strong approximation for zariski dense subgroups of semi simple algebraic groups 1 1 theorem let k be an algebraically closed field of characteristic different from 2 and 3 and g an almost simple connected and simply connected algebraic group defined over k let f be a finitely generated zariski dense subgroup of g k and a the subring of k generated by the traces tr ad y y e p then there exist b e a a subgroup f of finite index in f and a structure gab of a group scheme over ab on g such that f c ga ab and f is dense in gala b a

nonlocality asymmetry and distinguishing bipartite states entanglement is a useful resource because some global operations cannot be locally implemented using classical communication we prove a number of results about what is and what is not locally possible we focus on orthogonal states which can always be globally distinguished we establish the necessary and sufficient conditions for a general set of 2 ifmmode times else texttimes fi 2 quantum states to be locally distinguishable and for a general set of 2 ifmmode times else texttimes fi n quantum states to be distinguished given an initial measurement of the qubit these results reveal a fundamental asymmetry to nonlocality which is the origin of nonlocality without entanglement and we present a very simple proof of this phenomenon

local distinguishability of quantum states in infinite dimensional systems we investigate local distinguishability of quantum states by use of convex analysis of joint numerical range of operators on a hilbert space we show that any two orthogonal pure states are distinguishable by local operations and classical communications even for infinite dimensional systems an estimate of the local discrimination probability is also given for some families of more than two pure states

synchronization of stochastic bistable systems by biperiodic signals we study the nonlinear response of a noisy bistable system to a biperiodic signal through experiments with an electronic circuit schmitt trigger the signal we use is a biharmonic one i e a superposition of low and high frequency harmonic components it is shown that the mean switching frequency msf of the system can be locked at both low and high frequencies moreover the phenomenon of msf locking at the lower frequency can be induced and enhanced by the higher frequency excitation thus high frequency bias can control synchronization at the low frequency

deterministic stochastic resonance in a rossler oscillator we discuss the characteristics of stochastic resonancelike behavior observed in a deterministic system if a periodically forced rossler oscillator strays from the phase locking state it exhibits the intermittent behavior known as phase slips when the periodic force is modulated by a weak signal the phase slips synchronize with the weak signal statistically we numerically demonstrate in terms of interslip intervals and signal to noise ratio that the maximum synchronization can be achieved with the optimum intensity of chaotic fluctuations it is shown that the stochastic resonancelike behavior can be observed regardless of the choice of parameters the frequency dependence of the signal indicates that there is an optimum frequency for the maximum resonance the phase slip rate is derived based on the fact that the phase slips are caused by a boundary crisis caused by an unstable unstable pair bifurcation the interslip distributions obtained from the derived slip rate and the approximation theory of the time dependent poisson process agree with those obtained by numerical simulations in addition the maximum enhancement of a weak signal is shown to be achieved by adjusting the chaotic fluctuations even if a signal becomes mixed with noise

statistics of entrance times abstract the statistical properties of the transitions of a discrete markov process are investigated in terms of entrance times a simple formula for their density is given and used to measure the synchronization of a process with a periodic driving force for the mcnamara wiesenfeld model of stochastic resonance we find parameter regions in which the transition frequency of the process is locked with the frequency of the external driving

when do local operations and classical communication suffice for two qubit state discrimination in this paper we consider the conditions under which a given ensemble of two qubit states can be optimally distinguished by local operations and classical communication locc we begin by completing the perfect distinguishability problem of two qubit ensembles both for separable operations and locc by providing necessary and sufficient conditions for the perfect discrimination of one pure and one mixed state then for the well known task of minimum error discrimination it is shown that almost all two qubit ensembles consisting of three pure states cannot be optimally discriminated using locc this is surprising considering that any two pure states can be distinguished optimally by locc special attention is given to ensembles that lack entanglement and we prove an easy sufficient condition for when a set of three product states cannot be optimally distinguished by locc thus providing new examples of the phenomenon known as non locality without entanglement we next consider an example of n parties who each share the same state but who are ignorant of its identity the state is drawn from the rotationally invariant trine ensemble and we establish a tight connection between the n copy ensemble and shor s lifted single copy ensemble for any finite n we prove that optimal identification of the states cannot be achieved by locc however as n locc can indeed discriminate the states optimally this is the first result of its kind finally we turn to the task of unambiguous discrimination and derive new lower bounds on the locc inconclusive probability for symmetric states when applied to the double trine ensemble this leads to a rather different distinguishability character than when the minimum error probability is considered

maximality of galois actions for compatible systems in the sense of serre 19 of course the image of is not generally zariski dense in gln q so the maximality condition must be formulated relative to the zariski closure g of gal k k one might hope that the image of is a maximal compact subgroup of g q but this is too optimistic the center causes problems and we do not even know a priori that g is reductive to formulate a maximality conjecture which avoids such problems we introduce maps g g g

a family of calabi yau varieties and potential automorphy we prove potential modularity theorems for l adic representations of any dimension from these results we deduce the sato tate conjecture for all elliptic curves with nonintegral j invariant defined over a totally real field

local hypothesis testing between a pure bipartite state and the white noise state in this paper we treat a local discrimination problem in the framework of asymmetric hypothesis testing we choose a known bipartite pure state psi rangle as an alternative hypothesis and the completely mixed state as a null hypothesis as a result we analytically derive an optimal type 2 error and an optimal positive operator valued measure povm for one way local operations and classical communication locc povm and separable povm for two way locc povm we study a family of simple three step locc protocols and show that the best protocol in this family has strictly better performance than any one way locc protocol in low dimensional systems when there may exist differences between two way locc povm and one way locc povm

on quantum error correction by classical feedback in discrete time we consider the problem of correcting the errors incurred from sending quantum information through a noisy quantum environment by using classical information obtained from a measurement on the environment for discrete time markovian evolutions in the case of fixed measurement on the environment we give criteria for quantum information to be perfectly corrigible and characterize the related feedback then we analyze the case when perfect correction is not possible and in the qubit case we find optimal feedback maximizing the channel fidelity

distinguishability of quantum states by positive operator valued measures with positive partial transpose we study the distinguishability of bipartite quantum states by positive operator valued measures with positive partial transpose ppt povms the contributions of this paper include 1 we give a negative answer to an open problem of showing a limitation of a previous known method for detecting nondistinguishability 2 we show that a maximally entangled state and its orthogonal complement no matter how many copies are supplied cannot be distinguished by the ppt povms even unambiguously this result is much stronger than the previous known ones and 3 we study the entanglement cost of distinguishing quantum states it is proved that 2 3 00 1 3 11 is sufficient and necessary for distinguishing three bell states by the ppt povms an upper bound of entanglement cost of distinguishing a d d pure state and its orthogonal complement is obtained for separable operations based on this bound we are able to construct two orthogonal quantum states which cannot be distinguished unambiguously by separable povms but finite copies would make them perfectly distinguishable by local operations and classical communication we further observe that a two qubit maximally entangled state is always enough for distinguishing a d d pure state and its orthogonal complement by the ppt povms no matter the value of d in sharp contrast an entangled state with schmidt number at least d is always needed for distinguishing such two states by separable povms as an application we show that the entanglement cost of distinguishing a d d maximally entangled state and its orthogonal complement must be a maximally entangled state for d 2 which implies that teleportation is optimal and in general it could be chosen as o logd d

on the existence of locc distinguishable bases in three dimensional subspaces of bipartite 3 n systems we present numerical evidence showing that any three dimensional subspace of c 3 c n has an orthonormal basis which can be reliably distinguished using one way locc local operations and classical communication where a measurement is made first on the three dimensional part and the result used to select an optimal measurement on the n dimensional part we also show that the order of measurement is essential by providing an example of a three dimensional subspace of c 3 c 5 which does not have any basis that can be distinguished by measuring first on the five dimensional factor

shot noise in the leaky integrate and fire neuron we study the influence of noise on the transmission of temporal information by a leaky integrate and fire neuron using the theory of shot noise the model includes a finite number of synapses and has a membrane potential variance de facto modulated by the input signal the phenomenon of stochastic resonance in spiking neurons is analytically exhibited using an inhomogeneous poisson process model of the spike trains and links with the traditional ornstein uhlenbeck process obtained by a diffusion approximation are given it is shown that the modulated membrane potential variance inherent to the model gives better signal processing capabilities than the diffusion approximation

multifractal characterization of stochastic resonance we use a multifractal formalism to study the effect of stochastic resonance in a noisy bistable system driven by various input signals to characterize the response of a stochastic bistable system we introduce a new measure based on the calculation of a singularity spectrum for a return time sequence we use wavelet transform modulus maxima method for the singularity spectrum computations it is shown that the degree of multifractality defined as a width of singularity spectrum can be successfully used as a measure of complexity both in the case of periodic and aperiodic stochastic or chaotic input signals we show that in the case of periodic driving force singularity spectrum can change its structure qualitatively becoming monofractal in the regime of stochastic synchronization this fact allows us to consider the degree of multifractality as a new measure of stochastic synchronization also moreover our calculations have shown that the effect of stochastic resonance can be catched by this measure even from a very short return time sequence we use also the proposed approach to characterize the noise enhanced dynamics of a coupled stochastic neurons model

bounds on multipartite entangled orthogonal state discrimination using local operations and classical communication we show that entanglement guarantees difficulty in the discrimination of orthogonal multipartite states locally the number of pure states that can be discriminated by local operations and classical communication is bounded by the total dimension over the average entanglement a similar general condition is also shown for pure and mixed states these results offer a rare operational interpretation for three abstractly defined distancelike measures of multipartite entanglement

local indistinguishability more nonlocality with less entanglement we provide a first operational method for checking local indistinguishability of orthogonal states it originates from that in ghosh et al phys rev lett 87 5807 2001 though we deal with pure states our method shows that probabilistic local distinguishing is possible for a complete multipartite orthogonal basis if and only if all vectors are product also it leads to local indistinguishability of a set of orthogonal pure states of 3 multiply sign in circle 3 which shows that one can have more nonlocality with less entanglement where more nonlocality is in the sense of increased local indistinguishability of orthogonal states this is to our knowledge the only known example where d orthogonal states in d multiply sign in circle d are locally indistinguishable

limitations on separable measurements by convex optimization we prove limitations on locc and separable measurements in bipartite state discrimination problems using techniques from convex optimization specific results that we prove include an exact formula for the optimal probability of correctly discriminating any set of either three or four bell states via locc or separable measurements when the parties are given an ancillary partially entangled pair of qubits an easily checkable characterization of when an unextendable product set is perfectly discriminated by separable measurements along with the first known example of an unextendable product set that cannot be perfectly discriminated by separable measurements and an optimal bound on the success probability for any locc or separable measurement for the recently proposed state discrimination problem of yu duan and ying

asymmetric bistable systems subject to periodic and stochastic forcing in the strongly nonlinear regime switching time distributions a detailed theoretical analysis of the dynamics of a sinusoidally driven noisy asymmetric bistable system is presented the results are valid for any two state system however the specific case of the duffing potential is considered in detail the dynamics are considered in the weak noise limit i e when the response of the system to the external periodic field is strongly nonlinear the system asymmetry is created by a nonzero dc component of the external force and manifests itself as an asymmetry between the mean switching times between the potential wells we obtain explicit analytic expressions for the whole hierarchy of switching time distributions including the residence time and return time distributions we also obtain expressions for the average residence times and describe how they depend on asymmetry together with an explicit expression for the difference between the residence times in the weak noise limit the results are presented in the context of using the switching dynamics to detect weak dc target signals

synchronization under periodic modulation of symmetric double square wells in a bistable stochastic system the features of the first passage time density function are analyzed theoretically in terms of synchronization between noise and periodic signal in a symmetric double square well system resonance is demonstrated as a maximum synchronization between them to have the maximum cooperation between signal and noise it is shown that the noise strength at resonance should increase linearly with the frequency of the signal the time scale of the process at resonance is also shown to increase linearly with the period of the signal

distinguishability and indistinguishability by local operations and classical communication it is well known that orthogonal quantum states can be distinguished perfectly however if we assume that these orthogonal quantum states are shared by spatially separated parties the distinguishability of these shared quantum states may be completely different we show that a set of linearly independent quantum states formula see text where u m n are generalized pauli matrices cannot be discriminated deterministically or probabilistically by local operations and classical communication on the other hand any l maximally entangled states from this set are locally distinguishable if l l 1 or 2d the explicit projecting measurements are obtained to locally discriminate these states as an example we show that four werner states are locally indistinguishable

limit cycles and stochastic resonance in a periodically driven langevin equation subject to white noise we investigate stochastic resonance sr in a periodically driven langevin system on a circle the bifurcation parameter of the system and the amplitude of the periodic signal are controlled the response amplitude that characterizes the degree of the amplification of the input periodic signal and the quality factor that is a coherence measure of the spontaneous periodic motion sustained by noise are computed and plotted as functions of the noise intensity according to different parameter values four types of behaviour are observed as the results of interplay between two types of stochastic resonances the spontaneous sr and conventional sr respectively

limit cycles for extended bistable stochastic resonance system abstract bistable system is a typical model in stochastic resonance sr researching and it has been known that the deterministic dynamics of a noised system plays an important role in making sr phenomena occur by embedding a non autonomous system onto a cylinder or extending the one dimensional non autonomous system as a three dimensional autonomous system restricted on a cylinder this paper theoretically analyzes the dynamics of the well known periodically driven bistable system after three limit cycles equivalent to the periodic states of the un extended system are proved existent for subthreshold case they are shown to be preserved even in the suprathreshold case with large driving frequency moreover it is also proved in suprathreshold case that the three ones keep touching each other and combine into one larger globally stable limit cycle as the driving frequency decreases to some certain degree

vector representations of graphs and distinguishing quantum product states with one way locc abstract distinguishing sets of quantum states shared by two parties using only local operations and classical communication measurements is a fundamental topic in quantum communication and quantum information theory we introduce a graph theoretic approach based on the theory of vector representations of graphs to the core problem of distinguishing product states with one way locc we establish a number of results that show how distinguishing such states can be framed in terms of properties of the underlying graphs associated with a set of vector product states we also present a number of illustrative examples

distinguishability of quantum states by separable operations in this paper we study the distinguishability of multipartite quantum states by separable operations we first present a necessary and sufficient condition for a finite set of orthogonal quantum states to be distinguishable by separable operations an analytical version of this condition is derived for the case of d 1 pure states where d is the total dimension of the state space under consideration a number of interesting consequences of this result are then carefully investigated remarkably we show there exists a large class of 2 otimes 2 separable operations not being realizable by local operations and classical communication before our work only a class of 3 otimes 3 nonlocal separable operations was known bennett phys rev a 59 1070 1999 we also show that any basis of the orthogonal complement of a multipartite pure state is indistinguishable by separable operations if and only if this state cannot be a superposition of one or two orthogonal product states i e has an orthogonal schmidt number not less than three thus generalize the recent work about indistinguishable bipartite subspaces watrous phys rev lett 95 080505 2005 notably we obtain an explicit construction of indistinguishable subspaces of dimension 7 or 6 by considering a composite quantum system consisting of two qutrits resp three qubits which is slightly better than the previously known indistinguishable bipartite subspace with dimension 8

distinguishability of bell states more than two multipartite orthogonal states cannot always be discriminated if only local operations and classical communication locc are allowed we show that four bell states cannot be discriminated by locc even probabilistically using the separability properties of a four party unlockable bound entangled state using an existing inequality among the measures of entanglement we show that any three bell states cannot be discriminated with certainty by locc exploiting the inequality we calculate the distillable entanglement of a certain class of 4 multiply sign in circle 4 mixed states

congruence properties of zariski dense subgroups i this paper deals with the following general situation we are given an algebraic group g defined over a number field k and a subgroup f of the group g k of k rational points of g then what should it mean for f to be a large subgroup we might require f to be a lattice in g to be arithmetic to contain many elements of a specific kind to have a large closure in some natural topology et cetera there are many theorems proving implications between conditions of size of this kind we shall consider the case of g a k simple group usually q simple the zariski topology of g for which the closed sets are those defined by the vanishing of polynomial functions is very coarse on the other hand the various valuations v of k each give rise to a strong topology on g k if v is non archimedean and kv is the completion of k with respect to v then g kv is a non archimedean lie group and if is the ring of integers of kv the open subgroup g 5 j of g kv of integral points is defined for all but finitely many v the zariski closure f of a subgroup f of g k is a c algebraic subgroup of g while the strong closure fy is a lie subgroup of g kv for elementary reasons the dimension of tv is at most the dimension of f our results are in the opposite direction we show under suitable conditions on g that if f g then for almost all v we have that tv contains g ov to illustrate this with a specific example if ml 5 mk are matrices in sl2 q generating a group f which is zariskidense in sl2 then for all sufficiently large prime numbers p we have f p sl2 zp further this result is effective in the sense that we could in principle check the hypothesis for given mx mk and derive a bound on p beyond which the conclusion holds it is perhaps worth remarking that this special case which is the simplest application of our results may be proved with much less effort than the general theorem

distinguishing bipartitite orthogonal states using locc best and worst cases two types of results are presented for distinguishing pure bipartite quantum states using local operations and classical communications we examine sets of states that can be perfectly distinguished in particular showing that any three orthogonal maximally entangled states in c3 c3 form such a set in cases where orthogonal states cannot be distinguished we obtain upper bounds for the probability of error using locc taken over all sets of k orthogonal states in cn cm in the process of proving these bounds we identify some sets of orthogonal states for which perfect distinguishability is not possible

numerical analysis of noise induced regular oscillations abstract constructive sufficient conditions for regular oscillations in systems with stochastic resonance are given using these conditions a numerical procedure for indicating domains of parameters corresponding to the regular oscillations are proposed the regular oscillations in systems with additive and multiplicative noise are considered results of numerical experiments are presented

testing for a pure state with local operations and classical communication we examine the problem of using local operations and classical communication locc to distinguish a known pure state from an unknown possibly mixed state bounding the error probability from above and below we study the asymptotic rate of detecting multiple copies of the pure state and show that if the overlap of the two states is great enough then they can be distinguished asymptotically as well with locc as with global measurements otherwise the maximal schmidt coefficient of the pure state is sufficient to determine the asymptotic error rate

quantifying stochastic resonance in bistable systems response vs residence time distribution functions a wealth of research on stochastic resonance sr during the past decade has led to different ways of defining this phenomenon most prominent are measures based on the response function and on the residence time distribution function while the theory for the response functions is well developed a first fully systematic theory for the residence time distribution functions is developed in this paper subsequently we reconsider formerly introduced measures of sr based on the residence time distribution and compare with those based on the response function

mutually unbiased bases generalized spin matrices and separability abstract a collection of orthonormal bases for a complex d dimensional hilbert space is called mutually unbiased mub if for any two vectors v and w from different bases the square of the inner product equals 1 d v w 2 1 d the mub problem is to prove or disprove the existence of a maximal set of d 1 bases it has been shown in ann phys 191 1989 363 that such a collection exists if d is a power of a prime number p we revisit this problem and use d d generalizations of the pauli spin matrices to give a constructive proof of this result specifically we give explicit representations of commuting families of unitary matrices whose eigenvectors solve the mub problem additionally we give formulas from which the orthogonal bases can be readily computed we show how the techniques developed here provide a natural way to analyze the separability of the bases the techniques used require properties of algebraic field extensions and the relevant part of that theory is included in the appendix

on the chernoff distance for asymptotic locc discrimination of bipartite quantum states motivated by the recent discovery of a quantum chernoff theorem for asymptotic state discrimination we investigate the distinguishability of two bipartite mixed states under the constraint of local operations and classical communication locc in the limit of many copies while for two pure states a result of walgate et al shows that locc is just as powerful as global measurements data hiding states divincenzo et al show that locality can impose severe restrictions on the distinguishability of even orthogonal states here we determine the optimal error probability and measurement to discriminate many copies of particular data hiding states extremal d d werner states by a linear programming approach surprisingly the single copy optimal measurement remains optimal for n copies in the sense that the best strategy is measuring each copy separately followed by a simple classical decision rule we also put a lower bound on the bias with which states can be distinguished by separable operations

multipeaked probability distributions of recurrence times we determine probabilities of recurrence time into finite sized physically meaningful subsets of phase space we consider three different autonomous chaotic systems i scattering in a three peaked potential ii connected billiards and iii lorenz equations we find multipeaked probability distributions similar to the distributions found in driven stochastically resonant systems in nondriven systems such as ours only monotonic decaying distributions exponentials stretched exponentials power laws and slight variations or combinations of these have hitherto been reported discrete peaks in autonomous systems have as yet escaped attention in autonomous systems and correspond to specific trajectory subsets involving an integer number of loops

phase velocity and phase diffusion in periodically driven discrete state systems we develop a theory to calculate the effective phase diffusion coefficient and the mean phase velocity in periodically driven stochastic models with two discrete states this theory is applied to a dichotomically driven markovian two state system explicit expressions for the mean phase velocity the effective phase diffusion coefficient and the pe clet number are analytically calculated the latter indicates as a measure of phase coherence forced synchronization of the stochastic system with respect to the periodic driving and exhibits a bona fide resonance in a second step the theory is applied to a non markovian two state system modeling excitable systems the results prove again stochastic synchronization to the periodic driving and are in good agreement with simulations of a stochastic fitzhugh nagumo system

operator structures and quantum one way locc conditions we conduct the first detailed analysis in quantum information of recently derived operator relations from the study of quantum one way local operations and classical communications locc we show how operator structures such as operator systems operator algebras and hilbert c modules naturally arise in this setting we make use of these structures to derive new results and bounds in the study of one way locc and we use the approach to uncover new derivations of some previously established results

noise sensitivity of phase synchronization time in stochastic resonance theory and experiment recent numerical and heuristic arguments have revealed that the average phase synchronization time between the input and the output associated with stochastic resonance is highly sensitive to noise variation in particular there is evidence that this average time exhibits a cusplike behavior as the noise strength varies through the optimal value here we present an explicit formula for the average phase synchronization time in terms of the phase diffusion coefficient and the average frequency difference between the input and the output signals we also provide experimental evidence for the cusplike behavior by using a bistable microelectronic circuit system

markov analysis of stochastic resonance in a periodically driven integrate and fire neuron we model the dynamics of the leaky integrate and fire neuron under periodic stimulation as a markov process with respect to the stimulus phase this avoids the unrealistic assumption of a stimulus reset after each spike made in earlier papers and thus solves the long standing reset problem the neuron exhibits stochastic resonance both with respect to input noise intensity and stimulus frequency the latter resonance arises by matching the stimulus frequency to the refractory time of the neuron the markov approach can be generalized to other periodically driven stochastic processes containing a reset mechanism