unconditional security from noisy quantum storage we consider the implementation of two party cryptographic primitives based on the sole assumption that no large scale reliable quantum storage is available to the cheating party we construct novel protocols for oblivious transfer and bit commitment and prove that realistic noise levels provide security even against the most general attack such unconditional results were previously only known in the so called bounded storage model which is a special case of our setting our protocols can be implemented with present day hardware used for quantum key distribution in particular no quantum storage is required for the honest parties

quantifying measurement incompatibility of mutually unbiased bases quantum measurements based on mutually unbiased bases are commonly used in quantum information processing as they are generally viewed as being maximally incompatible and complementary here we quantify precisely the degree of incompatibility of mutually unbiased bases mub using the notion of noise robustness specifically for sets of k mub in dimension d we provide upper and lower bounds on this quantity notably we get a tight bound in several cases in particular for complete sets of k d 1 mub using the standard construction for d being a prime power on the way we also derive a general upper bound on the noise robustness for an arbitrary set of quantum measurements moreover we prove the existence of sets of k mub that are operationally inequivalent as they feature different noise robustness and we provide a lower bound on the number of such inequivalent sets up to dimension 32 finally we discuss applications of our results for einstein podolsky rosen steering

asymptotic formulae for the quantum renyi entropies of position application to the infinite well general asymptotic formulae are derived by means of the wkb approximation for the continuous and discrete renyi entropies of position of one dimensional quantum systems in energy eigenstates in terms of the corresponding entropies for a microcanonical ensemble of analogous classical systems these results are checked in the simplest particular case of the infinite potential well where the asymptotic formula for continuous entropies holds as an exact identity for the discrete entropies analytical expressions are obtained from which the asymptotic formulae given for the limiting cases of large and small measurement resolution can both be verified

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

the timoshenko system with history and cattaneo law in this paper we study a fully hyperbolic thermoelastic timoshenko system with past history where the thermal effects are given by cattaneo s law we obtain exponential stability of solutions if and only if a new condition on the wave speed of propagation is verified otherwise when that condition fails we obtain polynomial stability of solutions in this case optimal rates of decay are established

almost sure exponential stability of numerical solutions to stochastic delay hopfield neural networks stability of numerical solutions to stochastic delay differential equations have received an increasing attention but there has been so far little work on the stability analysis of numerical solutions to stochastic delay hopfield neural networks the aim of this paper is to study the almost sure exponential stability of numerical solutions to stochastic delay hopfield neural networks by using two approaches the euler method and the backward euler method under some reasonable conditions both the euler scheme and the backward euler scheme are proved to be almost sure exponential stability in particular the euler method and the backward euler method are mainly based on the semimartingale convergence theorem

energy decay for timoshenko systems of memory type abstract linear systems of timoshenko type equations for beams including a memory term are studied the exponential decay is proved for exponential kernels while polynomial kernels are shown to lead to a polynomial decay the optimality of the results is also investigated

rates of decay to non homogeneous timoshenko model with tip body abstract we consider the uniform stabilization of a hybrid elastic model consisting of a timoshenko beam and a tip load at the free end of the beam our main result proves that the semigroup e a t associated to this model is not exponentially stable moreover we prove that the semigroup decays polynomially to zero as t 1 2 when the damping mechanism is effective only on the boundary of the rotational angle the solution also decays polynomially as t 1 2 provided the wave speeds are equal otherwise it decays as t 1 4 for any initial data taken in d a

on classes of non gaussian asymptotic minimizers in entropic uncertainty principles abstract in this paper we revisit the bialynicki birula and mycielski uncertainty principle and its cases of equality this shannon entropic version of the well known heisenberg uncertainty principle can be used when dealing with variables that admit no variance in this paper we extend this uncertainty principle to renyi entropies we recall that in both shannon and renyi cases and for a given dimension n the only case of equality occurs for gaussian random vectors we show that as n grows however the bound is also asymptotically attained in the cases of n dimensional student t and student r distributions a complete analytical study is performed in a special case of a student t distribution we also show numerically that this effect exists for the particular case of a n dimensional cauchy variable whatever the renyi entropy considered extending the results of abe and illustrating the analytical asymptotic study of the student t case in the student r case we show numerically that the same behavior occurs for uniformly distributed vectors these particular cases and other ones investigated in this paper are interesting since they show that this asymptotic behavior cannot be considered as a gaussianization of the vector when the dimension increases

decomposition rules for quantum renyi mutual information with an application to information exclusion relations we prove decomposition rules for quantum renyi mutual information generalizing the relation i a b h a h a b to inequalities between renyi mutual information and renyi entropy of different orders the proof uses beigi s generalization of reisz thorin interpolation to operator norms j math phys 54 12 122202 2013 and a variation of the argument developed by dupuis j math phys 56 022203 2015 which was used to show chain rules for conditional renyi entropies the resulting decomposition rule is then applied to establish an information exclusion relation for renyi mutual information generalizing the original relation by hall phys rev lett 74 3307 1995

exponential stability of laminated timoshenko beams with boundary internal controls abstract for a laminated timoshenko system with slip along the interface we study existence and boundary interior stabilization of solutions our first main result using resolvent estimates in the frequency domain is to show that interior damping created by the interfacial slip in companion with boundary feedback controls acting on the complementary displacements traverse and rotation angle drives the solution to zero with exponential decay rate we impose neither conditions on the physical parameters of the model nor on the damping coefficients our second main result is to investigate the asymptotic behavior of solutions for partially dissipative problems assuming the condition that the waves travel at the same speed we prove the decay of solutions with exponential rate finally the same condition allows us to show that dissipative effect created by the interfacial slip is strong enough to exponentially stabilizes the solutions to zero

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

entropic bounds on semiclassical measures for quantized one dimensional maps quantum ergodicity asserts that almost all infinite sequences of eigenstates of quantized ergodic hamiltonian systems are equidistributed in phase space this however does not prohibit existence of exceptional sequences which might converge to different non liouville classical invariant measures it has been recently shown by n anantharaman and s nonnenmacher in 20 21 with h koch that for anosov geodesic flows the metric entropy of any semiclassical measure must satisfy a certain bound this remarkable result seems to be optimal for manifolds of constant negative curvature but not in the general case where it might become even trivial if the negative curvature of the riemannian manifold varies a lot it has been conjectured by the same authors that in fact a stronger bound valid in the general case should hold

complementary reductions for two qubits reduction of a state of a quantum system to a subsystem gives partial quantum information about the true state of the total system in connection with optimal state determination for two qubits the question was raised about the maximum number of pairwise complementary reductions the main result of the paper tells that the maximum number is 4 that is if a1 a2 ak are pairwise complementary or quasiorthogonal subalgebras of the algebra m4 c of all 4 4 matrices and they are isomorphic to m2 c then k 4 the proof is based on a cartan decomposition of su 4 in the way to the main result contributions are made to the understanding of the structure of complementary reductions

noise induced stabilization of the recurrent neural networks with mixed time varying delays and markovian switching parameters the stabilization of recurrent neural networks with mixed time varying delays and markovian switching parameters by noise is discussed first a new result is given for the existence of unique states of recurrent neural networks nns with mixed time varying delays and markovian switching parameters in the presence of noise without the need to satisfy the linear growth conditions required by general stochastic markovian switching systems next a delay dependent condition for stabilization of concerned recurrent nns is derived by applying the ltd formula the gronwall inequality the law of large numbers and the ergodic property of markovian chain the results show that there always exists an appropriate white noise such that any recurrent nns with mixed time varying delays and markovian switching parameters can be exponentially stabilized by noise if the delays are sufficiently small

uncertainty inequalities among frequency moments and radial expectation values applications to atomic systems rigorous and universal bounds on frequency moments of one particle densities in terms of radial expectation values in the conjugate space are obtained the results valid for any d dimensional quantum mechanical system are derived by using renyi like position momentum inequalities in an information theoretical framework especially interesting are the upper bounds on the dirac exchange and thomas fermi kinetic energies as well as the disequilibrium or self similarity of both position and momentum distributions a variety of bounds for these functionals in a given space are known but most usually in terms of quantities defined within the same space very few results including a density functional on one space and expectation values on the conjugate one are found in the literature a pioneering bound on the disequilibrium in terms of the kinetic energy is improved in this work a numerical study of the aforementioned relationships is carried out for atomic systems in their ground state some results ar

boundary control of the timoshenko beam it is shown that the timoshenko beam can be uniformly stabilized by means of a boundary control a numerical study on the spectrum is also presented

gelfand yaglom perez theorem for generalized relative entropy functionals the measure theoretic definition of kullback leibler relative entropy or simply kl entropy plays a basic role in defining various classical information measures on general spaces entropy mutual information and conditional forms of entropy can be expressed in terms of kl entropy and hence properties of their measure theoretic analogs will follow from those of measure theoretic kl entropy these measure theoretic definitions are key to extending the ergodic theorems of information theory to non discrete cases a fundamental theorem in this respect is the gelfand yaglom perez gyp theorem m s pinsker information and information stability of random variables and process 1960 holden day san francisco ca english ed 1964 translated and edited by amiel feinstein theorem 2 4 2 which states that measure theoretic relative entropy equals the supremum of relative entropies over all measurable partitions this paper states and proves the gyp theorem for renyi relative entropy of order greater than one consequently the result can be easily extended to tsallis relative entropy

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

higher entropic uncertainty relations for anti commuting observables uncertainty relations provide one of the most powerful formulations of the quantum mechanical principle of complementarity yet very little is known about such uncertainty relations for more than two measurements here we show that sufficient unbiasedness for a set of binary observables in the sense of mutual anticommutation is good enough to obtain maximally strong uncertainty relations in terms of the shannon entropy we also prove nearly optimal relations for the collision entropy this is the first systematic and explicit approach to finding an arbitrary number of measurements for which we obtain maximally strong uncertainty relations our results have immediate applications to quantum cryptography

the stability number of the timoshenko system with second sound abstract in this work we consider the timoshenko beam model with second sound we introduce a new number 0 that characterizes the exponential decay we prove that the corresponding semigroup associated to the system is exponentially stable if and only if 0 0 otherwise there is a lack of exponential stability in this case we prove that the semigroup decays as t 1 2 moreover we show that the rate is optimal

general entropy like uncertainty relations in finite dimensions we revisit entropic formulations of the uncertainty principle up for an arbitrary pair of positive operator valued measures povm a and b acting on finite dimensional hilbert space salicr generalized entropies including r nyi and tsallis ones among others are used as uncertainty measures associated with the distribution probabilities corresponding to the outcomes of the observables we obtain a nontrivial lower bound for the sum of generalized entropies for any pair of entropic functionals which is valid for both pure and mixed states the bound depends on the overlap triplet with ca respectively cb being the overlap between the elements of the povm a respectively b and the overlap between the pair of povm our approach is inspired by that of de vicente and s nchez ruiz 2008 phys rev a 77 042110 and consists in a minimization of the entropy sum subject to the landau pollak inequality that links the maximum probabilities of both observables we solve the constrained optimization problem in a geometrical way and furthermore when dealing with r nyi or tsallis entropic formulations of the up we overcome the h lder conjugacy constraint imposed on the entropic indices by the riesz thorin theorem in the case of nondegenerate observables we show that for given the bound obtained is optimal and that for r nyi entropies our bound improves deutsch one but maassen uffink bound prevails when finally we illustrate by comparing our bound with known previous results in particular cases of r nyi and tsallis entropies

asymptotic entropic uncertainty relations we analyze entropic uncertainty relations for two orthogonal measurements on a n dimensional hilbert space performed in two generic bases it is assumed that the unitary matrix u relating both bases is distributed according to the haar measure on the unitary group we provide lower bounds on the average shannon entropy of probability distributions related to both measurements the bounds are stronger than those obtained with use of the entropic uncertainty relation by maassen and uffink and they are optimal up to additive constants we also analyze the case of a large number of measurements and obtain strong entropic uncertainty relations which hold with high probability with respect to the random choice of bases the lower bounds we obtain are optimal up to additive constants and allow us to prove a conjecture by wehner and winter on the asymptotic behavior of constants in entropic uncertainty relations as the dimension tends to infinity as a tool we develop estimates on the maximum operator norm of a submatrix of a fixed size of a random unitary matrix distributed according to the haar measure which are of independent interest

entropy of semiclassical measures in dimension 2 we study the high energy asymptotic properties of eigenfunctions of the laplacian in the case of a compact riemannian surfacem of anosov type to do this we look at families of distributions associated to them on the cotangent bundle t m and we derive entropic properties on their accumulation points in the high energy limit the so called semiclassical measures we show that the kolmogorov sinai entropy of a semiclassical measure for the geodesic ow gt is bounded from below by half of the ruelle upper bound i e hks g 1 2 s m d where is the upper lyapunov exponent at point

multistability of two kinds of recurrent neural networks with activation functions symmetrical about the origin on the phase plane in this paper we investigate multistability of two kinds of recurrent neural networks with time varying delays and activation functions symmetrical about the origin on the phase plane one kind of activation function is with zero slope at the origin on the phase plane while the other is with nonzero slope at the origin on the phase plane we derive sufficient conditions under which these two kinds of n dimensional recurrent neural networks are guaranteed to have 2m 1 n equilibrium points with m 1 n of them being locally exponentially stable these new conditions improve and extend the existing multistability results for recurrent neural networks finally the validity and performance of the theoretical results are demonstrated through two numerical examples

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

randomizing quantum states constructions and applications the construction of a perfectly secure private quantum channel in dimension d is known to require 2 log d shared random key bits between the sender and receiver we show that if only near perfect security is required the size of the key can be reduced by a factor of two more specifically we show that there exists a set of roughly d log d unitary operators whose average effect on every input pure state is almost perfectly randomizing as compared to the d2 operators required to randomize perfectly aside from the private quantum channel variations of this construction can be applied to many other tasks in quantum information processing we show for instance that it can be used to construct locc data hiding schemes for bits and qubits that are much more efficient than any others known allowing roughly log d qubits to be hidden in 2 log d qubits the method can also be used to exhibit the existence of quantum states with locked classical correlations an arbitrarily large amplification of the correlation being accomplished by sending a negligibly small classical key our construction also provides the basic building block for a method of remotely preparing arbitrary d dimensional pure quantum states using approximately log d bits of communication and log d ebits of entanglement

an entropy based uncertainty principle for a locally compact abelian group abstract we classify all functions on a locally compact abelian group giving equality in an entropy inequality generalizing the heisenberg uncertainty principle in particular for functions on a real line we proof a conjecture of hirschman published in 1957

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

the lack of exponential stability of the hybrid bresse system abstract in this paper we consider the dissipative bresse system with an attached hollow tip body that contains granular material the resulting model being called hybrid system our main result is to show that the corresponding model is not exponentially stable moreover we show that the solution decays polynomially to zero as 1 t 1 2 when t

entropic heisenberg limits and uncertainty relations from the holevo information bound strong and general entropic and geometric heisenberg limits are obtained for estimates of multiparameter unitary displacements in quantum metrology such as the estimation of a magnetic field from the induced rotation of a probe state in three dimensions a key ingredient is the holevo bound on the shannon mutual information of a quantum communication channel this leads to a bayesian bound on performance in terms of the prior distribution of the displacement and the asymmetry of the input probe state with respect to the displacement group a geometric measure of performance related to entropy is proposed for general parameter estimation it is also shown how strong entropic uncertainty relations for mutually unbiased observables such as number and phase position and momentum energy and time and orthogonal spin 1 2 directions can be obtained from elementary applications of holevo s bound a geometric interpretation of results is emphasised in terms of the volumes of quantum and classical statistical ensembles

the fisher information based uncertainty relation cramer rao inequality and kinetic energy for the d dimensional central problem the inequality with l being the grand orbital quantum number and its conjugate relation for r2 p 2 are shown to be fulfilled in the d dimensional central problem their use has allowed us to improve the fisher information based uncertainty relation i i const and the cramer rao inequalities r2i d2 p2i d2 in addition the kinetic energy and the radial expectation value r2 are shown to be bounded from below by the fisher information in position and momentum spaces denoted by i and i respectively

stability analysis of markovian jumping stochastic cohen grossberg neural networks with mixed time delays in this letter the global asymptotical stability analysis problem is considered for a class of markovian jumping stochastic cohen grossberg neural networks cgnns with mixed delays including discrete delays and distributed delays an alternative delay dependent stability analysis result is established based on the linear matrix inequality lmi technique which can easily be checked by utilizing the numerically efficient matlab lmi toolbox neither system transformation nor free weight matrix via newton leibniz formula is required two numerical examples are included to show the effectiveness of the result

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

almost sure exponential stability of recurrent neural networks with markovian switching this paper presents new stability results for recurrent neural networks with markovian switching first algebraic criteria for the almost sure exponential stability of recurrent neural networks with markovian switching and without time delays are derived the results show that the almost sure exponential stability of such a neural network does not require the stability of the neural network at every individual parametric configuration next both delay dependent and delay independent criteria for the almost sure exponential stability of recurrent neural networks with time varying delays and markovian switching parameters are derived by means of a generalized stochastic halanay inequality the results herein include existing ones for recurrent neural networks without markovian switching as special cases finally simulation results in three numerical examples are discussed to illustrate the theoretical results

passivity analysis for discrete time stochastic markovian jump neural networks with mixed time delays in this paper passivity analysis is conducted for discrete time stochastic neural networks with both markovian jumping parameters and mixed time delays the mixed time delays consist of both discrete and distributed delays the markov chain in the underlying neural networks is finite piecewise homogeneous by introducing a lyapunov functional that accounts for the mixed time delays a delay dependent passivity condition is derived in terms of the linear matrix inequality approach the case of markov chain with partially unknown transition probabilities is also considered all the results presented depend upon not only discrete delay but also distributed delay a numerical example is included to demonstrate the effectiveness of the proposed methods

design of state dependent switching laws for stability of switched stochastic neural networks with time delays we study the stability properties of switched stochastic neural networks ssnns with time varying delays whose subsystem is not necessarily stable we introduce state dependent switching sds as a tool for stability analysis some sds laws for asymptotic stability and p th moment exponentially stable are designed by employing lyapunov krasovskii l k functional and lyapunov razumikhin l r method respectively it is shown that the stability of ssnns with time varying delays composed of unstable subsystems can be achieved by using sds law the control gains in the designed sds laws can be derived by solving the lmis in derived stability criteria two numerical examples are provided to demonstrate the effectiveness of the proposed sds laws

the capacity of the quantum channel with general signal states it is shown that the capacity of a classical quantum channel with arbitrary possibly mixed states equals the maximum of the entropy bound with respect to all a priori distributions this completes the recent result of hausladen jozsa schumacher westmoreland and wootters 1996 who proved the equality for the pure state channel

generalized halanay inequalities and their applications to neural networks with unbounded time varying delays in this brief we discuss some variants of generalized halanay inequalities that are useful in the discussion of dissipativity and stability of delayed neural networks integro differential systems and volterra functional differential equations we provide some generalizations of the halanay inequality which is more accurate than the existing results as applications we discuss invariant set dissipative synchronization and global asymptotic stability for the hopfield neural networks with infinite delays we also prove that the dynamical systems with unbounded time varying delays are globally asymptotically stable

new delay dependent stability criteria for neural networks with time varying delay in this letter a new method is proposed for stability analysis of neural networks nns with a time varying delay some less conservative delay dependent stability criteria are established by considering the additional useful terms which were ignored in previous methods when estimating the upper bound of the derivative of lyapunov functionals and introducing the new free weighting matrices numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

uniform decay in a timoshenko type system with past history abstract fernandez sare and rivera h d fernandez sare j e munoz rivera stability of timoshenko systems with past history j math anal appl 339 1 2008 482 502 considered the following timoshenko type system 1 t t k x x 0 2 t t b x x 0 g t x x t s d s k x 0 where g is a positive differentiable exponentially decaying function they established an exponential decay result in the case of equal wave speed propagation and a polynomial decay result in the case of nonequal wave speed propagation in this paper we study the same system for g decaying polynomially and prove polynomial stability results for the equal and nonequal wave speed propagation our results are established under conditions on the relaxation function weaker than those in h d fernandez sare j e munoz rivera stability of timoshenko systems with past history j math anal appl 339 1 2008 482 502

stability analysis for stochastic cohen grossberg neural networks with mixed time delays in this letter the global asymptotic stability analysis problem is considered for a class of stochastic cohen grossberg neural networks with mixed time delays which consist of both the discrete and distributed time delays based on an lyapunov krasovskii functional and the stochastic stability analysis theory a linear matrix inequality lmi approach is developed to derive several sufficient conditions guaranteeing the global asymptotic convergence of the equilibrium point in the mean square it is shown that the addressed stochastic cohen grossberg neural networks with mixed delays are globally asymptotically stable in the mean square if two lmis are feasible where the feasibility of lmis can be readily checked by the matlab lmi toolbox it is also pointed out that the main results comprise some existing results as special cases a numerical example is given to demonstrate the usefulness of the proposed global stability criteria

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

visibility for anharmonic fringes we examine a new approach to the visibility of interference fringes defined as the distance l2 to the uniform distribution we show that this approach is superior to the standard approach when examining anharmonic fringes while they coincide for harmonic fringes we demonstrate the close relationship between this formalism and other well studied measures of quantum uncertainty and information we also show that this approach preserves the connection between visibility and correlation functions irrespective of the complexity of the interferometric pattern

robust exponential stability of markovian jump impulsive stochastic cohen grossberg neural networks with mixed time delays this paper is concerned with the problem of exponential stability for a class of markovian jump impulsive stochastic cohen grossberg neural networks with mixed time delays and known or unknown parameters the jumping parameters are determined by a continuous time discrete state markov chain and the mixed time delays under consideration comprise both time varying delays and continuously distributed delays to the best of the authors knowledge till now the exponential stability problem for this class of generalized neural networks has not yet been solved since continuously distributed delays are considered in this paper the main objective of this paper is to fill this gap by constructing a novel lyapunov krasovskii functional and using some new approaches and techniques several novel sufficient conditions are obtained to ensure the exponential stability of the trivial solution in the mean square the results presented in this paper generalize and improve many known results finally two numerical examples and their simulations are given to show the effectiveness of the theoretical results

synchronization of complex dynamical networks with hybrid coupling delays on time scales by handling multitude kronecker product terms the problem of synchronization is studied for complex dynamical networks with hybrid coupling delays on time scales the hybrid coupling delays consist of both discrete and distributed coupling delays some novel and useful synchronization criteria of complex dynamical networks are derived based on stability theory of error dynamical system by employing the standard lyapunov krasovskii functional matrix expansion method to handle multitude kronecker product terms and the modified jensen s inequalities on time scale new sufficient conditions guaranteeing the global exponential stability of the origin of complex dynamical networks are established interms of linear matrix inequality lmi numerical examples are included to demonstrate the effectiveness of the proposed method

on input to state stability of stochastic retarded systems with markovian switching this note develops a razumikhin type theorem on pth moment input to state stability of hybrid stochastic retarded systems also known as stochastic retarded systems with markovian switching which is an improvement of an existing result an application to hybrid stochastic delay systems verifies the effectiveness of the improved result

brief paper input to state stability and integral input to state stability of nonlinear impulsive systems with delays this paper is concerned with analyzing input to state stability iss and integral iss iiss for nonlinear impulsive systems with delays razumikhin type theorems are established which guarantee iss iiss for delayed impulsive systems with external input affecting both the continuous dynamics and the discrete dynamics it is shown that when the delayed continuous dynamics are iss iiss but the discrete dynamics governing the impulses are not the iss iiss property of the impulsive system can be retained if the length of the impulsive interval is large enough conversely when the delayed continuous dynamics are not iss iiss but the discrete dynamics governing the impulses are the impulsive system can achieve iss iiss if the sum of the length of the impulsive interval and the time delay is small enough in particular when one of the delayed continuous dynamics and the discrete dynamics are iss iiss and the others are stable for the zero input the impulsive system can keep iss iiss no matter how often the impulses occur our proposed results are evaluated using two illustrative examples to show their effectiveness

necessary and sufficient conditions for 2p th moment stability of several classes of linear stochastic systems this technical note presents necessary and sufficient conditions for 2p th moment stability of several widely used linear stochastic systems by the matrix derivative operator and vectorial ito s formula we first derive two extended systems one is described by stochastic differential equation sde and the other by ordinary differential equation ode it is shown that the stochastic system is 2p th moment exponentially stable if and only if the sde is mean square exponentially stable or the ode is exponentially stable subsequently combining the quasi periodic homogeneous polynomial lyapunov function methods with the proposed techniques a series of nonconservative stability criteria are established for linear impulsive sampled data and switched stochastic systems under dwell time constraints a numerical example illustrates the proposed theoretical results

phase space localization of antisymmetric functions upper and lower bounds are written down for the minimum information entropy in phase space of an antisymmetric wave function in any number of dimensions similar bounds are given when the wave function is restricted to belong to any of the proper subspaces of the fourier transform operator

stability and synchronization of discrete time markovian jumping neural networks with mixed mode dependent time delays in this paper we introduce a new class of discrete time neural networks dnns with markovian jumping parameters as well as mode dependent mixed time delays both discrete and distributed time delays specifically the parameters of the dnns are subject to the switching from one to another at different times according to a markov chain and the mixed time delays consist of both discrete and distributed delays that are dependent on the markovian jumping mode we first deal with the stability analysis problem of the addressed neural networks a special inequality is developed to account for the mixed time delays in the discrete time setting and a novel lyapunov krasovskii functional is put forward to reflect the mode dependent time delays sufficient conditions are established in terms of linear matrix inequalities lmis that guarantee the stochastic stability we then turn to the synchronization problem among an array of identical coupled markovian jumping neural networks with mixed mode dependent time delays by utilizing the lyapunov stability theory and the kronecker product it is shown that the addressed synchronization problem is solvable if several lmis are feasible hence different from the commonly used matrix norm theories such as the m matrix method a unified lmi approach is developed to solve the stability analysis and synchronization problems of the class of neural networks under investigation where the lmis can be easily solved by using the available matlab lmi toolbox two numerical examples are presented to illustrate the usefulness and effectiveness of the main results obtained

on the stability and control of nonlinear dynamical systems via vector lyapunov functions vector lyapunov theory has been developed to weaken the hypothesis of standard lyapunov theory in order to enlarge the class of lyapunov functions that can be used for analyzing system stability in this paper we extend the theory of vector lyapunov functions by constructing a generalized comparison system whose vector field can be a function of the comparison system states as well as the nonlinear dynamical system states furthermore we present a generalized convergence result which in the case of a scalar comparison system specializes to the classical krasovskii lasalle invariant set theorem in addition we introduce the notion of a control vector lyapunov function as a generalization of control lyapunov functions and show that asymptotic stabilizability of a nonlinear dynamical system is equivalent to the existence of a control vector lyapunov function moreover using control vector lyapunov functions we construct a universal decentralized feedback control law for a decentralized nonlinear dynamical system that possesses guaranteed gain and sector margins in each decentralized input channel furthermore we establish connections between the recently developed notion of vector dissipativity and optimality of the proposed decentralized feedback control law finally the proposed control framework is used to construct decentralized controllers for large scale nonlinear systems with robustness guarantees against full modeling uncertainty

extended quantum conditional entropy and quantum uncertainty inequalities quantum states can be subjected to classical measurements whose incompatibility or uncertainty can be quantified by a comparison of certain entropies there is a long history of such entropy inequalities between position and momentum recently these inequalities have been generalized to the tensor product of several hilbert spaces and we show here how their derivations can be shortened to a few lines and how they can be generalized our proofs utilize the technique of the original derivation of strong subadditivity of the von neumann entropy

stochastic input to state stability and applications to global feedback stabilization notions of stochastic input to state stability are introduced and their lyapunov characterizations are established these notions constitute extensions of the deterministic iss proposed by e sonta

on stability of recurrent neural networks an approach from volterra integro differential equations the uniform asymptotic stability of recurrent neural networks rnns with distributed delay is analyzed by comparing rnns to linear volterra integro differential systems under lipschitz continuity of activation functions the stability criteria obtained have unified and extended many existing results on rnns

p th moment exponential input to state stability of delayed recurrent neural networks with markovian switching via vector lyapunov function in this paper the p th moment input to state exponential stability for delayed recurrent neural networks drnns with markovian switching is studied by using stochastic analysis techniques and classical razumikhin techniques a generalized vector mathcal l operator differential inequality including cross item is obtained without additional restrictive conditions on the time varying delay the sufficient criteria on the p th moment input to state exponential stability for drnns with markovian switching are derived by means of the vector mathcal l operator differential inequality when the input is zero an improved criterion on exponential stability is obtained two numerical examples are provided to examine the correctness of the derived results

renyi formulation of the entropic uncertainty principle for povms uncertainty relations for a pair of arbitrary measurements are posed in the form of inequalities using the renyi entropies the formulation deals with povm measurements on finite dimensional hilbert space both the entropic uncertainty relations with state dependent and state independent bounds are presented the results are illustrated on the example of measurements for state discrimination

differential entropy and dynamics of uncertainty we analyze the functioning of gibbs type entropy functionals in the time domain with emphasis on shannon and kullback leibler entropies of time dependent continuous probability distributions the shannon entropy validity is extended to probability distributions inferred from l 2 r n quantum wave packets in contrast to the von neumann entropy which simply vanishes on pure states the differential entropy quantifies the degree of probability de localization and its time development the associated dynamics of the fisher information functional quantifies nontrivial power transfer processes in the mean both in dissipative and quantum mechanical cases

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

entropic uncertainty relations and the stabilizer formalism entropic uncertainty relations express the quantum mechanical uncertainty principle by quantifying uncertainty in terms of entropy central questions include the derivation of lower bounds on the total uncertainty for given observables the characterization of observables that allow strong uncertainty relations and the construction of such relations for the case of several observables we demonstrate how the stabilizer formalism can be applied to these questions we show that the maassen uffink entropic uncertainty relation is tight for the measurement in any pair of stabilizer bases we compare the relative strengths of variance based and various entropic uncertainty relations for dichotomic anticommuting observables

polynomial stability of the timoshenko system by one boundary damping abstract in this paper we study the indirect boundary stabilization of the timoshenko system with only one dissipation law this system which models the dynamics of a beam is a hyperbolic system with two wave speeds assuming that the wave speeds are equal we prove non uniform stability and an optimal polynomial energy decay rate is obtained otherwise if the ratio of the wave speeds is a rational number we show that the decay rate is of polynomial type

decay rate estimates for the quasi linear timoshenko system with nonlinear control and damping terms in this work we consider a class of quasi linear timoshenko systems with nonlinear control and damping terms we investigate the stabilization of weak solutions to the initial boundary value problem and obtain explicit decay rate estimation depending on control and damping terms

stabilization of the nonuniform timoshenko beam in this paper we consider a timoshenko beam with variable physical parameters we prove that the model can be stabilize by one control force for both internal and boundary cases

uncertainty relations for joint localizability and joint measurability in finite dimensional systems two quantities quantifying uncertainty relations are examined busch and pearson j math phys 48 082103 2007 investigated the limitation on joint localizability and joint measurement of position and momentum by introducing overall width and error bar width in this paper we show a simple relationship between these quantities for finite dimensional systems our result indicates that if there is a bound on joint localizability it is possible to obtain a similar bound on joint measurability for finite dimensional systems uncertainty relations for a pair of general projection valued measures are obtained as by products

p attracting and p invariant sets for a class of impulsive stochastic functional differential equations in this paper a nonlinear and nonautonomous impulsive stochastic functional differential equation is considered by establishing an l operator differential inequality and stochastic analysis technique we obtain the p attracting set and p invariant set of the impulsive stochastic functional differential equation an example is also discussed to illustrate the efficiency of the obtained results

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

some extensions of the uncertainty principle abstract we study the formulation of the uncertainty principle in quantum mechanics in terms of entropic inequalities extending results recently derived by bialynicki birula i bialynicki birula formulation of the uncertainty relations in terms of the renyi entropies physical review a 74 5 2006 052101 and zozor et al s zozor c vignat on classes of non gaussian asymptotic minimizers in entropic uncertainty principles physica a 375 2 2007 499 517 those inequalities can be considered as generalizations of the heisenberg uncertainty principle since they measure the mutual uncertainty of a wave function and its fourier transform through their associated renyi entropies with conjugated indices we consider here the general case where the entropic indices are not conjugated in both cases where the state space is discrete and continuous we discuss the existence of an uncertainty inequality depending on the location of the entropic indices and in the plane our results explain and extend a recent study by luis a luis quantum properties of exponential states physical review a 75 2007 052115 where states with quantum fluctuations below the gaussian case are discussed at the single point 2 2

energy decay in a timoshenko type system of thermoelasticity of type iii in this paper we consider a one dimensional linear thermoelastic system of timoshenko type where the heat conduction is given by green and naghdi theories we prove the exponential stability by using the energy method

reformulation for arbitrary mixed states of jones bayes estimation of pure states abstract jones has cast the problem of estimating the pure state of a d dimensional quantum system into a bayesian framework the normalized uniform ray measure over such states is employed as the prior distribution the data consist of observed eigenvectors k k 1 n from an n trial analyzer that is a collection of n bases of the hilbert space c d the desired posterior inferred distribution is then simply proportional to the likelihood of k 1n k 2 here jones approach is extended to the more realistic experimental case of mixed input states as the unnormalized prior over the d d density matrices the recently developed reparameterization and unitarily invariant measure 2d 1 is utilized the likelihood is then taken to be k 1n k k reducing to that of jones when corresponds to a pure state the case of a pure state however the associated prior and posterior probabilities are then zero some analytical results for the case d 2 are presented

on the stabilization of timoshenko systems with memory and different speeds of wave propagation in this work we consider a one dimensional timoshenko system with different speeds of wave propagation and with only one control given by a viscoelastic term on the angular rotation equation for a wide class of relaxation functions and for sufficiently regular initial data we establish a general decay result for the energy of solution unlike the past history and internal feedback cases the second energy is not necessarily decreasing to overcome this difficulty a precise estimate of the second energy in terms of the initial data and the relaxation function is proved

stabilizability of systems of one dimensional wave equations by one internal or boundary control force we study the internal and boundary stabilizability of a system of wave equations by one control force we prove that the classical internal damping applied to only one of the equations never gives exponential stability if the wave speeds are different and if the wave speeds are the same we give explicit necessary and sufficient conditions for the stability to occur we also study the simultaneous boundary stabilization of the same system

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

pitt s inequality and the uncertainty principle associated with the quaternion fourier transform abstract the quaternion fourier transform a generalized form of the classical fourier transform has been shown to be a powerful analyzing tool in image and signal processing this paper investigates pitt s inequality and uncertainty principle associated with the two sided quaternion fourier transform it is shown that by applying the symmetric form f f 1 i f 2 f 3 j i f 4 j of quaternion from hitzer and the novel module or l p norm of the quaternion fourier transform f then any nonzero quaternion signal and its quaternion fourier transform cannot both be highly concentrated two part results are provided one part is heisenberg weyl s uncertainty principle associated with the quaternion fourier transform it is formulated by using logarithmic estimates which may be obtained from a sharp of pitt s inequality the other part is the uncertainty principle of donoho and stark associated with the quaternion fourier transform

on the spectrum of evolution operators generated by hyperbolic systems abstract we prove that the asymptotic behavior of semigroups generated by mixed initial value problems for hyperbolic systems in one space variable is determined by the zeroes of the characteristic equation the proof is based on the following reduction principle we construct a reduced system which is much simpler than the given one such that the difference of the semigroups is a compact operator the construction of the reduced system is presented in the non autonomous case because it has implifications in the study of systems which are time periodic