators in the dynamical equation and iv of the precise initial conditions as long as they are sufficiently steep the only remainders of the explicit form of the dynamical equation are the nonlinear solutions 8v and the three saddle point parameters v and d as our simulations confirm all our analytical predictions in every detail it can be concluded that we have a complete analytical understanding of the propagation mechanism and relaxation behavior of pulled fronts if they are uniformly translating for t 1 an immediate consequence of the slow algebraic relaxation is that the standard moving boundary approximation breaks down for weakly curved pulled fronts in two or three dimensions in addition to our main result for pulled fronts we also discuss the propagation and convergence of fronts emerging from

unified entropy trade off relations for a single quantum channel many important properties of quantum channels are quantified by means of entropic functionals characteristics of such a kind are closely related to different representations of a quantum channel in the jamiolkowski choi representation the given quantum channel is described by the so called dynamical matrix entropies of the rescaled dynamical matrix known as map entropies describe a degree of introduced decoherence within the so called natural representation the quantum channel is formally posed by another matrix obtained as the reshuffling of the dynamical matrix the corresponding entropies characterize an amount with which the receiver a priori knows the channel output as was previously shown the map and receiver entropies are mutually complementary characteristics indeed there exists a non trivial lower bound on their sum first we extend the concept of receiver entropy to the family of unified entropies developing the previous results we further derive non trivial lower bounds on the sum of the map and receiver q s entropies the derivation is essentially based on some inequalities with the schatten norms and anti norms

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

speed selection for traveling wave solutions to the diffusion reaction equation with cubic reaction term and burgers nonlinear convection the problem of traveling wave tw speed selection for solutions to a generalized murray burgers kpp fisher parabolic equation with a strictly positive cubic reaction term is considered theoretically and the initial boundary value problem is numerically solved in order to support obtained analytical results depending on the magnitude of a parameter inherent in the reaction term i the term is either a concave function or a function with the inflection point and ii transition from pulled to pushed tw solution occurs due to interplay of two nonlinear terms the reaction term and the burgers convection term explicit pushed tw solutions are derived it is shown that physically observable tw solutions i e solutions obtained by solving the initial boundary value problem with a sufficiently steep initial condition can be determined by seeking the tw solution characterized by the maximum decay rate at its leading edge in the appendix the developed approach is applied to a non linear diffusion reaction equation that is widely used to model premixed turbulent combustion

generalized quantum entropy the generalized quantum entropies are introduced in this paper some important properties such as nonnegativity continuity and concavity are proved but different from the von neumann entropy the subadditivity and additivity fail for the quantum unified r s entropy in general

concurrence of mixed bipartite quantum states in arbitrary dimensions we derive a lower bound for the concurrence of mixed bipartite quantum states valid in arbitrary dimensions as a corollary a weaker purely algebraic estimate is found which detects mixed entangled states with a positive partial transpose

concurrence of arbitrary dimensional bipartite quantum states we derive an analytical lower bound for the concurrence of a bipartite quantum state in arbitrary dimension a functional relation is established relating concurrence the peres horodecki criterion and the realignment criterion we demonstrate that our bound is exact for some mixed quantum states the significance of our method is illustrated by giving a quantitative evaluation of entanglement for many bound entangled states some of which fail to be identified by the usual concurrence estimation method

entangled pure state transformations via local operations assisted by finitely many rounds of classical communication we consider generic pure n qubit states and a general class of pure states of arbitrary dimensions and arbitrarily many subsystems we characterize those states which can be reached from some other state via local operations assisted by finitely many rounds of classical communication locc n for n qubits with n 3 we show that this set of states is of measure zero which implies that the maximally entangled set is generically of full measure if restricted to the practical scenario of locc n moreover we identify a class of states for which any locc n protocol can be realized via a concatenation of deterministic steps we show however that in general there exist state transformations which require a probabilistic step within the protocol which highlights the difference between bipartite and multipartite locc

canonical decompositions of n qubit quantum computations and concurrence the two qubit canonical decomposition su 4 su 2 su 2 su 2 su 2 writes any two qubit unitary operator as a composition of a local unitary a relative phasing of bell states and a second local unitary using lie theory we generalize this to an n qubit decomposition the concurrence canonical decomposition ccd su 2n kak the group k fixes a bilinear form related to the concurrence and in particular any unitary in k preserves the tangle i 1y i ny 2 for n even thus the ccd shows that any n qubit unitary is a composition of a unitary operator preserving this n tangle a unitary operator in a which applies relative phases to a set of ghz states and a second unitary operator which preserves the tangle as an application we study the extent to which a large random unitary may change concurrence the result states that for a randomly chosen a a su 22p the probability that a carries a state of tangle 0 to a state of maximum tangle approaches 1 as the even number of qubits approach

on unified entropy characterization of quantum channels we consider properties of quantum channels with the use of unified entropies extremal unravelings of quantum channel with respect to these entropies are examined the concept of map entropy is extended in terms of the unified entropies the map q s entropy is naturally defined as the unified q s entropy of a rescaled dynamical matrix of given quantum channel inequalities of fannes type are obtained for introduced entropies in terms of both the trace and frobenius norms of difference between corresponding dynamical matrices additivity properties of introduced map entropies are discussed the known inequality of lindblad with the entropy exchange is generalized to many of the unified entropies for the tensor product of a pair of quantum channels we derive a two sided estimate on the output entropy of a maximally entangled input state

inequalities between entropy and index of coincidence derived from information diagrams to any discrete probability distribution p we can associate its entropy h p spl sigma p sub i ln p sub i and its index of coincidence ic p spl sigma p sub i sup 2 the main result of the paper is the determination of the precise range of the map p spl rarr ic p h p the range looks much like that of the map p spl rarr p sub max h p where p sub max is the maximal point probability cf research from 1965 kovalevskij 1965 to 1994 feder and merhav 1994 the earlier results which actually focus on the probability of error 1 p sub max rather than p sub max can be conceived as limiting cases of results obtained by methods presented here ranges of maps as those indicated are called information diagrams the main result gives rise to precise lower as well as upper bounds for the entropy function some of these bounds are essential for the exact solution of certain problems of universal coding and prediction for bernoulli sources other applications concern shannon theory relations between various measures of divergence statistical decision theory and rate distortion theory two methods are developed one is topological the other involves convex analysis and is based on a lemma of replacement which is of independent interest in relation to problems of optimization of mixed type concave convex optimization

how to share a quantum secret we investigate the concept of quantum secret sharing in a k n threshold scheme a secret quantum state is divided into n shares such that any k of those shares can be used to reconstruct the secret but any set of k ensuremath 1 or fewer shares contains absolutely no information about the secret we show that the only constraint on the existence of threshold schemes comes from the quantum no cloning theorem which requires that nl2k and we give efficient constructions of all threshold schemes we also show that for k ensuremath le nl2k ensuremath 1 then any k n threshold scheme must distribute information that is globally in a mixed state

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

the maximally entangled set of 4 qubit states entanglement is a resource to overcome the natural restriction of operations used for state manipulation to local operations assisted by classical communication locc hence a bipartite maximally entangled state is a state which can be transformed deterministically into any other state via locc in the multipartite setting no such state exists there rather a whole set the maximally entangled set of states mes which we recently introduced is required this set has on the one hand the property that any state outside of this set can be obtained via locc from one of the states within the set and on the other hand no state in the set can be obtained from any other state via locc recently we studied locc transformations among pure multipartite states and derived the mes for three and generic four qubit states here we consider the non generic four qubit states and analyze their properties regarding local transformations as already the most coarse grained classification due to stochastic locc slo

maximum and minimum entropy states yielding local continuity bounds given an arbitrary quantum state we obtain an explicit construction of a state e respectively e which has the maximum respectively minimum entropy among all states which lie in a specified neighborhood e ball of computing the entropy of these states leads to a local strengthening of the continuity bound of the von neumann entropy i e the audenaert fannes inequality our bound is local in the sense that it depends on the spectrum of the states e and e depend only on the geometry of the e ball and are in fact optimizers for a larger class of entropies these include the renyi entropy and the minimum and maximum entropies providing explicit formulas for certain smoothed quantities this allows us to obtain local continuity bounds for these quantities as well in obtaining this bound we first derive a more general result which may be of independent interest namely a necessary and sufficient condition under which a state maximizes a concave

relations for certain symmetric norms and anti norms before and after partial trace changes of some unitarily invariant norms and anti norms under the operation of partial trace are examined the norms considered form a two parametric family including both the ky fan and schatten norms as particular cases the obtained results concern operators acting on the tensor product of two finite dimensional hilbert spaces for any such operator we obtain upper bounds on norms of its partial trace in terms of the corresponding dimensionality and norms of this operator similar inequalities but in the opposite direction are obtained for certain anti norms of positive matrices through the stinespring representation the results are put in the context of trace preserving completely positive maps we also derive inequalities between the unified entropies of a composite quantum system and one of its subsystems where traced out dimensionality is involved as well

monogamy equality in 2 2 d quantum systems there is an interesting property about multipartite entanglement called the monogamy of entanglement the property can be shown by the monogamy inequality called the coffman kundu wootters inequality phys rev a 61 052306 2000 coffman kundu woottersphys rev lett 96 220503 2006 and more explicitly by the monogamy equality in terms of the concurrence and the concurrence of assistance ca bc 2 cab2 caca 2 in the three qubit system in this paper we consider the monogamy equality in 2 2 d quantum systems we show that ca bc cab if and only if caca 0 and also show that if ca bc caca then cab 0 while there exists a state in a 2 2 d system such that cab 0 but ca bc caca

the rebit three tangle and its relation to two qubit entanglement the three tangle is a measure of three way entanglement in a system of three qubits for a pure state it can be understood as the residual entanglement not accounted for by pairwise entanglements between individual qubits here we define and evaluate the analogous quantity for three rebits that is binary systems in the real amplitude variant of quantum theory we find that the resulting formula is the same as in the complex case except that an overall absolute value sign is missing as a result the rebit three tangle can be negative expressing the possibility of non monogamous entanglement in real amplitude quantum theory for entanglement based on the convex roof construction we then relate the entanglement among three rebits to the entanglement of two qubits by re expressing the two qubit state as a three rebit state in the ubit model this article is part of a special issue of journal of physics a mathematical and theoretical devoted to 50 years of bell s theorem

strong monogamy conjecture for multiqubit entanglement the four qubit case we investigate the distribution of bipartite and multipartite entanglement in multiqubit states in particular we define a set of monogamy inequalities sharpening the conventional coffman kundu wootters constraints and we provide analytical proofs of their validity for relevant classes of states we present extensive numerical evidence validating the conjectured strong monogamy inequalities for arbitrary pure states of four qubits

dual monogamy inequality for entanglement we establish duality for monogamy of entanglement whereas monogamy of entanglement inequalities provide an upper bound for bipartite sharability of entanglement in a multipartite system as quantified by linear entropy we prove that the same quantity namely linear entropy provides a lower bound for distribution of bipartite entanglement in a multipartite system our theorem for monogamy of entanglement is used to establish relations between bipartite entanglement that separate one qubit from the rest versus separating two qubits from the rest

analytical and numerical study of travelling waves using the maxwell cattaneo relaxation model extended to reaction advection diffusion systems within the framework of the maxwell cattaneo relaxation model extended to reaction diffusion systems with nonlinear advection travelling wave tw solutions are analytically investigated by studying a normalized reaction telegraph equation in the case of the reaction and advection terms described by quadratic functions the problem involves two governing parameters i a ratio ensuremath varphi 2 of the relaxation time in the maxwell cattaneo model to the characteristic time scale of the reaction term and ii the normalized magnitude n of the advection term by linearizing the equation at the leading edge of the tw i necessary conditions for the existence of tw solutions that are smooth in the entire interval of ensuremath ensuremath infty l ensuremath zeta l ensuremath infty are obtained ii the smooth tw speed is shown to be less than the maximal speed ensuremath varphi ensuremath 1 of the propagation of a substance iii the lowest tw speed as a function of ensuremath varphi and n is determined if the necessary condition of ng ensuremath varphi ensuremath ensuremath varphi ensuremath 1 does not hold e g if the magnitude n of the nonlinear advection is insufficiently high in the case of ensuremath varphi 2 g1 then the studied equation admits piecewise smooth tw solutions with sharp leading fronts that propagate at the maximal speed ensuremath varphi ensuremath 1 with the substance concentration or its spatial derivative jumping at the front an increase in n can make the solution smooth in the entire spatial domain moreover an explicit tw solution to the considered equation is found provided that ng ensuremath varphi subsequently by invoking a principle of the maximal decay rate of tw solution at its leading edge relevant tw solutions are selected in a domain of ensuremath varphi n that admits the smooth tws application of this principle to the studied problem yields transition from pulled propagation speed is controlled by the tw leading edge to pushed propagation speed is controlled by the entire tw structure tw solutions at n n mathrm cr sqrt 1 ensuremath varphi 2 with the pulled pushed tw being relevant at smaller larger n an increase in the normalized relaxation time ensuremath varphi 2 results in increasing n mathrm cr thus promoting the pulled tw solutions the domains of ensuremath varphi n that admit either the smooth or piecewise smooth tws are not overlapped and therefore the selection problem does not arise for these two types of solutions all the aforementioned results and in particular the maximal decay rate principle or appearance of the piecewise smooth tw solutions are validated by numerically solving the initial boundary value problem for the reaction telegraph equation with natural initial conditions localized to a bounded spatial region

quantum codes of minimum distance two it is reasonable to expect the theory of quantum codes to be simplified in the case of codes of minimum distance 2 thus it makes sense to examine such codes in the hopes that techniques that prove effective there will generalize with this in mind we present a number of results on codes of minimum distance 2 we first compute the linear programming bound on the dimension of such a code then show that this bound can only be attained when the code either is of even length or is of length 3 or 5 we next consider questions of uniqueness showing that the optimal code of length 2 or 1 is unique implying that the well known one qubit in five single error correcting code is unique and presenting nonadditive optimal codes of all greater even lengths finally we compute the full automorphism group of the more important distance 2 codes allowing us to determine the full automorphism group of any gf 4 linear code

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

monogamy of multi qubit entanglement using renyi entropy we introduce a class of bipartite entanglement measures based on renyi entropy namely renyi entanglement with an analytic formula in two qubit systems for 1 we also show that multi qubit entanglement has a monogamy inequality in terms of renyi entanglement for all 2

central ideals and cartan invariants of symmetric algebras in this paper we investigate certain ideals in the center of a symmetric algebra a over an algebraically closed field of characteristic p 0 these ideals include the higman ideal and the reynolds ideal they are closely related to the p power map on a we generalize some results concerning these ideals from group algebras to symmetric algebras and we obtain some new results as well in case p 2 these ideals detect odd diagonal entries in the cartan matrix of a in a sequel to this paper we will apply our results to group algebras

a note on discontinuity waves in type iii thermoelasticity two recent nonlinear theories of thermoelasticity developed by green and naghdi are examined it is shown that in type ii theory second sound is permissible and both mechanical and temperature waves may propagate in type iii theory we show that the situation is more analogous to that in classical nonlinear thermoelasticity one wave propagates and a homothermal temperature wave is allowed

blocks of defect zero and products of elements of orderp abstract suppose thatgis a finite group and thatfis a field of characteristicp 0 which is a splitting field for all subgroups ofg lete0be the sum of the block idempotents of defect zero infg and let be the set of solutions togp 1 ing we show thate0 2 whenpis odd ande0 3 whenp 2 in the latter case 2 r whereris the set of real elements of 2 defect zero soe0 r r 2 we also show thate0 4 4 2 whenp 2 where 4is the set of solutions tog4 1 these results give us various criteria for the existence ofp blocks of defect zero

a stronger entanglement monogamy inequality in a 2 2 3 system in this paper we prove a stronger entanglement monogamy inequality in a 2 2 3 system s pure state abc specifically we show that the linear entropy of a which is the entanglement between a and bc is always larger than the sum of the square of concurrence between a and b and the square of concurrence of assistance between a and c our proof is based on direct generalizations of the qubit system s results our inequality is stronger than the known monogamy inequality of concurrence and shows that the entanglement of assistance always comes from the existing entanglement however our inequality also shows that unlike the three qubit case in higher dimensional systems the entanglement between a and bc cannot be completely transformed into bipartite entanglement with assistance through our proof we also give some cases when the inequality reduces to an equality

almost all multipartite qubit quantum states have trivial stabilizer the stabilizer group of an n qubit state is the set of all matrices of the form g g1 gn with g1 gn being any 2 2 invertible complex matrices that satisfy g we show that for 5 or more qubits except for a set of states of zero measure the stabilizer group of multipartite entangled states is trivial that is containing only the identity element we use this result to show that for 5 or more qubits the action of deterministic local operations and classical communication locc can almost always be simulated simply by local unitary lu operations this proves that almost all n qubit states with n 5 can neither be reached nor be converted into any other n partite entangled lu inequivalent state via deterministic locc we also find a simple and elegant expression for the maximal probability to convert one multi qubit entangled state to another for this generic set of states the stabilizer group of an n qubit state is the set of all matrices of the form g g1 gn with g1 gn being any 2 2 invertible complex matrices that satisfy g we show that for 5 or more qubits except for a set of states of zero measure the stabilizer group of multipartite entangled states is trivial that is containing only the identity element we use this result to show that for 5 or more qubits the action of deterministic local operations and classical communication locc can almost always be simulated simply by local unitary lu operations this proves that almost all n qubit states with n 5 can neither be reached nor be converted into any other n partite entangled lu inequivalent state via deterministic locc we also find a simple and elegant expression for the maximal probability to convert one multi qubit entangled state to another for this generic set of states

cartan invariants and central ideals of group algebras abstract in this paper we investigate general properties of cartan invariants of a finite group g in characteristic 2 one of our results shows that the cartan matrix of g in characteristic 2 contains an odd diagonal entry if and only if g contains a real element of 2 defect zero we also apply these results to 2 blocks of symmetric groups and to blocks with normal or abelian defect groups the second part of the paper deals with annihilators of certain ideals in centers of group algebras and blocks

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

generalized w class state and its monogamy relation we generalize the w class of states from n qubits to n qudits and prove that their entanglement is fully characterized by their partial entanglements even for the case of the mixture that consists of a w class state and a product state

the role of constraints within generalized nonextensive statistics the gibbs jaynes path for introducing statistical mechanics is based on the adoption of a specific entropic form sand of physically appropriate constraints for instance for the usual canonical ensemble one adopts i ii ipi 1 and iii ei eigenvalues of the hamiltonian u1 internal energy equilibrium consists in optimizing s1 with regard to pi in the presence of constraints ii and iii within the recently introduced nonextensive statistics i is generalized into sq k 1 ipiq q 1 q 1 reproduces s1 ii is maintained and iii is generalized in a manner which might involve piq in the present effort we analyze the consequences of some special choices for iii and their formal and practical implications for the various physical systems that have been studied in the literature to illustrate some mathematically relevant points we calculate the specific heat respectively associated with a nondegenerate two level system as well as with the classical and quantum harmonic oscillators