tripartite entanglement and quantum relative entropy we establish relations between tripartite pure state entanglement and additivity properties of the bipartite relative entropy of entanglement our results pertain to the asymptotic limit of local manipulations on a large number of copies of the state we show that additivity of the relative entropy would imply that there are at least two inequivalent types of asymptotic tripartite entanglement the methods used include the application of some useful lemmas that enable us to analytically calculate the relative entropy for some classes of bipartite states

iterative simulation methods abstract the standard methods of generating sample from univariate distributions often become hopelessly inefficient when applied to realizations of stochastic processes iterative methods are not widely known amongst statisticians but some are standard practice in statistical physics and chemistry the methods are surveyed and compared with particular reference to their convergence properties

open system trajectories specify fluctuating work but not heat within the framework of the recently developed stochastic thermodynamics fluctuating thermodynamic quantities are introduced this paper examines these quantities for a system coupled to a thermal bath through an arbitrary not necessarily weak interaction the authors conclude that such fluctuating quantities can be defined but not in a unique way

information relative entropy of entanglement and irreversibility previously proposed measures of entanglement such as entanglement of formation and assistance are shown to be special cases of the relative entropy of entanglement the difference between these measures for an ensemble of mixed states is shown to depend on the availability of classical information about particular members of the ensemble based on this relations between relative entropy of entanglement and mutual information are derived

on the relative entropy fora any subset of the bounded operators on a hilbert space containing the unit and and restrictions of states on toa ent a the entropy of relative to given the information ina is defined and given an axiomatic characterisation it is compared with ent the relative entropy introduced by umegaki and generalised by various authors which is defined only fora an algebra it is proved that ent and ent s agree on pairs of normal states on an injective von neumann algebra it is also proved that ent always has all the most important properties known for ent s monotonicity concavity w upper semicontinuity etc

computationally tractable stochastic image modeling based on symmetric markov mesh random fields in this paper the properties of a new class of causal markov random fields named symmetric markov mesh random field are initially discussed it is shown that the symmetric markov mesh random fields from the upper corners are equivalent to the symmetric markov mesh random fields from the lower corners based on this new random field a symmetric corner independent and isotropic image model is then derived which incorporates the dependency of a pixel on all its neighbors the introduced image model comprises the product of several local 1d density and 2d joint density functions of pixels in an image thus making it computationally tractable and practically feasible by allowing the use of histogram and joint histogram approximations to estimate the model parameters an image restoration application is also presented to confirm the effectiveness of the model developed the experimental results demonstrate that this new model provides an improved tool for image modeling purposes compared to the conventional markov random field models

bounds on relative entropy of entanglement for multi party systems we present upper and lower bounds to the relative entropy of entanglement of multi party systems in terms of the bi partite entanglements of formation and distillation and entropies of various subsystems we point out implications of our results to the local reversible convertibility of multi party pure states and discuss their physical basis in terms of deleting information

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

ml parameter estimation for markov random fields with applications to bayesian tomography markov random fields mrfs have been widely used to model images in bayesian frameworks for image reconstruction and restoration typically these mrf models have parameters that allow the prior model to be adjusted for best performance however optimal estimation of these parameters sometimes referred to as hyperparameters is difficult in practice for two reasons i direct parameter estimation for mrfs is known to be mathematically and numerically challenging ii parameters can not be directly estimated because the true image cross section is unavailable we propose a computationally efficient scheme to address both these difficulties for a general class of mrf models and we derive specific methods of parameter estimation for the mrf model known as generalized gaussian mrf ggmrf we derive methods of direct estimation of scale and shape parameters for a general continuously valued mrf for the ggmrf case we show that the ml estimate of the scale parameter spl sigma has a simple closed form solution and we present an efficient scheme for computing the ml estimate of the shape parameter p by an off line numerical computation of the dependence of the partition function on p we present a fast algorithm for computing ml parameter estimates when the true image is unavailable to do this we use the expectation maximization em algorithm we develop a fast simulation method to replace the e step and a method to improve the parameter estimates when the simulations are terminated prior to convergence experimental results indicate that our fast algorithms substantially reduce the computation and result in good scale estimates for real tomographic data sets

non markovianity and negative entropy production rates entropy production plays a fundamental role in nonequilibrium thermodynamics to quantify the irreversibility of open systems its positivity can be ensured for a wide class of setups but the entropy production rate can become negative sometimes this is often taken as an indicator of non markovianity we make this link precise by showing under which conditions a negative entropy production rate implies non markovianity and when it does not for a system coupled to a single heat bath this can be established within a unified language for two setups i the dynamics resulting from a coarse grained description of a markovian master equation and ii the classical hamiltonian dynamics of a system coupled to a bath the quantum version of the latter result is shown not to hold despite the fact that the integrated thermodynamic description is formally equivalent to the classical case the instantaneous fixed point of a non markovian dynamics plays an important role in our study our key contribution is to provide a consistent theoretical framework to study the finite time thermodynamics of a large class of dynamics with a precise link to its non markovianity

markov random field texture models we consider a texture to be a stochastic possibly periodic two dimensional image field a texture model is a mathematical procedure capable of producing and describing a textured image we explore the use of markov random fields as texture models the binomial model where each point in the texture has a binomial distribution with parameter controlled by its neighbors and number of tries equal to the number of gray levels was taken to be the basic model for the analysis a method of generating samples from the binomial model is given followed by a theoretical and practical analysis of the method s convergence examples show how the parameters of the markov random field control the strength and direction of the clustering in the image the power of the binomial model to produce blurry sharp line like and blob like textures is demonstrated natural texture samples were digitized and their parameters were estimated under the markov random field model a hypothesis test was used for an objective assessment of goodness of fit under the markov random field model overall microtextures fit the model well the estimated parameters of the natural textures were used as input to the generation procedure the synthetic microtextures closely resembled their real counterparts while the regular and inhomogeneous textures did not

an empirical study of the simulation of various models used for images markov random fields are typically used as priors in bayesian image restoration methods to represent spatial information in the image commonly used markov random fields are not in fact capable of representing the moderate to large scale clustering present in naturally occurring images and can also be time consuming to simulate requiring iterative algorithms which can take hundreds of thousands of sweeps of the image to converge markov mesh models a causal subclass of markov random fields are however readily simulated we describe an empirical study of simulated realizations from various models used in the literature and we introduce some new mesh type models we conclude however that while large scale clustering may be represented by such models strong directional effects are also present for all but very limited parameterizations it is emphasized that the results do not detract from the use of markov random fields as representers of local spatial properties which is their main purpose in the implementation of bayesian statistical approaches to image analysis brief allusion is made to the issue of parameter estimation

computation of image spatial entropy using quadrilateral markov random field shannon entropy is a powerful tool in image analysis but its reliable computation from image data faces an inherent dimensionality problem that calls for a low dimensional and closed form model for the pixel value distributions the most promising such models are markovian however the conventional markov random field is hampered by noncausality and its causal versions are also not free of difficulties for example the markov mesh random field has its own limitations due to the strong diagonal dependency in its local neighboring system a new model named quadrilateral markov random field qmrf is introduced in this paper in order to overcome these limitations a property of qmrf with neighboring size of 2 is then used to decompose an image prior into a product of 2 d joint pdfs in which they are estimated using a joint histogram under the homogeneity assumption in addition the paper includes an extension of the introduced method to the computation of image spatial mutual information comparisons on synthesized images as well as two applications with real images are presented to motivate the developments in this paper and demonstrate the advantages in the performance of the introduced method over the existing ones

inference for discrete markov fields the simplest nontrivial case abstract markov fields provide a general context for describing the strength and structure of spatial interactions the gibbs markov equivalence theorem preston 1974 parameterizes markov fields via their neighborhood structures yielding exponential families in canonical form likelihood inference is therefore apparently straightforward the requisite normalizing constants however are obstreperous even when asymptotic characterizations can be obtained substantial location errors arise during implementation moreover markov fields can exhibit phase transitions and long range interactions thereby creating identifiability problems these issues are illustrated in the simplest nontrivial case the classical ising model of ferromagnetism

entanglement measure for general pure multipartite quantum states we propose an explicit formula for a measure of entanglement of pure multipartite quantum states we discuss the mathematical structure of the measure and give a brief explanation of its physical motivation we apply the measure on some pure tripartite qubit states and demonstrate that in general the entanglement can depend on what actions are performed on the various subsystems and specifically if the parties in possession of the subsystems cooperate or not we also give some simple but illustrative examples of the entanglement of four qubit and m qubit states

quantification of entanglement by means of convergent iterations the relative entropy of entanglement of a given bipartite quantum state is calculated by means of a convergent iterative algorithm when this state turns out to be nonseparable the algorithm also provides the corresponding optimal entanglement witness measurement

unified picture of strong coupling stochastic thermodynamics and time reversals strong coupling statistical thermodynamics is formulated as the hamiltonian dynamics of an observed system interacting with another unobserved system a bath it is shown that the entropy production functional of stochastic thermodynamics defined as the log ratio of forward and backward system path probabilities is in a one to one relation with the log ratios of the joint initial conditions of the system and the bath a version of strong coupling statistical thermodynamics where the system bath interaction vanishes at the beginning and at the end of a process is as is also weak coupling stochastic thermodynamics related to the bath initially in equilibrium by itself the heat is then the change of bath energy over the process and it is discussed when this heat is a functional of the system history alone the version of strong coupling statistical thermodynamics introduced by seifert and jarzynski is related to the bath initially in conditional equilibrium with respect to the system this leads to heat as another functional of the system history which needs to be determined by thermodynamic integration the log ratio of forward and backward system path probabilities in a stochastic process is finally related to log ratios of the initial conditions of a combined system and bath it is shown that the entropy production formulas of stochastic processes under a general class of time reversals are given by the differences of bath energies in a larger underlying hamiltonian system the paper highlights the centrality of time reversal in stochastic thermodynamics also in the case of strong coupling

landauer s erasure error correction and entanglement classical and quantum error correction are presented in the form of maxwell9s demon and their efficiency analysed from the thermodynamic point of view we explain how landauer9s principle of information erasure applies to both cases by then extending this principle to entanglement manipulations we rederive upper bounds on purification procedures thereby linking the no local increase of entanglement principle to the second law of thermodynamics

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

stationary markov random fields on a finite rectangular lattice this paper provides a complete characterization of stationary markov random fields on a finite rectangular non toroidal lattice in the basic case of a second order neighborhood system equivalently it characterizes stationary markov fields on z sup 2 whose restrictions to finite rectangular subsets are still markovian i e even on the boundaries until now pickard random fields formed the only known class of such fields first we derive a necessary and sufficient condition for markov random fields on a finite lattice to be stationary it is shown that their joint distribution factors in terms of the marginal distribution on a generic 2 spl times 2 cell which must fulfil some consistency constraints second we solve the consistency constraints and provide a complete characterization of such measures in three cases symmetric measures and gaussian measures are shown to necessarily belong to the pickard class whereas binary measures belong either to the pickard class or to a new nontrivial class which is further studied in particular the corresponding fields admit a simple parameterization and may be simulated in a simple although nonunilateral manner

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

remarks on entanglement measures and non local state distinguishability we investigate the properties of three entanglement measures that quantify the statistical distinguishability of a given state with the closest disentangled state that has the same reductions as the primary state in particular we concentrate on the relative entropy of entanglement with reversed entries we show that this quantity is an entanglement monotone which is strongly additive thereby demonstrating that monotonicity under local quantum operations and strong additivity are compatible in principle in accordance with the presented statistical interpretation which is provided this entanglement monotone however has the property that it diverges on pure states with the consequence that it cannot distinguish the degree of entanglement of different pure states we also prove that the relative entropy of entanglement with respect to the set of disentangled states that have identical reductions to the primary state is an entanglement monotone we finally investigate the trace norm measure and demonstrate that it is also a proper entanglement monotone

logarithmic negativity a full entanglement monotone that is not convex it is proven that logarithmic negativity does not increase on average under a general positive partial transpose preserving operation a set of operations that incorporate local operations and classical communication as a subset and in the process a further proof is provided that the negativity does not increase on average under the same set of operations given that the logarithmic negativity is not a convex function this result is surprising as it is generally considered that convexity describes the local physical process of losing information the role of convexity and in particular its relation or lack thereof to physical processes is discussed and importance of continuity in this context is stressed

mosaic models for textures this paper deals with a class of image models based on random geometric processes theoretical and empirical results on properties of patterns generated using these models are summarized these properties can be used as aids in fitting the models to images

spatial statistics and bayesian computation on wednesday may 6th 1992 professor b w silverman in the chair summary markov chain monte carlo mcmc algorithms such as the gibbs sampler have provided a bayesian inference machine in image analysis and in other areas of spatial statistics for several years founded on the pioneering ideas of ulf grenander more recently the observation that hyperparameters can be included as part of the updating schedule and the fact that almost any multivariate distribution is equivalently a markov random field has opened the way to the use of mcmc in general bayesian computation in this paper we trace the early development of mcmc in bayesian inference review some recent computational progress in statistical physics based on the introduction of auxiliary variables and discuss its current and future relevance in bayesian applications we briefly describe a simple mcmc implementation for the bayesian analysis of agricultural field experiments with which we have some practical experience

generalized schmidt decomposability and its relation to projective norms in multipartite entanglement projective norms are capable of measuring entanglement of multipartite quantum states however typically the explicit computation of these distance based geometric entanglement monotones is very difficult even for finite dimensional systems motivated by the significance of schmidt decompositions for our quantitative understanding of bipartite quantum entanglement a generalization of this concept to multipartite scenarios is proposed in the sense that generalized schmidt decomposability of a multipartite pure state implies that its projective norm can be calculated in a simple way analogous to the bipartite case thus this concept of generalized schmidt decomposability of multipartite quantum states is linked in a natural way to projective norms as entanglement monotones therefore it may not only be a convenient tool for calculations but may also shed new light onto the intricate features of multipartite entanglement in an analogous way as the classical schmidt decomposition does for bipartite quantum systems