a maximum likelihood time delay estimator in a multipath environment using importance sampling in this paper we present a new implementation of the maximum likelihood criterion for the estimation of the time delays in a multipath environment and then extend it to the estimation of the time difference of arrival when the transmitted signal is unknown the new technique implements the concept of importance sampling is to find the global maximum of the compressed likelihood function in a modest computational manner it thereby avoids traditional complex multidimensional grid search or initialization dependent iterative methods indeed one of the most interesting features is that it transforms the multi dimensional search inherent to multipath propagation into a much simpler one dimensional optimization problem in the delays dimension moreover it guarantees convergence to the global maximum contrarily to the popular iterative implementation of the maximum likelihood criterion by the well known expectation maximization em algorithm comparisons with some other methods such as the em algorithm music and accelerated random search ars demonstrates the superiority of the proposed is based multipath delay estimator in terms of estimation performance and complexity

reducing the quantum communication cost of quantum secret sharing we demonstrate a new construction for perfect quantum secret sharing qss schemes based on imperfect ramp secret sharing combined with classical encryption in which the individual parties shares are split into quantum and classical components allowing the former to be of lower dimension than the secret itself we show that such schemes can be performed with smaller quantum components and lower overall quantum communication than required for existing methods we further demonstrate that one may combine both imperfect quantum and imperfect classical secret sharing to produce an overall perfect qss scheme and that examples of such schemes which we construct can have the smallest quantum and classical share components possible for their access structures something provably not achievable using perfect underlying schemes our construction has significant potential for being adapted to other qss schemes based on stabilizer codes

all maximally entangled four qubit states we find an operational interpretation for the 4 tangle as a type of residual entanglement somewhat similar to the interpretation of the 3 tangle using this remarkable interpretation we are able to find the class of maximally entangled four qubits states which is characterized by four real parameters the states in the class are maximally entangled in the sense that their average bipartite entanglement with respect to all possible bipartite cuts is maximal we show that while all the states in the class maximize the average tangle there are only a few states in the class that maximize the average tsillas or renyi entropy of entanglement quite remarkably we find that up to local unitaries there exists two unique states one maximizing the average tsallis entropy of entanglement for all 2 while the other maximizing it for all 0 2 including the von neumann case of 1 furthermore among the maximally entangled four qubits states there are only three maximally entangled states that have the property that for two out of the three bipartite cuts consisting of two qubits verses two qubits the entanglement is 2 ebits and for the remaining bipartite cut the entanglement between the two groups of two qubits is 1 ebit the unique three maximally entangled states are the three cluster states that are related by a swap operator we also show that the cluster states are the only states up to local unitaries that maximize the average renyi entropy of entanglement for all 2

time delay estimation from low rate samples a union of subspaces approach time delay estimation arises in many applications in which a multipath medium has to be identified from pulses transmitted through the channel previous methods for time delay recovery either operate on the analog received signal or require sampling at the nyquist rate of the transmitted pulse in this paper we develop a unified approach to time delay estimation from low rate samples this problem can be formulated in the broader context of sampling over an infinite union of subspaces although sampling over unions of subspaces has been receiving growing interest previous results either focus on unions of finite dimensional subspaces or finite unions the framework we develop here leads to perfect recovery of the multipath delays from samples of the channel output at the lowest possible rate even in the presence of overlapping transmitted pulses and allows for a variety of different sampling methods the sampling rate depends only on the number of multipath components and the transmission rate but not on the bandwidth of the probing signal this result can be viewed as a sampling theorem over an infinite union of infinite dimensional subspaces by properly manipulating the low rate samples we show that the time delays can be recovered using the well known esprit algorithm combining results from sampling theory with those obtained in the context of direction of arrival estimation we develop sufficient conditions on the transmitted pulse and the sampling functions in order to ensure perfect recovery of the channel parameters at the minimal possible rate

an importance sampling maximum likelihood direction of arrival estimator we present a new implementation for maximum likelihood ml estimation of the direction of arrival doa of multiple narrow band plane waves in noise the proposed estimator can be applied to the estimation of doas of both deterministic and stochastic signals in this paper we discuss the estimation of doas for stochastic signals only the proposed method uses a global optimization procedure to maximize the compressed likelihood function which is a function of only the doas the procedure is based on monte carlo importance sampling it is shown via simulations that the method allows for estimation of doas at low angular separation and in situations for which other suboptimal techniques may fail the improved performance of this method is due to its guaranteed convergence to a global maximum which is not true for the iterative ml methods as for example the wsf mode x and em algorithms we compare our method to the latter algorithms to show that the proposed method outperforms the iterative approaches for closely spaced narrow band sources

tangent processes on wiener space abstract this paper deals with the study of the malliavin calculus of euclidean motions on wiener space i e transformations induced by general measure preserving transformations called rotations and h valued shifts and the associated flows on abstract wiener spaces

stochastic calculus with anticipating integrands we study the stochastic integral defined by skorohod in 24 of a possibly anticipating integrand as a function of its upper limit and establish an extended ito formula we also introduce an extension of stratonovich s integral and establish the associated chain rule in all the results the adaptedness of the integrand is replaced by a certain smoothness requirement

exact maximum likelihood parameter estimation of superimposed exponential signals in noise a unified framework for the exact maximum likelihood estimation of the parameters of superimposed exponential signals in noise encompassing both the time series and the array problems is presented an exact expression for the ml criterion is derived in terms of the linear prediction polynomial of the signal and an iterative algorithm for the maximization of this criterion is presented the algorithm is equally applicable in the case of signal coherence in the array problem simulation shows the estimator to be capable of providing more accurate frequency estimates than currently existing techniques the algorithm is similar to those independently derived by kumaresan et al in addition to its practical value the present formulation is used to interpret previous methods such as prony s pisarenko s and modifications thereof

weak levi civita connection for the damped metric on the riemannian path space and vanishing of ricci tensor in adapted differential geometry abstract we shall establish in the context of adapted differential geometry on the path space p m o m a weitzenbock formula which generalizes that in a b cruzeiro and p malliavin j funct anal 177 2000 219 253 without hypothesis on the ricci tensor the renormalized ricci tensor will be vanished the connection introduced in a b cruzeiro and s fang 1997 j funct anal 143 400 414 will play a central role

markovian connection curvature and weitzenbock formula on riemannian path spaces abstract we shall consider on a riemannian path space p m o m the cruzeiro malliavin s markovian connection the laplace operator will be defined as the divergence of the gradient we shall compute explicitly the associated curvature tensor a weitzenbock formula will be established to this end we shall introduce an inner product between the tangent processes and simple vector fields

controlling spatiotemporal chaos in oscillatory reaction diffusion systems by time delay autosynchronization abstract diffusion induced turbulence in spatially extended oscillatory media near a supercritical hopf bifurcation can be controlled by applying global time delay autosynchronization we consider the complex ginzburg landau equation in the benjamin feir unstable regime and analytically investigate the stability of uniform oscillations depending on the feedback parameters we show that a noninvasive stabilization of uniform oscillations is not possible in this type of system the synchronization diagram in the plane spanned by the feedback parameters is derived numerical simulations confirm the analytical results and give additional information on the spatiotemporal dynamics of the system close to complete synchronization

finite dimensional approximation of riemannian path space geometry abstract in this paper we construct a finite dimensional approximation for the geometry on the path space over a compact riemannian manifold this approximation allows to construct the horizontal lift of the ornstein uhlenbeck process on the path space through the markovian connection we also prove a representation formula for the heat semigroup on adapted vector fields as well as a commutation formula for its derivative

a non data aided maximum likelihood time delay estimator using importance sampling in this paper we present a new time delay maximum likelihood estimator based on importance sampling is we show that a grid search and lack of convergence from which most iterative estimators suffer can be avoided it is assumed that the transmitted data are completely unknown at the receiver moreover the carrier phase is considered as an unknown nuisance parameter the time delay remains constant over the observation interval and the received signal is corrupted by additive white gaussian noise awgn we use importance sampling to find the global maximum of the compressed likelihood function based on a global optimization procedure the main idea of the new estimator is to generate realizations of a random variable using an importance function which approximates the actual compressed likelihood function we will see that the algorithm parameters affect the estimation performance and that with an appropriate parameter choice even over a small observation interval the time delay can be accurately estimated at far lower computational cost than with classical iterative methods

circular quantum secret sharing a circular quantum secret sharing protocol is proposed which is useful and efficient when one of the parties of secret sharing is remote to the others who are in adjacent especially the parties are more than three we describe the process of this protocol and discuss its security when the quantum information carrying is polarized single photons running circularly it will be shown that entanglement is not necessary for quantum secret sharing moreover the theoretic efficiency is improved to approach 100 as almost all the instances can be used for generating the private key and each photon can carry one bit of information without quantum storage it is straightforwardly to utilize this topological structure to complete quantum secret sharing with multi level two particle entanglement in high capacity securely

how to share a quantum secret we investigate the concept of quantum secret sharing in a k n threshold scheme a secret quantum state is divided into n shares such that any k of those shares can be used to reconstruct the secret but any set of k ensuremath 1 or fewer shares contains absolutely no information about the secret we show that the only constraint on the existence of threshold schemes comes from the quantum no cloning theorem which requires that nl2k and we give efficient constructions of all threshold schemes we also show that for k ensuremath le nl2k ensuremath 1 then any k n threshold scheme must distribute information that is globally in a mixed state

the maximally entangled set of 4 qubit states entanglement is a resource to overcome the natural restriction of operations used for state manipulation to local operations assisted by classical communication locc hence a bipartite maximally entangled state is a state which can be transformed deterministically into any other state via locc in the multipartite setting no such state exists there rather a whole set the maximally entangled set of states mes which we recently introduced is required this set has on the one hand the property that any state outside of this set can be obtained via locc from one of the states within the set and on the other hand no state in the set can be obtained from any other state via locc recently we studied locc transformations among pure multipartite states and derived the mes for three and generic four qubit states here we consider the non generic four qubit states and analyze their properties regarding local transformations as already the most coarse grained classification due to stochastic locc slo

parameter estimation of superimposed signals using the em algorithm a computationally efficient algorithm for parameter estimation of superimposed signals based on the two step iterative em estimate and maximize with an e step and an m step algorithm is developed the idea is to decompose the observed data into their signal components and then to estimate the parameters of each signal component separately the algorithm iterates back and forth using the current parameter estimates to decompose the observed data better and thus increase the likelihood of the next parameter estimates the application of the algorithm to the multipath time delay and multiple source location estimation problems is considered

quantum cryptography without bell s theorem ekert has described a cryptographic scheme in which einstein podolsky rosen epr pairs of particles are used to generate identical random numbers in remote places while bell s theorem certifies that the particles have not been measured in transit by an eavesdropper we describe a related but simpler epr scheme and without invoking bell s theorem prove it secure against more general attacks including substitution of a fake epr source finally we show our scheme is equivalent to the original 1984 key distribution scheme of bennett and brassard which uses single particles instead of epr pairs

entropy energy and negativity in fermi resonance coupled states of substituted methanes several measures of entanglement have attracted considerable interest in the relationship of a measure of entanglement with other quantities the dynamics of entropy energy and negativity is studied for fermi resonance coupled vibrations in substituted methanes with three kinds of initial mixed states which are the mixed density matrices of binomial states thermal states and squeezed states on two vibrational modes respectively it is demonstrated that for mixed binomial states and mixed thermal states with small magnitudes the entropies of the stretch and the bend are anti correlated in the same oscillatory frequency so do the energies for each kind of state with small magnitudes whereas the entropies exhibit positive correlations with the corresponding energies furthermore for small magnitudes quantum mutual entropy is positively correlated with the interacting energy analytic forms of entropies and energies are provided with initial conditions in which they are stationary and the agreement between analytic and numerical simulations is satisfactory the dynamical entanglement measured by negativity is examined for those states and conditions it is shown that negativity displays a sudden death for mixed binomial states and mixed thermal states with small magnitudes and the time averaged negativity has the minimal value under the conditions of stationary entropies and energies moreover negativity is positively correlated with the mutual entropy and the interacting energy just for mixed squeezed states with small magnitudes those are useful for molecular quantum information processing and dynamical entanglement

active high resolution time delay estimation for large bt signals two different high resolution time delay estimation hrtde methods a temporal method and a frequency method specially adapted to large bandwidth duration bt product time resolvent signals are described the performance gain of these methods is shown to be about four times better in comparison with the classical time delay resolution methods the frequency hrtde method is applied to real data obtained from an ocean acoustic experiment although classic methods cannot distinguish close signal components the method presented yields estimates of the delay differences and the attenuation associated with each propagation path

private algebras in quantum information and infinite dimensional complementarity we introduce a generalized framework for private quantum codes using von neumann algebras and the structure of commutants this leads naturally to a more general notion of complementary channel which we use to establish a generalized complementarity theorem between private and correctable subalgebras that applies to both the finite and infinite dimensional settings linear bosonic channels are considered and specific examples of gaussian quantum channels are given to illustrate the new framework together with the complementarity theorem

an entanglement measure based on two order minors in this paper a new entanglement measure called emm the entanglement measure based on minors has been constructed by the convex roof method and proved to be a good entanglement measure according to the axiomatic point of view computation of emm can be finished directly by the two order minors of a coefficient matrix instead of the eigenvalues of the density operator required by most of the other entanglement measures so it is very fast and very easy on the other hand emm is related to the modified bures distance between and the closest separable state so it has geometry meaning we also investigate the relations between emm and the entanglement of formation negativity and logarithmic negativity and discover that emm is always smaller than or equal to them emm is equivalent to concurrence however their definitions and methods of proof are completely different emm will improve the efficiency of searching for maximally entangled multipartite states

private quantum subsystems and quasiorthogonal operator algebras we generalize a recently discovered example of a private quantum subsystem to find private subsystems for abelian subgroups of the n qubit pauli group which exist in the absence of private subspaces in doing so we also connect these quantum privacy investigations with the theory of quasiorthogonal operator algebras through the use of tools from group theory and operator theory

symplectically entangled states and their applications to coding an angular momentum 2j 1 dimensional hilbert space h is considered symplectic transformations s on the tensor product of n of these spaces h h are studied for the case when the 2j 1 is a power of a prime galois case the corresponding operators are calculated numerically the formalism is applied to quantum coding a simple repetition code based on the space ha spanned by the direct products of n angular momentum states with the same m has distance 1 it is shown that a code based on the symplectically transformed space sha has in general larger distance an example with three qutrits is discussed in detail

the ryu takayanagi formula from quantum error correction i argue that a version of the quantum corrected ryu takayanagi formula holds in any quantum error correcting code i present this result as a series of theorems of increasing generality with the final statement expressed in the language of operator algebra quantum error correction in ads cft this gives a purely boundary interpretation of the formula i also extend a recent theorem which established entanglement wedge reconstruction in ads cft when interpreted as a subsystem code to the more general and i argue more physical case of subalgebra codes for completeness i include a self contained presentation of the theory of von neumann algebras on finite dimensional hilbert spaces as well as the algebraic definition of entropy the results confirm a close relationship between bulk gauge transformations edge modes soft hair on black holes and the ryu takayanagi formula they also suggest a new perspective on the homology constraint which basically is to get rid of it in a way that preserves the validity of the formula but which removes any tension with the linearity of quantum mechanics moreover they suggest a boundary interpretation of the bit threads recently introduced by freedman and headrick

su 1 1 symmetry of multimode squeezed states we show that a class of multimode optical transformations that employ linear optics plus two mode squeezing can be expressed as su 1 1 operators these operations are relevant to state of the art continuous variable quantum information experiments including quantum state sharing quantum teleportation and multipartite entangled states using this su 1 1 description of these transformations we obtain a new basis for such transformations that lies in a useful representation of this group and lies outside the often used restriction to gaussian states we analyze this basis show its application to a class of transformations and discuss its extension to more general quantum optical networks

renormalized differential geometry on path space structural equation curvature abstract the theory of integration in infinite dimensions is in some sense the backbone of probability theory on this backbone the stochastic calculus of variations has given rise to the flesh of differential calculus its first step is the construction at each point of the probability space of a cameron martin like tangent space in which the desired differential calculus can be developed this construction proceeds along the lines of first order differential geometry in this paper we address the following questions what could be the meaning of curvature of the probability space how and why how can curvatures be defined and computed why could a second order differential geometry be relevant to stochastic analysis we try to answer these questions for the probability space associated to the brownian motion of a compact riemannian manifold why a basicenergy identity for anticipative stochastic integralswill be obtained as a byproduct of our computation of curvature how there are essentially four bottlenecks in the development of differential geometry on wiener riemann manifolds i the difficulty of finding an atlas of local charts such that the changes of charts preserve the class of the wiener like measures together with their associated cameron martin like tangent spaces ii the difficulty of finding cylindrical approximations preserving the natural geometrical objects iii the difficulty of renormalizing the divergent series to which the summation operations of finite dimensional differential geometry give rise in the non intrinsic context of local charts iv the nonavailability of the computational procedures analogous to the local coordinates systems of the classical differential geometry in the context of path space the ito filtration provides a much richer structure than that available in the framework of an abstract wiener riemann manifold our work is a systematic attempt to replace the machinery of local charts with amethodology of moving frames in our context stochastic parallel transport provides a canonical moving frame on the path space the concept of a cylindrical approximation has to be reshaped in our new situation into some geometric limit theorems establishing that the riemannian geometric objects of the cylindrical approximations induce by a limiting procedure geometric objects on the path space those limit theorems are reminiscent of the classical theorems which say that a stratonovich sde is the limit of an appropriate sequence of ode the canonical coordinate system provided by the moving frame will make it possible to proceed to the needed renormalizations byintrinsicstochastic integrals in this context the anticipative stochastic integral theory of nualart and pardoux will play a decisive role finally the moving frame will provide aneffective algorithm of computation for this differential geometry in infinite dimensions in our study we encounter a new type of renormalization thehypoelliptic renormalization which corresponds to the fact that the bracket of smooth vector fields taking their values in the cameron martin space can get out of this cameron martin space this hypoelliptic problem induces the nonrenormalizability of some geometrical objects it leads also to a concept oftangent processesto probability spaces extending that based on the cameron martin theorem for tangent processes a formula of integration by parts still holds furthermore the tangent processes form a lie algebra under the bracket on the other hand tangent processes cannot be stochastically integrated this operation is well defined only for cameron martin type vector fields

on accelerated random search a new variant of pure random search prs for function optimization is introduced the basic finite descent accelerated random search ars algorithm is simple the search is confined to shrinking neighborhoods of a previous record generating value with the search neighborhood reinitialized to the entire space when a new record is found local maxima are avoided by including an automatic restart feature which reinitializes the search neighborhood after some number of shrink steps have been performed one goal of this article is to provide rigorous mathematical comparisons of ars to prs it is shown that the sequence produced by the ars process converges with probability one to the maximum of a continuous objective function faster than that of the prs process by adjustably large multiples of the time step theorem regarding an infinite descent no automatic restart version of ars it is shown that if the objective function satisfies a local nonflatness condition then the right tails of the distributions of inter record times are exponentially smaller than those of prs theorem performance comparisons between ars prs and three quasi newton type optimization routines are reported in attempting to find extrema of i each of a small collection of standard test functions of two variables and ii d dimensional polynomials with random roots also reported is a three way performance comparison between ars prs and a simulated annealing algorithm in attempting to solve traveling salesman problems

efficient sharing of a continuous variable quantum secret we propose an efficient scheme for sharing a continuous variable quantum secret using passive optical interferometry and squeezers this efficiency is achieved by showing that a maximum of two squeezers is required to extract the secret state and we obtain the cheapest configuration in terms of total squeezing cost squeezing is a cost for the dealer of the secret as well as for the receivers and we quantify limitations to the fidelity of the extracted secret state in terms of the squeezing employed by the dealer

frame bundle of riemannian path space and ricci tensor in adapted differential geometry abstract the vanishing of the renormalized ricci tensor of the path space above a ricci flat riemannian manifold is discussed

analysis of music and esprit frequency estimates for sinusoidal signals with lowpass envelopes in this correspondence the music and esprit frequency estimates of sinusoidal signals with lowpass envelopes are analyzed to achieve computational simplicity the frequency estimation is conducted as if the signal had a constant amplitude the aim of the correspondence is to analyze the degradation of performance induced by the aforementioned mismodeling unified expressions for the bias and variances of the music and esprit frequency estimators are derived under the hypothesis of small bandwidth of the signal envelope numerical simulations illustrate the agreement between theoretical and empirical results and study the influence of the envelope bandwidth on the frequency estimation performance

le processus d ornstein uhlenbeck sur l espace des chemins riemanniens et le probleme des martingales resume we discuss the ornstein uhlenbeck process over a compact riemannian manifold in the framework of a martingale problem we obtain a solution to this problem as the limit of approximate finite dimensional processes to this end we prove a kolmogorov type estimate by making use of an expression of the ornstein uhlenbeck operator

ito maps and analysis on path spaces we consider versions of malliavin calculus on path spaces of compact manifolds with diffusion measures defining gross sobolev spaces of differentiable functions and proving their intertwining with solution maps mathcal i of certain stochastic differential equations this is shown to shed light on fundamental uniqueness questions for this calculus including uniqueness of the closed derivative operator d and markov uniqueness of the associated dirichlet form a continuity result for the divergence operator by kree and kree is extended to this situation the regularity of conditional expectations of smooth functionals of classical wiener space given mathcal i is considered and shown to have strong implications for these questions a major role is played by the possibly sub riemannian connections induced by stochastic differential equations damped markovian connections are used for the covariant derivatives