generalized entropic uncertainty relations a new class of uncertainty relations is derived for pairs of observables in a finite dimensional hilbert space which do not have any common eigenvector this class contains an entropic uncertainty relation which improves a previous result of deutsch and confirms a recent conjecture by kraus some comments are made on the extension of these relations to the case where the hilbert space is infinite dimensional

orthomodularity and quadratic transformations in probabilistic theories of physics a characterization of orthomodularity of a set of effects is given in terms of a triangle closedness of this set this leads to a simple probabilistic characterization of observables with a boolean range quadratic transformations on expectation functionals of observables are studied in order to investigate the derivability of the heisenberg inequality and the form of the lower bound of such an inequality for a pair of observables

measurement of body segment parameters using dual energy x ray absorptiometry and three dimensional geometry an application in gait analysis abstract body segment parameters bsp are essential input for the computations in kinetics of motion applied in the field of biomechanics these data are usually obtained from population specific predictive equations which present limitations in being representative of the population under study more recently medical imaging techniques have been adopted but are limited to two dimensional 2 d measurements or required extensive tomographic images for three dimensional 3 d reconstruction we proposed an in vivo method to measure 3 d bsp using x ray imaging and 3 d exterior geometry criterion values of the bsp were determined using magnetic resonance imaging mri which has previously been validated errors for all bsp values were less than 2 when values derived from our method were compared to the criterion values we found no significant difference between our method and four selected bsp models in both stance and swing phase significant phase effects were observed for our method and other bsp models between stance and swing phase significant differences p

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

universality in uncertainty relations for a quantum particle a general theory of preparational uncertainty relations for a quantum particle in one spatial dimension is developed we derive conditions which determine whether a given smooth function of the particle s variances and its covariance is bounded from below whenever a global minimum exists an uncertainty relation has been obtained the squeezed number states of a harmonic oscillator are found to be universal no other pure or mixed states will saturate any such relation geometrically we identify a convex uncertainty region in the space of second moments which is bounded by the inequality derived by robertson and schrodinger our approach provides a unified perspective on existing uncertainty relations for a single continuous variable and it leads to new inequalities for second moments which can be checked experimentally

equivalence theorem of uncertainty relations we present an equivalence theorem to unify the two classes of uncertainty relations i e the variance based ones and the entropic forms showing that the entropy of an operator in a quantum system can be built from the variances of a set of commutative operators this means that an uncertainty relation in the language of entropy may be mapped onto a variance based one and vice versa employing the equivalence theorem alternative formulations of entropic uncertainty relations are obtained for the qubit system that are stronger than the existing ones in the literature and variance based uncertainty relations for spin systems are reached from the corresponding entropic uncertainty relations

mri derived body segment parameters of children differ from age based estimates derived using photogrammetry abstract body segment parameters are required when researching joint kinetics using inverse dynamics models however the only regression equations for estimating pediatric body segment parameters across a wide age range were developed using photogrammetry based on 12 boys and have not been validated to date jensen r k 1986 body segment mass radius and radius of gyration proportions of children journal of biomechanics 19 359 368 to assess whether these equations could validly be applied to girls we asked whether body segment parameters estimated by the equations differ from parameters measured using a validated magnetic resonance imaging mri method if so do the differences cause significant differences in joint kinetics during normal gait body segment parameters were estimated from axial mris of the left thigh and shank of 10 healthy girls 9 6 0 9 years and compared to those from jensen s equations kinematics and kinetics were collected for 10 walking trials extrema in hip and knee moments and powers were compared between the two sets of body segment parameters with the exception of the shank mass center and radius of gyration body segment parameters measured using mri were significantly different from those estimated using regression equations these systematic differences in body segment parameters resulted in significant differences in sagittal plane joint moments and powers during gait nevertheless it is doubtful that even the greatest differences in kinetics are practically meaningful 0 3 bw ht and 0 7 bw ht s for moments and power at the hip respectively therefore body segment parameters estimated using jensen s regression equations are a suitable substitute for more detailed anatomical imaging of 8 10 year old girls when quantifying joint kinetics during gait

quantum harmonic analysis on phase space relative to an irreducible representation of the canonical commutation relations convolutions between quantum mechanical operators and between functions and operators are defined for which the usual weyl transform acts as a fourier transform basic properties of these operations are developed in close analogy to harmonic analysis on r2n using the quantum version of wiener s approximation theorem a natural one to one correspondence between the closed phase space translation invariant subspaces of classical and quantum observables is established

l estimates in optimal mass transportation we show that in any complete metric space the probability measures with compact and connected support are the ones having the property that the optimal transportation distance to any other probability measure living on the support of is bounded below by a positive function of the l transportation distance between and the function giving the lower bound depends only on the lower bound of the measures of balls centered at the support of and on the cost function used in the optimal transport we obtain an essentially sharp form of this function in the case of strictly convex cost functions we show that a similar estimate holds on the level of optimal transport plans if and only if the support of is compact and sufficiently close to being a geodesic metric space in the quantitative sense that between any two points there exists a sequence along which the cost can be cyclically decreased we also study when convergence of compactly supported measures in lp transportation distance implies convergence in l transportation distance for measures with connected supports this property is characterized by uniform lower bounds on the measures of balls centered at the supports of the measures or equivalently by the hausdorff convergence of the supports

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

wehrl s entropy of spin states and lieb s conjecture wehrl s entropy is the entropy of the probability distribution in the phase space corresponding to the q representation antinormal ordering of operators of a quantum state in terms of coherent states the hilbert space of a system of n spins or n two level atoms is of 2n dimensions the subspace with maximum total spin n 2 is of n 1 dimensions all discussions are restricted within this subspace the probability amplitude for an arbitrary pure state in this subspace is a polynomial of degree n which can be factorised into the product of n linear factors and each root can be identified with one point on the unit sphere hence an arbitrary state in the subspace can be represented geometrically by n unit vectors the general expression for the wehrl entropy is obtained as a finite series expansion in terms of some symmetric functions of sin2 omega ij 2 where omega ij is the angle between a pair of unit vectors the special cases of coherent and almost coherent spin states are then considered

a transform of complementary aspects with applications to entropic uncertainty relations even though mutually unbiased bases and entropic uncertainty relations play an important role in quantum cryptographic protocols they remain ill understood here we construct special sets of up to 2n 1 mutually unbiased bases mubs in dimension d 2 n which have particularly beautiful symmetry properties derived from the clifford algebra more precisely we show that there exists a unitary transformation that cyclically permutes such bases this unitary can be understood as a generalization of the fourier transform which exchanges two mubs to multiple complementary aspects we proceed to prove a lower bound for min entropic entropic uncertainty relations for any set of mubs and show that symmetry plays a central role in obtaining tight bounds for example we obtain for the first time a tight bound for four mubs in dimension d 4 which is attained by an eigenstate of our complementarity transform finally we discuss the relation to other symmetries obtained by transformations in discrete phase space and note that the extrema of discrete wigner functions are directly related to min entropic uncertainty relations for mubs

entropic measures of joint uncertainty effects of lack of majorization we compute renyi entropies for the statistics of a noisy simultaneous observation of two complementary observables in two dimensional quantum systems the relative amount of uncertainty between two states depends on the uncertainty measure used these results are not reproduced by a more standard duality relation we show that these behaviors are consistent with the lack of majorization relation between the corresponding statistics

a 3d reconstruction method of the body envelope from biplanar x rays evaluation of its accuracy and reliability the aim of this study was to propose a novel method for reconstructing the external body envelope from the low dose biplanar x rays of a person the 3d body envelope was obtained by deforming a template to match the surface profiles in two x rays images in three successive steps global morphing to adopt the position of a person and scale the template s body segments followed by a gross deformation and a fine deformation using two sets of pre defined control points to evaluate the method a biplanar x ray acquisition was obtained from head to foot for 12 volunteers in a standing posture up to 172 radio opaque skin markers were attached to the body surface and used as reference positions each envelope was reconstructed three times by three operators results showed a bias lower than 7 mm and a confidence interval 95 of reproducibility lower than 6 mm for all body parts comparable to other existing methods matching a template onto stereographic photographs the proposed method offers the possibility of reconstructing body shape in addition to the skeleton using a low dose biplanar x rays system

uncertainty in quantum measurements the object of this letter is to show that except in the case of canonically conjugate observables the generalized heisenberg inequality does not properly express the quantum uncertainty principle it is in general too weak an inequality is obtained which does express the principle

universal joint measurement uncertainty relation for error bars we formulate and prove a new universally valid uncertainty relation for the necessary error bar widths in any approximate joint measurement of position and momentum

measurement uncertainty relations for discrete observables relative entropy formulation we introduce a new information theoretic formulation of quantum measurement uncertainty relations based on the notion of relative entropy between measurement probabilities in the case of a finite dimensional system and for any approximate joint measurement of two target discrete observables we define the entropic divergence as the maximal total loss of information occurring in the approximation at hand for fixed target observables we study the joint measurements minimizing the entropic divergence and we prove the general properties of its minimum value such a minimum is our uncertainty lower bound the total information lost by replacing the target observables with their optimal approximations evaluated at the worst possible state the bound turns out to be also an entropic incompatibility degree that is a good information theoretic measure of incompatibility indeed it vanishes if and only if the target observables are compatible it is state independent and it enjoys all the invariance properties which are desirable for such a measure in this context we point out the difference between general approximate joint measurements and sequential approximate joint measurements to do this we introduce a separate index for the tradeoff between the error of the first measurement and the disturbance of the second one by exploiting the symmetry properties of the target observables exact values lower bounds and optimal approximations are evaluated in two different concrete examples 1 a couple of spin 1 2 components not necessarily orthogonal 2 two fourier conjugate mutually unbiased bases in prime power dimension finally the entropic incompatibility degree straightforwardly generalizes to the case of many observables still maintaining all its relevant properties we explicitly compute it for three orthogonal spin 1 2 components

positive operator valued measures covariant with respect to an irreducible representation given an irreducible representation of a group g we show that all the covariant positive operator valued measures based on g z where z is a central subgroup are described by trace class trace one positive operators

phase space quantization and the operator moment problem we consider questions related to a quantization scheme in which a classical variable f r on a phase space is associated with a preferably unique semispectral measure ef such that the moment operators of ef are required to be of the form fk with a suitable mapping from the set of classical variables to the set of not necessarily bounded operators in the hilbert space of the quantum system in particular we investigate the situation where the map is implemented by the operator integral with respect to some fixed positive operator measure the phase space is first taken to be an abstract measurable space then a locally compact unimodular group and finally r2 where we determine explicitly the relevant operators fk for certain variables f in the case where the quantization map is implemented by a translation covariant positive operator measure in addition we consider the question under what conditions a positive operator measure is projection valued

entropy power uncertainty relations towards a tight inequality for all gaussian pure states we show that a proper expression of the uncertainty relation for a pair of canonically conjugate continuous variables relies on entropy power a standard notion in shannon information theory for real valued signals the resulting entropy power uncertainty relation is equivalent to the entropic formulation of the uncertainty relation due to bialynicki birula and mycielski but can be further extended to rotated variables hence based on a reasonable assumption we give a partial proof of a tighter form of the entropy power uncertainty relation taking correlations into account and provide extensive numerical evidence of its validity interestingly it implies the generalized rotation invariant schrodinger robertson uncertainty relation exactly as the original entropy power uncertainty relation implies heisenberg relation it is saturated for all gaussian pure states in contrast with hitherto known entropic formulations of the uncertainty principle

constrained steepest descent in the 2 wasserstein metric we study several constrained variational problems in the 2 wasserstein metric for which the set of probability densities satisfying the constraint is not closed for example given a probability density f0 on d and a time step h 0 we seek to minimize i f hs f w 2 2 f0 f over all of the probability densities f that have the same mean and variance as f0 where s f i sthe entropy of f w eprove existence of minimizers we also analyze the induced geometry of the set of densities satisfying the constraint on the variance and means and we determine all of the geodesics on it from this we determine a criterion for convexity of functionals in the induced geometry it turns out for example that the entropy is uniformly strictly convex on the constrained manifold though not uniformly convex without the constraint the problems solved here arose in a study of a variational approach to constructing and studying solutions of the nonlinear kinetic fokker planck equation which is briefly described here and fully developed in a companion paper

measurement uncertainty relations measurement uncertainty relations are quantitative bounds on the errors in an approximate joint measurement of two observables they can be seen as a generalization of the error disturbance tradeoff first discussed heuristically by heisenberg here we prove such relations for the case of two canonically conjugate observables like position and momentum and establish a close connection with the more familiar preparation uncertainty relations constraining the sharpness of the distributions of the two observables in the same state both sets of relations are generalized to means of order rather than the usual quadratic means and we show that the optimal constants are the same for preparation and for measurement uncertainty the constants are determined numerically and compared with some bounds in the literature in both cases the near saturation of the inequalities entails that the state resp observable is uniformly close to a minimizing one

characterizing entanglement via uncertainty relations we derive a family of necessary separability criteria for finite dimensional systems based on inequalities for variances of observables we show that every pure bipartite entangled state violates some of these inequalities furthermore a family of bound entangled states and true multipartite entangled states can be detected the inequalities also allow us to distinguish between different classes of true tripartite entanglement for qubits we formulate an equivalent criterion in terms of covariance matrices this allows us to apply criteria known from the regime of continuous variables to finite dimensional systems

entropic uncertainty bound for open pointer based simultaneous measurements of conjugate observables we discuss the information entropy for a general open pointer based simultaneous measurement and show how it is bound from below this entropic uncertainty bound is a direct consequence of the structure of the entropy and can be obtained from the formal solution of the measurement dynamics furthermore the structural properties of the entropy allow us to give an intuitive interpretation of the noisy influence of the pointers and the environmental heat bath on the measurement results

measurement theory in local quantum physics in this paper we aim to establish foundations of measurement theory in local quantum physics for this purpose we discuss a representation theory of completely positive cp instruments on arbitrary von neumann algebras we introduce a condition called the normal extension property nep and establish a one to one correspondence between cp instruments with the nep and statistical equivalence classes of measuring processes we show that every cp instrument on an atomic von neumann algebra has the nep extending the well known result for type i factors moreover we show that every cp instrument on an injective von neumann algebra is approximated by cp instruments with the nep the concept of posterior states is also discussed to show that the nep is equivalent to the existence of a strongly measurable family of posterior states for every normal state two examples of cp instruments without the nep are obtained from this result it is thus concluded that in local quantum physics not every cp instrument represents a measuring process but in most of physically relevant cases every cp instrument can be realized by a measuring process within arbitrary error limits as every approximately finite dimensional von neumann algebra on a separable hilbert space is injective to conclude the paper the concept of local measurement in algebraic quantum field theory is examined in our framework in the setting of the doplicher haag roberts and doplicher roberts theory describing local excitations we show that an instrument on a local algebra can be extended to a local instrument on the global algebra if and only if it is a cp instrument with the nep provided that the split property holds for the net of local algebras

entropic energy time uncertainty relation energy time uncertainty plays an important role in quantum foundations and technologies and it was even discussed by the founders of quantum mechanics however standard approaches e g robertson s uncertainty relation do not apply to energy time uncertainty because in general there is no hermitian operator associated with time following previous approaches we quantify time uncertainty by how well one can read off the time from a quantum clock we then use entropy to quantify the information theoretic distinguishability of the various time states of the clock our main result is an entropic energy time uncertainty relation for general time independent hamiltonians stated for both the discrete time and continuous time cases our uncertainty relation is strong in the sense that it allows for a quantum memory to help reduce the uncertainty and this formulation leads us to reinterpret it as a bound on the relative entropy of asymmetry because of the operational relevance of entropy we anticipate that our uncertainty relation will have information processing applications

positive operator valued measures and feller markov kernels abstract a positive operator valued measure povm is a map f b x l s h from the borel algebra of a topological space x to the space of positive self adjoint operators on a hilbert space h we assume x to be hausdorff locally compact and second countable and prove that a povm f is commutative if and only if it is the smearing of a spectral measure e by means of a feller markov kernel moreover we prove that the smearing can be realized by means of a strong feller markov kernel if and only if f is uniformly continuous finally we prove that a povm which is norm bounded by a finite measure admits a strong feller markov kernel that provides a characterization of the smearing which connects a commutative povm f to a spectral measure e and is relevant both from the mathematical and the physical viewpoint since smearings of spectral measures form a large and very relevant subclass of povms they are paradigmatic for the modeling of certain standard forms of noise in quantum measurements they provide optimal approximators as marginals in joint measurements of incompatible observables 21 they are important for a range of quantum information processing protocols where classical post processing plays a role 27 the mathematical and physical relevance of the results is discussed and particular emphasis is given to the connections between the markov kernel and the imprecision of the measurement process

sharp uncertainty relations for number and angle we study uncertainty relations for pairs of conjugate variables like number and angle of which one takes integer values and the other takes values on the unit circle the translation symmetry of the problem in either variable implies that measurement uncertainty and preparation uncertainty coincide quantitatively and the bounds depend only on the choice of two metrics used to quantify the difference of number and angle outputs respectively for each type of observable we discuss two natural choices of metric and discuss the resulting optimal bounds with both numerical and analytical methods we also develop some simple and explicit albeit not sharp lower bounds using an apparently new method for obtaining certified lower bounds to ground state problems

stronger uncertainty relations for all incompatible observables the heisenberg robertson uncertainty relation expresses a limitation in the possible preparations of the system by giving a lower bound to the product of the variances of two observables in terms of their commutator notably it does not capture the concept of incompatible observables because it can be trivial i e the lower bound can be null even for two noncompatible observables here we give two stronger uncertainty relations relating to the sum of variances whose lower bound is guaranteed to be nontrivial whenever the two observables are incompatible on the state of the system

entropy of ideal quantum gases as a lie function we investigate the lie series representation of the canonical transformations in a complex phase space it is shown that any canonical mapping in the complex domain can be labelled by two different functions one of these functions corresponds to an observable in the sense of classical mechanics the second one has special analytic properties and can be used to form quantities which are important in quantum statistical mechanics in particular we show that the entropy of ideal quantum gases generates a special canonical transformation and moreover the entropy itself can be represented as a lie function formed by a special characteristic function

quantifying the incompatibility of quantum measurements relative to a basis motivated by quantum resource theories we introduce a notion of incompatibility for quantum measurements relative to a reference basis the notion arises by considering states diagonal in that basis and investigating whether probability distributions associated with different quantum measurements can be converted into one another by probabilistic postprocessing the induced preorder over quantum measurements is directly related to multivariate majorization and gives rise to families of monotones i e scalar quantifiers that preserve the ordering for the case of orthogonal measurement we establish a quantitative connection between incompatibility quantum coherence and entropic uncertainty relations we generalize the construction to include arbitrary positive operator valued measurements and report complete families of monotones

the classical moment problem as a self adjoint finite difference operator abstract this is a comprehensive exposition of the classical moment problem using methods from the theory of finite difference operators among the advantages of this approach is that the nevanlinna functions appear as elements of a transfer matrix and convergence of pade approximants appears as the strong resolvent convergence of finite matrix approximations to a jacobi matrix as a bonus of this we obtain new results on the convergence of certain pade approximants for series of hamburger

heisenberg inequality and the complex field in quantum mechanics observables a and b satisfy the heisenberg inequality if the product of their variances has a positive lower bound independent of the state of the system in the hilbert space formulation of quantum mechanics it is a consequence of the schwarz inequality that the heisenberg type inequality var a var b 1 4 a b b a 2 holds for any pair of observables a and b represented as self adjoint operators and for any vector state represented as a unit vector if inf a b b a dom a dom b 0 then a and b satisfy the heisenberg inequality in the present paper the derivability of the heisenberg type inequality is analyzed within the general theoretical frame of a sum logic it is shown that any real valued non negative function a f a of observables a and of states which has a symmetry property f a b f a b 2f a 2f b with respect to observables satisfies the heisenberg type inequality f a f b 1 4 f a b f a f b 2 for all observables a and

determination of a new uniform thorax density representative of the living population from 3d external body shape modeling body segment parameters bsp for each body s segment are needed for biomechanical analysis to provide population specific bsp precise estimation of body s segments volume and density are needed widely used uniform densities provided by cadavers studies did not consider the air present in the lungs when determining the thorax density the purpose of this study was to propose a new uniform thorax density representative of the living population from 3d external body shape modeling bi planar x ray radiographies were acquired on 58 participants allowing 3d reconstructions of the spine rib cage and human body shape three methods of computing the thorax mass were compared for 48 subjects 1 the dempster uniform density method currently in use for bsps calculation using dempster density data 2 the personalized method using full description of the thorax based on 3d reconstruction of the rib cage and spine and 3 the improved uniform density method using a uniform thorax density resulting from the personalized method for 10 participants comparison was made between the body mass obtained from a force plate and the body mass computed with each of the three methods the dempster uniform density method presented a mean error of 4 8 in the total body mass compared to the force plate vs 0 2 for the personalized method and 0 4 for the improved uniform density method the adjusted thorax density found from the 3d reconstruction was 0 74g cm 3 for men and 0 73g cm 3 for women instead of the one provided by dempster 0 92g cm 3 leading to a better estimate of the thorax mass and body mass

the simulation of aerial movement ii a mathematical inertia model of the human body a mathematical inertia model which permits the determination of personalized segmental inertia parameter values from anthropometric measurements is described the human body is modelled using 40 geometric solids which are specified by 95 anthropometric measurements a stadium solid is introduced for modelling the torso segments using perimeter and width measurements this procedure is more accurate than the use of elliptical discs of given width and depth and permits a smaller number of such solids to be used inertia parameter values may be obtained for body models of up to 20 segments errors in total body mass estimates from this and other models are discussed with reference to the unknown lung volumes

on the isolated points in the space of groups we investigate the isolated points in the space of finitely generated groups we give a workable characterization of isolated groups and study their hereditary properties various examples of groups are shown to yield isolated groups we also discuss a connection between isolated groups and solvability of the word problem

linear sofic groups and algebras we introduce and systematically study linear sofic groups and linear sofic algebras this generalizes amenable and lef groups and algebras we prove that a group is linear sofic if and only if its group algebra is linear sofic we show that linear soficity for groups is a priori weaker than soficity but stronger than weak soficity we also provide an alternative proof of a result of elek and szabo which states that sofic groups satisfy kaplansky s direct finiteness conjecture