uniformity of quantum circuit families for error free algorithms in order to establish the computational equivalence between quantum turing machines qtms and quantum circuit families qcfs using yao s quantum circuit simulation of qtms we have previously introduced the class of uniform qcfs based on an infinite set of elementary gates which has been shown to be computationally equivalent to polynomial time qtms up to bounded error simulation however the complexity classes zqp and eqp introduced by bernstein and vazirani for qtms do not appear to equal their counterparts for uniform qcfs recently we have introduced a subclass of uniform qcfs the class of finitely generated uniform qcfs and showed that they are perfectly equivalent to the class of polynomial time qtms in the sense that both classes can be exactly simulated with each other here we further investigate the power of uniform qcfs comparing with that of finitely generated uniform qcfs in detail we obtain the following results i if a permutation mf x f x can be implemented with zero error by a uniform qcf then both f and f 1 can be exactly computed by uniform qcfs ii the quantum fourier transform qft of any order cannot be implemented with zero error by any finitely generated uniform qcf while it has been shown in contrast by mosca and zalka that the qft of any order can be exactly implemented by a uniform qcf

characterization of entanglement transformation via group representation theory entanglement transformation of composite quantum systems is investigated in the context of group representation theory representation of the direct product group sl 2 c sl 2 c composed of local operators acting on the binary composite system is realized in the four dimensional complex space in terms of a set of novel bases that are pseudo orthonormalized the two to one homomorphism is then established for the group sl 2 c sl 2 c onto the so 4 c it is shown that the resulting representation theory leads to the complete characterization for the entanglement transformation of the binary composite system

presence of quantum correlations results in a nonvanishing ergotropic gap the paradigm of extracting work from an isolated quantum system through a cyclic hamiltonian process is a topic of immense research interest the optimal work extracted under such a process is termed ergotropy europhys lett 67 565 2004 here in a multiparty scenario we consider only a class of such cyclic processes that can be implemented locally giving rise to the concept of local ergotropy eventually the presence of quantum correlations results in a nonvanishing thermodynamic quantity called an ergotropic gap measured by the difference between global and local ergotropy however the converse does not hold in general i e its nonzero value does not necessarily imply the presence of quantum correlations for arbitrary multiparty states we quantify this gap we also evaluate the difference between maximum global and local extractable work for arbitrary states when the system is no longer isolated but put in contact with a bath of the same local temperature

local distinguishability of quantum states in infinite dimensional systems we investigate local distinguishability of quantum states by use of convex analysis of joint numerical range of operators on a hilbert space we show that any two orthogonal pure states are distinguishable by local operations and classical communications even for infinite dimensional systems an estimate of the local discrimination probability is also given for some families of more than two pure states

partial recovery of quantum entanglement suppose alice and bob try to transform an entangled state shared between them into another one by local operations and classical communications then in general a certain amount of entanglement contained in the initial state will decrease in the process of transformation however an interesting phenomenon called partial entanglement recovery shows that it is possible to recover some amount of entanglement by adding another entangled state and transforming the two entangled states collectively in this paper we are mainly concerned with the feasibility of partial entanglement recovery the basic problem we address is whether a given state is useful in recovering entanglement lost in a specified transformation in the case where the source and target states of the original transformation satisfy the strict majorization relation a necessary and sufficient condition for partial entanglement recovery is obtained for the general case we give two sufficient conditions we also give an efficient algorithm for the feasibility of partial entanglement recovery in polynomial time as applications we establish some interesting connections between partial entanglement recovery and the generation of maximally entangled states quantum catalysis mutual catalysis and multiple copy entanglement transformation

a statistical rainfall runoff mixture model with heavy tailed components 1 we present a conditional density model of river runoff given covariate information which includes precipitation at four surrounding stations the proposed model is nonparametric in the central part of the distribution and relies on extreme value theory parametric assumptions for the upper tail of the distribution from the trained conditional density model we can compute quantiles of various levels the median can serve to simulate river runoff quantiles of level 5 and 95 can be used to form a 90 confidence interval and finally extreme quantiles can estimate the probability of large runoff the conditional density model is based on a mixture of hybrid paretos the hybrid pareto is built by stitching a truncated gaussian with a generalized pareto distribution the mixture is made conditional by considering its parameters as functions of covariates a neural network is used to implement those functions a penalty term on the tail indexes is added to the conditional log likelihood to guide the maximum likelihood estimator toward solutions that are preferred this alleviates the difficulties encountered with the maximum likelihood estimator of the tail index on small training sets we evaluate the proposed model on rainfall runoff data from the orgeval basin in france the effect of the tail penalty is further illustrated on synthetic data

a phenomenon of reciprocity in the universal steenrod algebra we compute the cohomology algebra of certain subalgebras l r and certain quotients k s of the mod 2 universal steenrod algebra q the algebra of cohomology operations for h ring spectra we prove that ext l 7b hr f 2 f 2 k k 1 ext k 7b hs f 2 f 2 l s 1 with r s integers and r 1 s 0 we also observe that some of the algebras l r k s are well known objects in stable homotopy theory and in fact our computation generalizes the fact h a l opp and h opp a l here a l is the steenrod algebra for simplicial restricted lie algebras and is the e 1 term of the adams spectral sequence

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

a k nearest neighbor simulator for daily precipitation and other weather variables a multivariate nonparametric time series simulation method is provided to generate random sequences of daily weather variables that honor the statistical properties of the historical data of the same weather variables at the site a vector of weather variables solar radiation maximum temperature minimum temperature average dew point temperature average wind speed and precipitation on a day of interest is resampled from the historical data by conditioning on the vector of the same variables feature vector on the preceding day the resampling is done from the k nearest neighbors in state space of the feature vector using a weight function this approach is equivalent to a nonparametric approximation of a multivariate lag 1 markov process it does not require prior assumptions as to the form of the joint probability density function of the variables an application of the resampling scheme with 30 years of daily weather data at salt lake city utah is provided results are compared with those from the application of a multivariate autoregressive model similar to that of richardson 1981

relative submajorization and its use in quantum resource theories we introduce and study a generalization of majorization called relative submajorization and show that it has many applications to the resource theories of thermodynamics bipartite entanglement and quantum coherence relative majorization is an ordering on pairs of vectors induced by stochastic transformations one pair of vectors relatively majorizes another when there exists a stochastic transformation taking the former to the latter relative submajorization is a weakened version in which a substochastic matrix need only generate a vector pair obeying certain positivity conditions relative to the input pair in the context of resource theories we show that the relative submajorization characterizes both the probability and approximation error that can be obtained when transforming one resource to another also when assisted by additional standard resources such as useful work or maximally entangled states these characterizations have a geometric formulation as the ratios or differences respectively between the lorenz curves associated with the input and output resources making them efficient to compute we also find several interesting bounds on the reversibility of a given transformation in terms of the properties of the forward transformation the main technical tool used to establish these results is the linear programming duality which is used to show that any instance of relative submajorization can be dilated to an instance of strict relative majorization we introduce and study a generalization of majorization called relative submajorization and show that it has many applications to the resource theories of thermodynamics bipartite entanglement and quantum coherence relative majorization is an ordering on pairs of vectors induced by stochastic transformations one pair of vectors relatively majorizes another when there exists a stochastic transformation taking the former to the latter relative submajorization is a weakened version in which a substochastic matrix need only generate a vector pair obeying certain positivity conditions relative to the input pair in the context of resource theories we show that the relative submajorization characterizes both the probability and approximation error that can be obtained when transforming one resource to another also when assisted by additional standard resources such as useful work or maximally entangled states these characterizations have a geometric formulation as the ratios or differences respectively

the second laws of quantum thermodynamics the second law of thermodynamics places constraints on state transformations it applies to systems composed of many particles however we are seeing that one can formulate laws of thermodynamics when only a small number of particles are interacting with a heat bath is there a second law of thermodynamics in this regime here we find that for processes which are approximately cyclic the second law for microscopic systems takes on a different form compared to the macroscopic scale imposing not just one constraint on state transformations but an entire family of constraints we find a family of free energies which generalize the traditional one and show that they can never increase the ordinary second law relates to one of these with the remainder imposing additional constraints on thermodynamic transitions we find three regimes which determine which family of second laws govern state transitions depending on how cyclic the process is in one regime one can cause an apparent violation of the usual second law through a process of embezzling work from a large system which remains arbitrarily close to its original state these second laws are relevant for small systems and also apply to individual macroscopic systems interacting via long range interactions by making precise the definition of thermal operations the laws of thermodynamics are unified in this framework with the first law defining the class of operations the zeroth law emerging as an equivalence relation between thermal states and the remaining laws being monotonicity of our generalized free energies

streamflow simulation a nonparametric approach in this paper kernel estimates of the joint and conditional probability density functions are used to generate synthetic streamflow sequences streamflow is assumed to be a markov process with time dependence characterized by a multivariate probability density function kernel methods are used to estimate this multivariate density function simulation proceeds by sequentially resampling from the conditional density function derived from the kernel estimate of the underlying multivariate probability density function this is a nonparametric method for the synthesis of streamflow that is data driven and avoids prior assumptions as to the form of dependence e g linear or nonlinear and the form of the probability density functions e g gaussian we show using synthetic examples with known underlying models that the nonparametric method presented is more flexible than the conventional models used in stochastic hydrology and is capable of reproducing both linear and nonlinear dependence the effectiveness of this model is illustrated through its application to simulation of monthly streamflow from the beaver river in utah

the asymptotic spectrum of locc transformations we study the exact non deterministic conversion of multipartite pure quantum states into one another via local operations and classical communication locc and asymptotic entanglement transformation under such channels in particular we consider the maximal number of copies of any given target state that can be extracted exactly from many copies of any given initial state as a function of the exponential decay in the success probability known as the converse error exponent we give a formula for the optimal rate presented as an infimum over the asymptotic spectrum of locc conversion a full understanding of exact asymptotic extraction rates between pure states in the converse regime thus depends on a full understanding of this spectrum we present a characterization of spectral points and use it to describe the spectrum in the bipartite case this leads to a full description of the spectrum and thus an explicit formula for the asymptotic extraction rate between pure bipartite states given a converse error exponent this extends the result on entanglement concentration in 1 where the target state is fixed as the bell state in the limit of vanishing converse error exponent the rate formula provides an upper bound on the exact asymptotic extraction rate between two states when the probability of success goes to 1 in the bipartite case we prove that this bound holds with equality

on the units of bipartite entanglement is sixteen ounces of entanglement always equal to one pound in a good physical theory dimensionless quantities such as the ratio mp me of the mass of the proton to the mass of the electron do not depend on the system of units being used this paper demonstrates that one widely used method for defining measures of entanglement violates this principle specifically in this approach dimensionless ratios e e of entanglement measures may depend on what state is chosen as the basic unit of entanglement this observation leads us to suggest three novel approaches to the quantification of entanglement these approaches lead to unit free definitions for the entanglement of formation and the distillable entanglement and suggest natural measures of entanglement for multipartite systems we also show that the behaviour of one of these novel measures the entanglement of computation is related to some open problems in computational complexity

effective and efficient global optimization for conceptual rainfall runoff models the successful application of a conceptual rainfall runoff crr model depends on how well it is calibrated despite the popularity of crr models reports in the literature indicate that it is typically difficult if not impossible to obtain unique optimal values for their parameters using automatic calibration methods unless the best set of parameters associated with a given calibration data set can be found it is difficult to determine how sensitive the parameter estimates and hence the model forecasts are to factors such as input and output data error model error quantity and quality of data objective function used and so on results are presented that establish clearly the nature of the multiple optima problem for the research crr model sixpar these results suggest that the crr model optimization problem is more difficult than had been previously thought and that currently used local search procedures have a very low probability of successfully finding the optimal parameter sets next the performance of three existing global search procedures are evaluated on the model sixpar finally a powerful new global optimization procedure is presented entitled the shuffled complex evolution sce ua method which was able to consistently locate the global optimum of the sixpar model and appears to be capable of efficiently and effectively solving the crr model optimization problem

the role of singular values in single copy entanglement manipulations and unambiguous state discrimination unambiguous non orthogonal state discrimination usd has a fundamental importance in quantum information and quantum cryptography various aspects of two state and multiple state usd are studied here using singular value decomposition of the evolution operator that describes a given state discriminating system in particular we relate the minimal angle between states to the ratio of the minimal and maximal singular values this is supported by a simple geometrical picture in two state usd furthermore by studying the singular vectors population we find that the minimal angle between input vectors in multiple state usd is always larger than the minimal angle in two state usd in the same system as an example we study what pure states can be probabilistically transformed into maximally entangled pure states in a given system

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

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

extending a characterization of majorization to infinite dimensions abstract we consider recent work linking majorization and trumping two partial orders that have proven useful with respect to the entanglement transformation problem in quantum information with general dirichlet polynomials mellin transforms and completely monotone sequences we extend a basic majorization result to the more physically realistic infinite dimensional setting through the use of generalized dirichlet series and riemann stieltjes integrals

a resource framework for quantum shannon theory quantum shannon theory is loosely defined as a collection of coding theorems such as classical and quantum source compression noisy channel coding theorems entanglement distillation etc which characterize asymptotic properties of quantum and classical channels and states in this paper we advocate a unified approach to an important class of problems in quantum shannon theory consisting of those that are bipartite unidirectional and memoryless

α z renyi relative entropies we consider a two parameter family of renyi relative entropies d z that are quantum generalisations of the classical renyi divergence d p q this family includes many known relative entropies or divergences such as the quantum relative entropy the recently defined quantum renyi divergences as well as the quantum renyi relative entropies all its members satisfy the quantum generalizations of renyi s axioms for a divergence we consider the range of the parameters z for which the data processing inequality holds we also investigate a variety of limiting cases for the two parameters obtaining explicit formulas for each one of them

catalytic transformations for bipartite pure states entanglement catalysis is a phenomenon that usually enhances the conversion probability in the transformation of entangled states by the temporary involvement of another entangled state so called catalyst where after the process is completed the catalyst is returned to the same state for some pairs of bipartite pure entangled states catalysis enables a transformation with unit probability of success in which case the respective schmidt coefficients of the states are said to satisfy the trumping relation a mathematical relation which is an extension of the majorization relation this paper provides all necessary and sufficient conditions for the trumping and two other associated relations using these conditions the least upper bound of conversion probabilities using catalysis is also obtained moreover best conversion ratios achievable with catalysis are found for transformations involving many copies of states

a nearest neighbor bootstrap for resampling hydrologic time series a nonparametric method for resampling scalar or vector valued time series is introduced multivariate nearest neighbor probability density estimation provides the basis for the resampling scheme developed the motivation for this work comes from a desire to preserve the dependence structure of the time series while bootstrapping resampling it with replacement the method is data driven and is preferred where the investigator is uncomfortable with prior assumptions as to the form e g linear or nonlinear of dependence and the form of the probability density function e g gaussian such prior assumptions are often made in an ad hoc manner for analyzing hydrologic data connections of the nearest neighbor bootstrap to markov processes as well as its utility in a general monte carlo setting are discussed applications to resampling monthly streamflow and some synthetic data are presented the method is shown to be effective with time series generated by linear and nonlinear autoregressive models the utility of the method for resampling monthly streamflow sequences with asymmetric and bimodal marginal probability densities is also demonstrated

self catalytic conversion of pure quantum states conversion of entangled states under stochastic local operations and classical communication s locc admits the phenomenon of catalysis here we explore the possibility of a copy of the initial state itself performing as a catalyst which we call a self catalytic process we show explicit examples of self catalysis necessary and sufficient conditions for the phenomenon to take place are discussed we numerically estimate how frequent it is and we show that increasing the number of copies used as catalyst can increase the probability of conversion but does not make the process deterministic by the end we conjecture that under locc the probability of finding a self catalytic reaction does not increase monotonically with the dimensions whereas under slocc it does increase

passivity complete passivity and virtual temperatures we give a simple and intuitive proof that the only states which are completely passive i e those states from which work cannot be extracted even with infinitely many copies are gibbs states at positive temperatures the proof makes use of the idea of virtual temperatures i e the association of temperatures to pairs of energy levels transitions we show that 1 passive states are those where every transition is at a positive temperature and 2 completely passive states are those where every transition is at the same positive temperature

on the homology spectral sequence for topological hochschild homology marcel b6kstedt has computed the homotopy type of the topological hochschild homology of z p using his definition of topological hochschild homology for a functor with smash product here we show that easy conceptual proofs of his main technical result of are possible in the context of the homotopy theory of s algebras as introduced by elmendorf kriz mandell and may we give algebraic arguments based on naturality properties of the topological hochschild homology spectral sequence in the process we demonstrate the utility of the unstable lower notation for the dyer lashof algebra

single site monthly streamflow simulation using entropy theory 1 using entropy theory a new method for single site monthly streamflow simulation is developed which is capable of preserving mean standard deviation skewness and lag one correlation the method entails deriving joint and conditional probability density functions using the entropy theory determining the lagrange multipliers using the information obtained from the historical record and then simulating streamflow by sequential sampling from the conditional distribution the advantage of the entropy based method is that it does not make any assumptions about the probability distribution of the streamflow data it can also preserve the cross correlation between streamflow of the last month of the previous year and the first month of the current year and avoid the generation of negative values the method can also be extended to incorporate higher order moments and more lag correlations if needed the disadvantage is that the method will be cumbersome when more statistics need to be preserved and the bimodality that may exist in the empirical probability density function cannot yet be resolved application to the colorado river basin shows that the entropy based method satisfactorily simulates monthly streamflow

error exponents for entanglement concentration consider entanglement concentration schemes that convert n identical copies of a pure state into a maximally entangled state of a desired size with success probability being close to one in the asymptotic limit we give the distillable entanglement the number of bell pairs distilled per copy as a function of an error exponent which represents the rate of decrease in failure probability as n tends to infinity the formula fills the gap between the least upper bound of distillable entanglement in probabilistic concentration which is the well known entropy of entanglement and the maximum attained in deterministic concentration the method of types in information theory enables the detailed analysis of the distillable entanglement in terms of the error rate in addition to the probabilistic argument we consider another type of entanglement concentration scheme where the initial state is deterministically transformed into a possibly mixed final state whose fidelity to a maximally entangled state of a desired size converges to one in the asymptotic limit we show that the same formula as in the probabilistic argument is valid for the argument on fidelity by replacing the success probability with the fidelity furthermore we also discuss entanglement yield when optimal success probability or optimal fidelity converges to zero in the asymptotic limit strong converse and give the explicit formulae for those cases

the minimum entropy output of a quantum channel is locally additive we show that the minimum von neumann entropy output of a quantum channel is locally additive hastings counterexample for the additivity conjecture makes this result quite surprising in particular it indicates that the nonadditivity of the minimum entropy output is a global effect of quantum channels

time reversal frameness and superselection we show that appropriate superpositions of motional states are a reference frame resource that enables breaking of time reversal superselection so that two parties lacking knowledge about the other s direction of time can still communicate we identify the time reversal reference frame resource states and determine the corresponding frameness monotone which connects time reversal frameness to entanglement in contradistinction to other studies of reference frame quantum resources this is the first analysis that involves an antiunitary rather than unitary representation

general entanglement assisted transformation for bipartite pure quantum states we introduce the general catalysts for pure entanglement transformations under local operations and classical communications in such a way that we disregard the profit and loss of entanglement of the catalysts per se as such the possibilities of pure entanglement transformations are greatly expanded we also design an efficient algorithm to detect whether a k k general catalyst exists for a given entanglement transformation this algorithm can also be exploited to witness the existence of standard catalysts

matrix pencils and entanglement classification quantum entanglement plays a central role in quantum information processing a main objective of the theory is to classify different types of entanglement according to their interconvertibility through manipulations that do not require additional entanglement to perform while bipartite entanglement is well understood in this framework the classification of entanglements among three or more subsystems is inherently much more difficult in this paper we study pure state entanglement in systems of dimension 2 m n two states are considered equivalent if they can be reversibly converted from one to the other with a nonzero probability using only local quantum resources and classical communication slocc we introduce a connection between entanglement manipulations in these systems and the well studied theory of matrix pencils all previous attempts to study general slocc equivalence in such systems have relied on somewhat contrived techniques which fail to reveal the elegant structure of the problem that

two component mixtures of normal gamma and gumbel distributions for hydrological applications 1 whether mixtures of distributions are employed as a flexible modeling device to estimate densities or are used to model data thought to arise from several populations they provide an efficient tool to approximate a distribution indeed mixtures of distributions can model multiple modes different types of skewness etc but they can also be employed to classify observations from heterogeneous data sets in this paper we study mixtures of distributions with normal gamma and gumbel components moving away from the standard normal setting gamma mixtures are developed in order to model strictly positive hydrological data and gumbel mixtures for extreme variates since the data analyzed can exhibit dependency through time we treat both the independent and dependent cases where the latter is modeled through a markov process a fairly unified approach is adopted for the different distributions and the problem is treated from the bayesian perspective which enables us to use marginal densities to automatically compare the adequacy of the different models for a given data set this model selection framework allows us to formally test the relevance of using mixture models by computing the marginal likelihoods of single distribution models and to verify the presence of a persistence in the time series by comparing independent and identically distributed iid and markovian mixture models

entanglement entropy of non unitary conformal field theory here we show that the renyi entanglement entropy of a region of large size l in a one dimensional critical model whose ground state breaks conformal invariance such as in those described by non unitary conformal field theories behaves as ceff n 1 2n log l where ceff c 24delta 0 is the effective central charge c which may be negative is the central charge of the conformal field theory and delta 0 is the lowest holomorphic conformal dimension in the theory we also obtain results for models with boundaries and with a large but finite correlation length and we show that if the lowest conformal eigenspace is logarithmic then there is an additional term proportional to log log l these results generalize the well known expressions for unitary models we provide a general proof and report on numerical evidence for a non unitary spin chain and an analytical computation using the corner transfer matrix method for a non unitary lattice model we use a new algebraic technique for studying the branching that arises within the replica approach and find a new expression for the entanglement entropy in terms of correlation functions of twist fields for non unitary models

tripartite to bipartite entanglement transformation by stochastic local operations and classical communication and the structure of matrix spaces we study the problem of transforming a tripartite pure state to a bipartite one using stochastic local operations and classical communication slocc it is known that the tripartite to bipartite slocc convertibility is characterized by the maximal schmidt rank of the given tripartite state i e the largest schmidt rank over those bipartite states lying in the support of the reduced density operator in this paper we further study this problem and exhibit novel results in both multi copy and asymptotic settings utilizing powerful results from the structure of matrix spaces in the multi copy regime we observe that the maximal schmidt rank is strictly super multiplicative i e the maximal schmidt rank of the tensor product of two tripartite pure states can be strictly larger than the product of their maximal schmidt ranks we then provide a full characterization of those tripartite states whose maximal schmidt rank is strictly super multiplicative when taking tensor product with itself notice that such tripartite states admit strict advantages in tripartite to bipartite slocc transformation when multiple copies are provided in the asymptotic setting we focus on determining the tripartite to bipartite slocc entanglement transformation rate computing this rate turns out to be equivalent to computing the asymptotic maximal schmidt rank of the tripartite state defined as the regularization of its maximal schmidt rank despite the difficulty caused by the super multiplicative property we provide explicit formulas for evaluating the asymptotic maximal schmidt ranks of two important families of tripartite pure states by resorting to certain results of the structure of matrix spaces including the study of matrix semi invariants these formulas turn out to be powerful enough to give a sufficient and necessary condition to determine whether a given tripartite pure state can be transformed to the bipartite maximally entangled state under slocc in the asymptotic setting applying the recent progress on the non commutative rank problem we can verify this condition in deterministic polynomial time

on quantum renyi entropies a new generalization and some properties the renyi entropies constitute a family of information measures that generalizes the well known shannon entropy inheriting many of its properties they appear in the form of unconditional and conditional entropies relative entropies or mutual information and have found many applications in information theory and beyond various generalizations of renyi entropies to the quantum setting have been proposed most prominently petz s quasi entropies and renner s conditional min max and collision entropy however these quantum extensions are incompatible and thus unsatisfactory we propose a new quantum generalization of the family of renyi entropies that contains the von neumann entropy min entropy collision entropy and the max entropy as special cases thus encompassing most quantum entropies in use today we show several natural properties for this definition including data processing inequalities a duality relation and an entropic uncertainty relation

dirichlet polynomials majorization and trumping majorization and trumping are two partial orders which have proved useful in quantum information theory we show some relations between these two partial orders and generalized dirichlet polynomials mellin transforms and completely monotone functions these relations are used to prove a succinct generalization of turgut s characterization of trumping

entanglement cost of two qubit orthogonal measurements the entanglement cost of a bipartite measurement is the amount of shared entanglement two participants need to use up in order to carry out the given measurement by means of local operations and classical communication we numerically investigate the entanglement cost of generic orthogonal measurements on two qubits our results strongly suggest that for almost all measurements of this kind the entanglement cost is strictly greater than the average entanglement of the eigenstates associated with the measurements implying that the nonseparability of a two qubit orthogonal measurement is generically distinct from the nonseparability of its eigenstates

extremal distributions under approximate majorization although an input distribution may not majorize a target distribution it may majorize a distribution which is close to the target here we consider a notion of approximate majorization for any distribution and given a distance we find the approximate distributions which majorize are majorized by all other distributions within the distance we call these the steepest and flattest approximation this enables one to compute how close one can get to a given target distribution under a process governed by majorization we show that the flattest and steepest approximations preserve ordering under majorization furthermore we give a notion of majorization distance this has applications ranging from thermodynamics entanglement theory and economics

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

a fractal like algebraic splitting of the classifying space for vector bundles the connected covers of the classifying space bo induce a decreasing filtration b of h b o 212 by sub hopf algebras over the steenrod algebra a we describe a multiplicative grading on h b o 212 inducing a direct sum splitting of b over a where a is the usual increasing filtration of a the pieces in the splittings are finite and the grading extends that of h r2s3 which splits it into brown gitler modules we also apply the grading to the thomifications m of b where it induces splittings of the corresponding cobordism modules over the entire steenrod algebra these generalize algebraically the previously known topological splittings of the connective cobordism spectra m o m s o and mspin introduction the classifying space for vector bundles bo is of longstanding interest in topology we will describe a splitting of the mod 2 homology algebra of bo having applications to connective cobordism thom spectra the splitting will be multiplicative in other words it will be fully compatible with whitney sums of vector bundles it differs from other familiar splittings in topology in the way it interacts with the connected covers of bo and the steenrod algebra a of cohomology operations we will explain how this interaction is analogous to the geometric properties of the boundary of the fractal mandelbrot set or m set pr the boundary of the m set has two attributes first patterns become more elaborate upon magnification second patterns visible at one level of magnification actually reappear under further magnification self similarity the second property is mandelbrot s idea of a fractal structure mi while the first is an additional feature of certain fractals like the boundary of the m set our results about certain subalgebras of the algebra h bo over the hopf algebra a reveal precisely these two features specifically consider the decreasing algebra filtration b of h bo provided by the images of the connected covers and the standard increasing hopf algebra filtration a of a where a is generated by the first 2 steenrod squares the analogy to the geometric properties of the boundary of the m set is now made precise by interpreting pattern to mean a multiplicative direct sum splitting of an algebra b over the hopf algebra a magnification as descending in the filtration b and more elaborate as ascending in the filtration a received by the editors may 15 1987 1980 mathematics subject classification 1985 revision primary 55r40 55r45 571390 57t05

stochastic downscaling of precipitation with neural network conditional mixture models 1 we present a new class of stochastic downscaling models the conditional mixture models cmms which builds on neural network models cmms are mixture models whose parameters are functions of predictor variables these functions are implemented with a one layer feed forward neural network by combining the approximation capabilities of mixtures and neural networks cmms can in principle represent arbitrary conditional distributions we evaluate the cmms at downscaling precipitation data at three stations in the french mediterranean region a discrete dirac component is included in the mixture to handle the no rain events positive rainfall is modeled with a mixture of continuous densities which can be either gaussian log normal or hybrid pareto an extension of the generalized pareto cmms are stochastic weather generators in the sense that they provide a model for the conditional density of local variables given large scale information in this study we did not look for the most appropriate set of predictors and we settled for a decent set as the basis to compare the downscaling models the set of predictors includes the national centers for environmental prediction national center for atmospheric research ncep ncar reanalyses sea level pressure fields on a 6 6 grid cell region surrounding the stations plus three date variables we compare the three distribution families of cmms with a simpler benchmark model which is more common in the downscaling community the difference between the benchmark model and cmms is that positive rainfall is modeled with a single gamma distribution the results show that cmm with hybrid pareto components outperforms both the cmm with gaussian components and the benchmark model in terms of log likelihood however there is no significant difference with the log normal cmm in general the additional flexibility of mixture models as opposed to using a single distribution allows us to better represent the distribution of rainfall both in the central part and in the upper tail

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

monotones and invariants for multi particle quantum states we introduce new entanglement monotones which generalize to the case of many parties those which give rise to the majorization based partial ordering of bipartite states entanglement we give some examples of restrictions they impose on deterministic and probabilistic conversion between multipartite states via local actions and classical communication these include restrictions which do not follow from any bipartite considerations we derive supermultiplicativity relations between each state s monotones and the monotones for collective processing when the parties share several states we also investigate polynomial invariants under local unitary transformations and show that a large class of these are invariant under collective unitary processing and also multiplicative putting restrictions for example on the exact conversion of multiple copies of one state to multiple copies of another

exact distribution of the peak streamflow 1 iacobellis and fiorentino 2000 and fiorentino et al 2006 proposed modeling the peak of direct streamflow as a product of two independent random variables one gamma distributed and the other weibull distributed however the papers did not provide any results on the theoretical probability distribution of the peak streamflow in this note we derive explicit expressions for the probability density function cumulative distribution function and the moment measures of the peak streamflow we also show how one could determine the percentiles of the peak streamflow the results of this note could be applied more widely than just for the modeling of peak streamflow

the existence of quantum entanglement catalysts without additional resources it is often impossible to transform one entangled quantum state into another with local quantum operations and classical communication jonathan and plenio phys rev lett vol 83 p 3566 1999 presented an interesting example showing that the presence of another state called a catalyst enables such a transformation without changing the catalyst they also pointed out that in general it is very hard to find an analytical condition under which a catalyst exists in this paper we study the existence of catalysts for two incomparable quantum states for the simplest case of 2 spl times 2 catalysts for transformations from one 4 spl times 4 state to another a necessary and sufficient condition for existence is found for the general case we give an efficient polynomial time algorithm to decide whether a k spl times k catalyst exists for two n spl times n incomparable states where k is treated as a constant

transformations of w type entangled states the transformations of w type entangled states by using local operations assisted with classical communication are investigated for this purpose a parametrization of the w type states which remains invariant under local unitary transformations is proposed and a complete characterization of the local operations carried out by a single party is given these are used for deriving the necessary and sufficient conditions for deterministic transformations a convenient upper bound for the maximum probability of distillation of arbitrary target states is also found

sheared algebra maps and operation bialgebras for mod 2 homology and cohomology the mod 2 steenrod algebraa and dyer lashof al gebra r have both striking similarities and dierences arising from their common origins in lower indexed algebraic operations these algebraic operations and their relations generate a bigraded bialgebrak whose module actions are equivalent to but quite dif ferent from those ofa andr the exact relationships emerge as sheared algebra bijections which also illuminate the role of the cohomology ofk as a bialgebra k has a particularly attractive and potentially useful structure providing a bridge between those ofa andr and suggesting possible applications to the miller spectral sequence and thea structure of dickson algebras

second order asymptotics of conversions of distributions and entangled states based on rayleigh normal probability distributions we discuss the asymptotic behavior of conversions between two independent and identical distributions up to the second order conversion rate when the conversion is produced by a deterministic function from the input probability space to the output probability space to derive the second order conversion rate we introduce new probability distributions named rayleigh normal distributions the family of rayleigh normal distributions includes a rayleigh distribution and coincides with the standard normal distribution in the limit case using this family of probability distributions we represent the asymptotic second order rates for the distribution conversion as an application we also consider the asymptotic behavior of conversions between the multiple copies of two pure entangled states in quantum systems when only local operations and classical communications locc are allowed this problem contains entanglement concentration entanglement dilution and a kind of cloning problem with locc restriction as special cases

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

an entropic analysis of approximate quantum error correction abstract the concept of entropy and the correct application of the second law of thermodynamics are essential in order to understand the reason why quantum error correction is thermodynamically possible and no violation of the second law occurs during its execution we report in this work our first steps towards an entropic analysis extended to approximate quantum error correction qec special emphasis is devoted to the link among quantum state discrimination qsd quantum information gain and quantum error correction in both the exact and approximate qec scenarios

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

catalyst assisted probabilistic entanglement transformation we are concerned with catalyst assisted probabilistic entanglement transformations a necessary and sufficient condition is presented under which there exist partial catalysts that can increase the maximal transforming probability of a given entanglement transformation we also design an algorithm which leads to an efficient method for finding the most economical partial catalysts with minimal dimension the mathematical structure of catalyst assisted probabilistic transformation is carefully investigated

operator monotones the reduction criterion and the relative entropy we introduce the theory of operator monotone functions and employ it to derive a new inequality relating the quantum relative entropy and the quantum conditional entropy we present applications of this new inequality and in particular we prove a new lower bound on the relative entropy of entanglement and other properties of entanglement measures

monthly river flow simulation with a joint conditional density estimation network 1 river flow synthesizing and downscaling are required for the analysis of risks associated with water resources management plans and for regional impact studies of climate change this paper presents a probabilistic model that synthesizes and downscales monthly river flow by estimating the joint distribution of flows of two adjacent months conditional on covariates the covariates may consist of lagged and aggregated flow variables synthesizing exogenous climatic variables downscaling or combinations of these two types the joint distribution is constructed by connecting two marginal distributions in terms of copulas the relationship between covariates and distribution parameters is approximated by an artificial neural network which is calibrated using the principle of maximum likelihood outputs of the neural network yield parameters of the joint distribution from the estimated joint distribution a conditional distribution of river flow of current month given the estimation of the previous month can be derived depending on the different types of covariate information this conditional distribution may serve as the engine for synthesizing or downscaling river flow sequences the idea of the proposed model is illustrated using three case studies the first case deals with synthetic data and shows that the model is capable of fitting a nonstationary joint distribution second the model is utilized to synthesize monthly river flow at four sample stations on the main stream of the colorado river results reveal that the model reproduces essential evaluation statistics fairly well third a simple illustrative example for river flow downscaling is presented analysis indicates that the model can be a viable option to downscale monthly river flow as well

independence of work and entropy for equal energetic finite quantum systems passive state energy as an entanglement quantifier although entropy is a necessary and sufficient quantity to characterize the order of work content for equal energetic ee states in the asymptotic limit for the finite quantum systems the relation is not so linear and requires detailed investigation toward this we have considered a resource theoretic framework taking the energy preserving operations epos as free to compare the amount of extractable work from two different quantum states under the epo majorization becomes a necessary criterion for state transformation it is also shown that the passive state energy is a concave function and for ee states it becomes proportional to the ergotropy in absolute sense invariance of the passive state energy under unitary action on the given state makes it an entanglement measure for the pure bipartite states furthermore due to the nonadditivity of passive state energy for the different system hamiltonians one can generate vidal s monotones which would give the optimal probability for pure entangled state transformation this measure also quantifies the ergotropic gap which is employed to distinguish some specific classes of three qubit pure entangled states

strong converse for the classical capacity of entanglement breaking and hadamard channels via a sandwiched renyi relative entropy a strong converse theorem for the classical capacity of a quantum channel states that the probability of correctly decoding a classical message converges exponentially fast to zero in the limit of many channel uses if the rate of communication exceeds the classical capacity of the channel along with a corresponding achievability statement for rates below the capacity such a strong converse theorem enhances our understanding of the capacity as a very sharp dividing line between achievable and unachievable rates of communication here we show that such a strong converse theorem holds for the classical capacity of all entanglement breaking channels and all hadamard channels the complementary channels of the former these results follow by bounding the success probability in terms of a sandwiched renyi relative entropy by showing that this quantity is subadditive for all entanglement breaking and hadamard channels and by relating this quantity to the holevo capacity prior results regarding strong converse theorems for particular covariant channels emerge as a special case of our results

homology operations on a new infinite loop space boyer et al 1 defined a new infinite loop space structure on the space mo hrni k z 2n such that the total chern class map bu mo is an infinite loop map this is a sort of riemann roch theorem without denominators for example it implies fulton macpherson s theorem that the chern classes of the direct image of a vector bundle e under a given finite covering map are determined by the rank and chern classes of e we compute the dyer lashof operations on the homology of mo they provide a new explanation for kochman s calculation of the operations on the homology of bu and they suggest a possible characterization of the infinite loop structure on mo the total chern class of the direct sum of two vector bundles c e g f is not the sum but rather the product of the total chern classes c e e f c e c f in other words for a topological space x the total chern class map c k x fnl h2n x z is not a homomorphism of abelian groups for the obvious additive group structure on the set ln 1 h2n x z but only for a multiplicative abelian group structure on it let m x 1 hn 1 h2n x z with the appropriate multiplicative group structure since the group kox is the 0th term of a cohomology theory k x 0 connective k theory it is natural to expect that m x is also the 0th term of a cohomology theory m x with the property that the map c k x kox m x extends to a map of cohomology theories k x m x recently boyer lawson lima filho mann and michelsohn 1 defined a cohomology theory m with this property if mo denotes the infinite loop space such that x mo m x then mo fl 1 k z 2n as a space and we know the h space structure on mo it is not the usual h space structure on a product of eilenberg mac lane spaces in this paper we continue the analysis of the infinite loop space mo by computing the araki kudo dyer lashof operations on h mo z p the computation starts with kochman s calculation of these operations on h bu 4 but there is a pleasant side effect to our analysis we only need kochman s calculation in the lowest nontrivial dimension and with that as input the rich structure of mo it is the multiplicative e space which underlies one component of an e ring space allows us to find all the operations on h mo and hence on h bu in particular one could say that the existence of bllmm s theory gives a conceptual explanation for the simplicity of kochman s formulas received by the editors august 20 1993 1991 mathematics subject classification primary 55s12 secondary 55p47 this paper was supported by an nsf postdoctoral fellowship 1995 american mathematical society