rotators periodicity and absence of diffusion in cyclic cellular automata cyclic cellular automata are two dimensional cellular automata which generalize lattice versions of the lorentz gas and certain biochemistry models of artificial life we show that rotators and time reversibility play a special role in the creation of closed orbits in cyclic cellular automata we also prove that almost every orbit is closed periodic and the absence of diffusion for the flipping rotator model also known as the ant

coexistence does not imply joint measurability one of the hallmarks of quantum theory is the realization that distinct measurements cannot in general be performed simultaneously in stark contrast to classical physics in this context the notions of coexistence and joint measurability are employed to analyze the possibility of measuring together two general quantum observables characterizing different degrees of compatibility between measurements it is known that two jointly measurable observables are always coexistent and that the converse holds for various classes of observables including the case of observables with two outcomes here we resolve in the negative the open question of whether this equivalence holds in general our resolution strengthens the notions of coexistence and joint measurability by showing that both are robust against small imperfections in the measurement setups

typical local measurements in generalized probabilistic theories emergence of quantum bipartite correlations what singles out quantum mechanics as the fundamental theory of nature here we study local measurements in generalized probabilistic theories gpts and investigate how observational limitations affect the production of correlations we find that if only a subset of typical local measurements can be made then all the bipartite correlations produced in a gpt can be simulated to a high degree of accuracy by quantum mechanics our result makes use of a generalization of dvoretzky s theorem for gpts the tripartite correlations can go beyond those exhibited by quantum mechanics however

scaling of particle trajectories on a lattice the scaling behavior of the closed trajectories of a moving particle generated by randomly placed rotators or mirrors on a square or triangular lattice is studied numerically on both lattices for most concentrations of the scatterers the trajectories close exponentially fast for special critical concentrations infinitely extended trajectories can occur which exhibit a scaling behavior similar to that of the perimeters of percolation clusters at criticality in addition to the two critical exponents 15 7 anddf 7 4 found before the critical exponent 3 7 appears this exponent determines structural scaling properties of closed trajectories of finite size when they approach infinity new scaling behavior was found for the square lattice partially occupied by rotators indicating a different universality class than that of percolation clusters near criticality in the critical region two scaling functions were determined numerically f x related to the trajectory length s distributionns andh x related to the trajectory sizers gyration radius distribution respectively the scaling functionf x is in most cases found to be a symmetric double gaussian with the same characteristic size exponent 0 43 3 7 as at criticality leading to a stretched exponential dependence ofns ons ns exp s6 7 however for the rotator model on the partially occupied square lattice an alternative scaling function is found leading to a new exponent 1 6 0 3 and a superexponential dependence ofns ons h x is essentially a constant which depends on the type of lattice and the concentration of the scatterers the appearance of the same exponent 3 7 at and near a critical point is discussed

lorentz gas cellular automata on graphs lorentz gas cellular automata lgca are models of parallel many tape turing machines generated by the motion of localized point objects particles signals wave trains etc on a graph in each vertex v of the graph we store a symbol a read write head of the turing machine is represented as an object that hops from one vertex of the graph to another according to a rule symbol stored in the vertex thus the symbols stored in the vertices represent scattering rules or simply scatterers of the lattice gas it is assumed that initially the scatterers are randomly distributed among the vertices of the graph the random environment formed by the scatterers may either be fixed or evolve due to collisions with the moving object the collisions simulate storing of a new symbol in the vertex of the graph we investigate these models with fixed environment in general types of graphs and the models with evolving environments on trees remarkably it occurred that all models with fixed environments and many models with evolving environment behave like a depth first search on the underlying graph observe that such behavior occurs for any initial random distribution of scatterers rather than for some specially prepared initial configurations of scatterers we also give estimates of periods of orbits on finite graphs

diffusion in lorentz lattice gas cellular automata the honeycomb and quasi lattices compared with the square and triangular lattices we study numerically the nature of the diffusion process on a honeycomb and a quasi lattice where a point particle moving along the bonds of the lattice scatters from randomly placed scatterers on the lattice sites according to strictly deterministic rules for the honeycomb lattice fully occupied by fixed rotators two symmetric isolated critical points appear to be present with the same hyperscaling relation as for the square and the triangular lattices no such points appear to exist for the quasi lattice a comprehensive comparison is made with the behavior on the previously studied square and triangular lattices a great variety of diffusive behavior is found ranging from propagation superdiffusion normal quasi normal and anomalous to absence of diffusion the influence of the scattering rules as well as of the lattice structure on the diffusive behavior of a point particle moving on the all lattices studied so far is summarized

entanglement breaking channels with general outcome operator algebras a unit preserving and completely positive linear map or a channel a ain between c algebras a and ain is called entanglement breaking eb if idb is a separable state for any c algebra b and any state on the injective c tensor product ain b in this paper we establish the equivalence of the following conditions for a channel with a quantum input space and with a general outcome c algebra generalizing the known results in finite dimensions i is eb ii has a measurement prepare form holevo form iii n copies of are compatible for all 2 n iv countably infinite copies of are compatible by using this equivalence we also show that the set of randomization equivalence classes of normal eb channels with a fixed input von neumann algebra is upper and lower dedekind closed i e the supremum or infimum of any randomization increasing or decreasing net of eb channels is also eb as an example we construct an injective normal eb channel with an arbitrary outcome operator algebra m acting on an infinite dimensional separable hilbert space by using the coherent states and the bargmann measure

equivalence of deterministic walks on regular lattices on the plane abstract we consider deterministic walks on square triangular and hexagonal two dimensional lattices in each case there is a scatterer at every lattice site that can be in one of two states that forces the walker to turn either to his her immediate right or left after the walker is scattered the scatterer changes state a lattice with an arrangement of scatterers is an environment we show that there are only two environments for which the scattering rules are injective mirrors or rotators on the three lattices on hexagonal lattices webb and cohen 2014 proved that if a walker with a given initial position and velocity moves through an environment of mirrors rotators then there is an environment of rotators mirrors through which the walker would move with the same trajectory we refer to these trajectories on mirror and rotator environments as equivalent walks we prove the equivalence of walks on square and triangular lattices and include a proof of the equivalence of walks on hexagonal lattices the proofs are based both on the geometry of the lattice and the structure of the scattering rule

preparation uncertainty implies measurement uncertainty in a class of generalized probabilistic theories in quantum theory it is known for a pair of noncommutative observables that there is no state on which they take simultaneously definite values and that there is no joint measurement of them they are called preparation uncertainty and measurement uncertainty respectively and research has unveiled that they are not independent from but related with each other in a quantitative way this study aims to reveal whether similar relations to quantum ones hold also in generalized probabilistic theories gpts in particular a certain class of gpts is considered which can be characterized by transitivity and self duality and regarded as extensions of quantum theory it is proved that there are close connections expressed quantitatively between two types of uncertainty on a pair observables also in those theories if preparation uncertainty exists then measurement uncertainty also exists and they are described by similar inequalities our results manifest that their correspondences are not specific to quantum theory but more universal ones

nonlocality distillation and postquantum theories with trivial communication complexity we first present a protocol for deterministically distilling nonlocality building upon a recent result of forster et al phys rev lett 102 120401 2009 our protocol which is optimal for two copy distillation works efficiently for a specific class of postquantum nonlocal boxes which we term correlated nonlocal boxes in the asymptotic limit all correlated nonlocal boxes are distilled to the maximally nonlocal box of popescu and rohrlich then taking advantage of a result of brassard et al phys rev lett 96 250401 2006 we show that all correlated nonlocal boxes make communication complexity trivial and therefore appear very unlikely to exist in nature astonishingly some of these nonlocal boxes are arbitrarily close to the set of classical correlations this result therefore gives new insight to the problem of why quantum nonlocality is limited

flat bundles and residues for foliations in this note we compute the residues for a vector field preserving a foliation we assume the vector field disappears only to first order along its singular set and that its singular set consists of closed separated leaves under these conditions the residue is completely determined by the characteristic classes of the flat bundle v o which is the normal bundle v of the foliation restricted to the singular set and the action of the vector field on v o for a foliation of even codimension q whose normal bundle has euler class zero we interpret the pontrjagin ring of the normal bundle in dimension 2q as an obstruction to the existence of such a vector field we show that if the euler class of the normal bundle of a foliation is zero and it admits such a vector field then many of its secondary characteristic classes must be also be zero this is one of the few results relating the geometry of a foliation to its characteristic classes we will make extensive use of the material in 6 it will be very helpful to the reader to be familiar with this paper

lattice lorentz gas in cellular automaton fluids where binary collision laws admit reflections the stosszahl ansatz and the boltzmann equation are no longer valid at low densities this is proven for a class of lorentz gas models defined on cubic lattices for which the diffusion coefficient is calculated from a self consistent ring kinetic equation or effective medium theory the calculated results are in excellent agreement with results from molecular dynamics simulations over the whole density interval

coexistence on reflecting hyperplane in generalized probability theories the coexistence of effects in a certain class of generalized probability theories is investigated the effect space corresponding to an even sided regular polygon state space has a central hyperplane that contains all the nontrivial extremal effects the existence of such a hyperplane called a reflecting hyperplane is closely related to the point symmetry of the corresponding state space the effects on such a hyperplane can be regarded as the generalized unbiased effects a necessary and sufficient condition for a pair of unbiased effects in the even sided regular polygon theories is presented this result reproduces a low dimensional analogue of known results of qubit effects in a certain limit the coexistence of effects in a certain class of generalized probability theories is investigated the effect space corresponding to an even sided regular polygon state space has a central hyperplane that contains all the nontrivial extremal effects the existence of such a hyperplane called a reflecting hyperplane is closely related to the point symmetry of the corresponding state space the effects on such a hyperplane can be regarded as the generalized unbiased effects a necessary and sufficient condition for a pair of unbiased effects in the even sided regular polygon theories is presented this result reproduces a low dimensional analogue of known results of qubit effects in a certain limit

the red queen s walk abstract we study a new type of walk with memory which might serve as a toy model for the behavior one must adopt to avoid exhaustion of resources and attraction of parasites and predators the walk takes place on a regular square lattice with periodic boundary conditions although the walk is completely deterministic it mimics a true self avoiding walk i e a random walk with weak autocorrelation this shows that the red queen effect can lead to aperiodic behavior in addition to the case of single walkers in a flat landscape we also study the cases of hilly landscapes and of several walkers performing simultaneous walks

hull generating walks abstract a hull generating walk hgw is a type of kinetic random walk that generates the hull or perimeter of a percolation cluster and thus has a fractal dimension of 1 75 some examples of hgws for site and bond percolation on a square lattice are described

bounding the set of quantum correlations we introduce a hierarchy of conditions necessarily satisfied by any distribution p ensuremath alpha ensuremath beta representing the probabilities for two separate observers to obtain outcomes ensuremath alpha and ensuremath beta when making local measurements on a shared quantum state each condition in this hierarchy is formulated as a semidefinite program among other applications our approach can be used to obtain upper bounds on the quantum violation of an arbitrary bell inequality it yields for instance tight bounds for the violations of the collins et al inequalities

temporal quantum correlations and leggett garg inequalities in multilevel systems we show that the quantum bound for temporal correlations in a leggett garg test analogous to the tsirelson bound for spatial correlations in a bell test strongly depends on the number of levels n that can be accessed by the measurement apparatus via projective measurements we provide exact bounds for small n that exceed the known bound for the leggett garg inequality and we show that in the limit n the leggett garg inequality can be violated up to its algebraic maximum

on the existence of quantum representations for two dichotomic measurements under which conditions do outcome probabilities of measurements possess a quantum mechanical model this kind of problem is solved here for the case of two dichotomic von neumann measurements which can be applied repeatedly to a quantum system with trivial dynamics the solution uses methods from the theory of operator algebras and the theory of moment problems the ensuing conditions reveal surprisingly simple relations between certain quantum mechanical probabilities it also shown that generally none of these relations holds in general probabilistic models this result might facilitate further experimental discrimination between quantum mechanics and other general probabilistic theories

sequences of projective measurements in generalized probabilistic models we define a simple rule that allows us to describe sequences of projective measurements for a broad class of generalized probabilistic models this class embraces quantum mechanics and classical probability theory but for example also the hypothetical popescu rohrlich box for quantum mechanics the definition yields the established luders rule which is the standard rule for updating the quantum state after a measurement for the general case it can be seen as being the least disturbing or most coherent way of performing sequential measurements we show as an example that the spekkens toy model spekkens 2007 phys rev a 75 032110 provides an instance of our definition we also demonstrate the possibility of strong postquantum correlations as well as the existence of triple slit correlations for certain nonquantum toy models

novel phenomena in lorentz lattice gases abstract in lorentz lattice gases a point particle moves along the bonds of a lattice whose lattice sites are occupied by randomly placed scatterers which scatter the particle according to certain a priori given scattering rules we consider here mainly the simplest case of a square lattice fully or partly covered with two kinds of scatterers which scatter the particle to its right or its left respectively either according to probabilistic or strictly deterministic scattering rules although the global probability of the particle to be scattered to its right or left is equal for the two scattering rules the local probability is very different leading to a completely different diffusive behavior for the two cases while the probabilistic scattering rules lead to gaussian diffusion the deterministic rules lead either to anomalous or no diffusion depending on the concentrations of the scatterers on the lattice in the first case the mean square displacement is still proportional to the time so that a diffusion coefficient can be defined but the diffusion is non gaussian while in the second case the mean square displacement is bounded and all particles are trapped in a finite time in both cases this behavior is due to the existence of closed periodic orbits which in the first case can be of infinite extent extended closed orbits while in the second case they can only be of finite extent the lengths of the extended closed orbits show for a lattice fully occupied equally by right and left scatterers a scaling behavior identical to that of percolation clusters at the bond percolation threshold of a related bond percolation problem for special concentrations on a not fully occupied lattice the same scaling behavior is found leading to two critical lines but no known related percolation like problem exists in this case this critical behavior of the closed orbits in anomalous diffusion appears to obtain for all two dimensional lattices studied so far a number of extensions of the above results are indicated

unifying typical entanglement and coin tossing on randomization in probabilistic theories it is well known that pure quantum states are typically almost maximally entangled and thus have close to maximally mixed subsystems we consider whether this is true for probabilistic theories more generally and not just for quantum theory we derive a formula for the expected purity of a subsystem in any probabilistic theory for which this quantity is well defined it applies to typical entanglement in pure quantum states coin tossing in classical probability theory and randomization in post quantum theories a simple generalization yields the typical entanglement in anti symmetric quantum subspaces the formula is exact and simple only containing the number of degrees of freedom and the information capacity of the respective systems it allows us to generalize statistical physics arguments in a way which depends only on coarse properties of the underlying theory the proof of the formula generalizes several randomization notions to general probabilistic theories this includes a generalization of purity contributing to the recent effort of finding appropriate generalized entropy measures

nondisturbing quantum measurements we consider pairs of discrete quantum observables povms and analyze the relation between the notions of nondisturbance joint measurability and commutativity we specify conditions under which these properties coincide or differ depending for instance on the interplay between the number of outcomes and the hilbert space dimension or on algebraic properties of the effect operators we also show that non disturbance is in general not a symmetric relation and that it can be decided and quantified by means of a semidefinite program

comment on on the complete integrability of the hirota satsuma system the authors show that the aforementioned paper by chowdhury and mukherjee ibid vol 17 p l231 1984 is false

a kinetic theorist s look at lattice gas cellular automata abstract the diffusion behavior of a number of lorentz lattice gases is studied in its dependence on collision rules and its similarity to corresponding lorentz gases that are continuous in space but have the same discrete velocity space the difference in behavior resulting from probabilistic or deterministic collision rules is discussed

entanglement and the three dimensionality of the bloch ball we consider a very natural generalization of quantum theory by letting the dimension of the bloch ball be not necessarily three we analyze bipartite state spaces where each of the components has a d dimensional euclidean ball as state space in addition to this we impose two very natural assumptions the continuity and reversibility of dynamics and the possibility of characterizing bipartite states by local measurements we classify all these bipartite state spaces and prove that except for the quantum two qubit state space none of them contains entangled states equivalently in any of these non quantum theories interacting dynamics is impossible this result reveals that existence of entanglement is the requirement with minimal logical content which singles out quantum theory from our family of theories

generalized probability theories what determines the structure of quantum theory the framework of generalized probabilistic theories is a powerful tool for studying the foundations of quantum physics it provides the basis for a variety of recent findings that significantly improve our understanding of the rich physical structure of quantum theory this review paper tries to present the framework and recent results to a broader readership in an accessible manner to achieve this we follow a constructive approach starting from a few basic physically motivated assumptions we show how a given set of observations can be manifested in an operational theory furthermore we characterize consistency conditions limiting the range of possible extensions in this framework classical and quantum theory appear as special cases and the aim is to understand what distinguishes quantum mechanics as the fundamental theory realized in nature it turns out that non classical features of single systems can equivalently result from higher dimensional classical theories that have been restricted entanglement and non locality however are shown to be genuine non classical features

recurrence properties of lorentz lattice gas cellular automata recurrence properties of a point particle moving on a regular lattice randomly occupied with scatterers are studied for strictly deterministic nondeterministic and purely random scattering rules

dynamics of a class of ants on a one dimensional lattice a one dimensional virtual ant is an automaton evolving in the lattice z each cell of z may have white or black color the ant represented by an arrow in a cell moves to a neighbor and may change the color of the current cell depending on its previous color in this paper we characterize into classes the dynamics of 64 ant s rules taking into account bounded or unbounded evolution as well as the periods and the steady state behavior we describe in a detailed way the behavior of each of the rules determining the steady state velocity period and transient time

quantum measuring processes of continuous observables the purpose of this paper is to provide a basis of theory of measurements of continuous observables we generalize von neumann s description of measuring processes of discrete quantum observables in terms of interaction between the measured system and the apparatus to continuous observables and show how every such measuring process determines the state change caused by the measurement we establish a one to one correspondence between completely positive instruments in the sense of davies and lewis and the state changes determined by the measuring processes we also prove that there are no weakly repeatable completely positive instruments of nondiscrete observables in the standard formulation of quantum mechanics so that there are no measuring processes of nondiscrete observables whose state changes satisfy the repeatability hypothesis a proof of the wigner araki yanase theorem on the nonexistence of repeatable measurements of observables not commuting conserved quantities is given in our framework we also discuss the implication of these results for the recent results due to srinivas and due to mercer on measurements of continuous observables

langton s flies langton s ant is an automaton defined over a two dimensional grid its movement is governed by the environment in a very simple way it turns to the left over white vertices and to the right over black vertices this definition only applies on a two dimensional space we look for generalizations of this automaton to n dimensional lattices remembering the different ways through which the ant was originally defined we consider two approaches the first comes from physics lattice gas and the second from artificial life virtual ants two generalizations are proposed defining two families of dynamical systems from the physics point of view the ant is seen as a particle and hence it has no internal state other than its velocity from the artificial life point of view the ant is viewed as an insect and it has an orientation in space which we represent by an orthogonal basis this constitutes the ant s internal state this formulation allows us to define the ant s behaviour without drawing upon any information relative to the global system of external coordinates each model yields different sets of rules with distinctive behaviours we characterize all the possible rules satisfying some basic restrictions we found that many rules produce trajectories which are restricted to a diagonal plane and are equivalent to a version of langton s ant over a two dimensional grid squared or hexagonal in the particle model only two of them use the whole space and it is shown that such rules do not admit periodical trajectories this result reinforces a previous one reported by leonid bunimovich who states that the skeleton of any bounded trajectory cannot contain any three dimensional polyhedron

global invariants for measured foliations new exotic invariants for measured foliations are constructed which we call the u classes of a pair f u the dependence of the s classes on the geometry of the foliation gis examined and the dynamics of a foliation is shown to determine the u classes in many cases we use the u classes to study the classifying space bfsl of foliations with a transverse invariant volume form and we show the homotopy groups of bfsl are uncountably generated starting in degrees q 3 new invariants for groups of volume preserving diffeomorphisms also arise from the t classes these invariants are nontrivial and related to the geometric aspects of the group action relations between the tl classes and the secondary classes of a foliation are exhibited 0 introduction in this paper we construct new exotic characteristic classes for foliations which have a transverse invariant measure these invariants which we call the t classes are similar to the secondary classes and take values in the real cohomology h m of the foliated manifold m theorem 1 6 the values of the m classes are strongly related to the geometry of the foliation proposition 3 4 the u classes have applications to the study of foliations with a transverse invariant volume form theorems 5 1 and 5 2 to the computations of the homology groups of the discrete group of volume preserving diffeomorphisms of rw theorem 7 4 and to the problem of relating the secondary classes of a foliation with its global geometry 15 201 the a classes arose from an attempt to obtain general invariants of a foliation which are intermediate between the leaf and secondary classes they are a special case of a family of universal invariants associated to a c2 foliation the weil operators in codimension one the introduction of the weil operator is a decisive ingredient in duminy s elegant proof of the sullivan conjecture about the godbillon vey class 9 the properties of the weil operators in higher codimensions are given in 15 where they are used to study the residuable secondary classes we briefly describe the construction of the weil operators and their relations with the l classes and other foliation invariants in 2 for a foliation with all leaves compact we note that the weil operators are identically zero proposition 2 6 we denote by f a c2 foliation of codimension q on a paracompact manifold m and i denotes a transverse invariant measure for sf recall that ti assigns to each received by the editors june 28 1982 and in revised form november 9 1982 1980 mathematics subject classification primary 57r30 57r20 58f1 1 secondary 58h10 28d15

diffusion and propagation in triangular lorentz lattice gas cellular automata the diffusion process of point particles moving on regular triangular and random lattices randomly occupied with stationary scatterers a lorentz lattice gas cellular automaton is studied for strictly deterministic scattering rules as a function of the concentration of the scatterers in addition to the normal and various kinds of retarded diffusion found before on the regular square lattice straight line propagation through the scatterers is observed

topological dynamics of flipping lorentz lattice gas models we study the topological dynamics of the flipping mirror model of ruijgrok and cohen with one or an infinite number of particles in particular we prove the topological transitivity and topological mixing up to a natural first integral for the one particle model

low viscosity lattice gases a class of lattice gas models are studied which are variants of the fchc model the aim is to achieve the highest possible reynolds coefficient inverse dimensionless viscosity for efficient simulations of the three dimensional incompressible navier stokes equations the models include an arbitrary number of rest particles and violation of semi detailed balance within the framework of the boltzmann approximation exact expressions are obtained for the reynolds coefficients the minimization of the viscosity is done by solving a hitchcock type optimization problem for the fine tuning of the collision rules when the number of rest particles exceeds one there is a range of densities at which the viscosity takes negative values various optimal models with up to 26 bits per node have been implemented on a cray 2 and their true transport coefficients have been measured with good accuracy fairly large discrepancies with boltzmann values are observed when semi detailed balance is violated in particular no negative viscosity is obtained still the best model has a reynolds coefficient of 13 5 twice that of the best previously implemented model and thus is about 16 times more efficient computationally suggestions are made for further improvements it is proposed to use models with very high reynolds coefficients for sub grid scale modeling of turbulent flows