an ergodic theorem for the quantum relative entropy we prove the ergodic version of the quantum stein s lemma which was conjectured by hiai and petz the result provides an operational and statistical interpretation of the quantum relative entropy as a statistical measure of distinguishability and contains as a special case the quantum version of the shannon mcmillan theorem for ergodic states a version of the quantum relative asymptotic equipartition property aep is given

quantum hypothesis testing with group symmetry the asymptotic discrimination problem of two quantum states is studied in the setting where measurements are required to be invariant under some symmetry group of the system we consider various asymptotic error exponents in connection with the problems of the chernoff bound the hoeffding bound and stein s lemma and derive bounds on these quantities in terms of their corresponding statistical distance measures a special emphasis is put on the comparison of the performances of group invariant and unrestricted measurements

the proper formula for relative entropy and its asymptotics in quantum probability umegaki s relative entropys trd logd logd of states and with density operatorsd andd respectively is shown to be an asymptotic exponent considered from the quantum hypothesis testing viewpoint it is also proved that some other versions of the relative entropy give rise to the same asymptotics as umegaki s one as a byproduct the inequality tra logab tra loga logb is obtained for positive definite matricesa andb

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

large deviations and chernoff bound for certain correlated states on a spin chain in this paper we extend the results of lenci and rey bellet j stat phys 119 715 2005 on the large deviation upper bound of the distribution measures of local hamiltonians with respect to a gibbs state in the setting of translation invariant finite range interactions we show that a certain factorization property of the reference state is sufficient for a large deviation upper bound to hold and that this factorization property is satisfied by gibbs states of the above kind as well as finitely correlated states as an application of the methods the chernoff bound for correlated states with factorization property is studied in the specific case of the distributions of the ergodic averages of a one site observable with respect to an ergodic finitely correlated state the spectral theory of positive maps is applied to prove the full large deviation principle

on the quantum renyi relative entropies and related capacity formulas following csiszar s approach in classical information theory it is shown that the quantum relative entropies with parameter 0 1 can be represented as generalized cutoff rates and hence a direct operational interpretation of the quantum relative entropies are provided it is also shown that various generalizations of the holevo capacity defined in terms of the relative entropies coincide for the parameter range 0 2 and an upper bound on the one shot e capacity of a classical quantum channel in terms of these capacities is given

generalized relative entropies and the capacity of classical quantum channels we provide lower and upper bounds on the information transmission capacity of one single use of a classical quantum channel the lower bound is expressed in terms of the hoeffding capacity which we define similarly to the holevo capacity but replacing the relative entropy with the hoeffding distance similarly our upper bound is in terms of a quantity obtained by replacing the relative entropy with the recently introduced max relative entropy in the definition of the divergence radius of a channel

brief paper tracking and synchronisation for a class of pwa systems in this paper the tracking problem for a class of discontinuous piecewise affine pwa systems is addressed we propose an observer based output feedback control design consisting of a feedforward a piecewise affine feedback law and a model based observer solving the tracking problem these synthesis results can also be employed to tackle the master slave synchronisation problem for pwa systems it is shown that for certain classes of pwa systems the design is characterised in terms of linear matrix inequalities the results are illustrated by application to mechanical systems with discontinuous friction characteristics

asymptotic error rates in quantum hypothesis testing we consider the problem of discriminating between two different states of a finite quantum system in the setting of large numbers of copies and find a closed form expression for the asymptotic exponential rate at which the error probability tends to zero this leads to the identification of the quantum generalisation of the classical chernoff distance which is the corresponding quantity in classical symmetric hypothesis testing

optimal sequence of quantum measurements in the sense of stein s lemma in quantum hypothesis testing we derive a necessary and sufficient condition for a sequence of quantum measurements to achieve the optimal performance in quantum hypothesis testing we discuss what quantum measurement we should perform in order to attain the optimal exponent of the second error probability under the condition that the first error probability goes to 0 as an asymptotically optimal measurement we propose a projection measurement characterized by the irreducible representation theory of the special linear group sl especially in the spin 1 2 system it is realized by the simultaneous measurement of the total momentum and a momentum of a specified direction as a by product we obtain another proof of quantum stein s lemma in addition an asymptotically optimal measurement is constructed in the quantum gaussian case and it is physically meaningful

quantum hypothesis testing for gaussian states quantum analogues of χ 2 t and f tests we consider quantum counterparts of testing problems for which the optimal tests are the 2 t and f tests these quantum counterparts are formulated as quantum hypothesis testing problems concerning gaussian state families and they contain nuisance parameters which have group symmetry the quantum hunt stein theorem removes some of these nuisance parameters but other difficulties remain in order to remove them we combine the quantum hunt stein theorem and other reduction methods to establish a general reduction theorem that reduces a complicated quantum hypothesis testing problem to a fundamental quantum hypothesis testing problem using these methods we derive quantum counterparts of the 2 t and f tests as optimal tests in the respective settings

near surface attenuation estimation using wave propagation modeling the effect of the near surface on seismic land data can be so severe that static corrections are insufficient full waveform inversion followed by redatuming may be an alternative but inversion will work only if the starting model is sufficiently close to the true model as a first step toward determining a viscoelastic near surface model we assume that existing methods can provide a horizontally layered velocity and density model because near surface attenuation is strongest we propose a method to estimate the p wave attenuation based on viscoacoustic finite difference modeling we compare energy decay along traveltime curves of reflection and refraction events in the modeled and observed seismic data for a range of attenuation parameters the best match provides an estimate of the attenuation first we estimate only the attenuation of the top layer and study the sensitivity to depth and velocity perturbations then we consider multiple layers we apply the method to synthetic and real data and investigate the effect of source wavelet and topography the method is robust against depth and velocity perturbations smaller than 10 the results are sensitive to the source wavelet incorporating the surface topography in the computed traveltimes reduces the uncertainty of the attenuation estimates especially for deeper layers

discriminating quantum states the multiple chernoff distance we consider the problem of testing multiple quantum hypotheses rho 1 otimes n ldots rho r otimes n where an arbitrary prior distribution is given and each of the r hypotheses is n copies of a quantum state it is known that the minimal average error probability p e decays exponentially to zero that is p e exp xi n o n however this error exponent xi is generally unknown except for the case that r 2 in this paper we solve the long standing open problem of identifying the above error exponent by proving nussbaum and szkola s conjecture that xi min i neq j c rho i rho j the right hand side of this equality is called the multiple quantum chernoff distance and c rho i rho j max 0 leq s leq1 log operatorname tr rho i s rho j 1 s has been previously identified as the optimal error exponent for testing two hypotheses rho i otimes n versus rho j otimes n the main ingredient of our proof is a new upper bound for the average error probability for testing an ensemble of finite dimensional but otherwise general quantum states this upper bound up to a states dependent factor matches the multiple state generalization of nussbaum and szkola s lower bound specialized to the case r 2 we give an alternative proof to the achievability of the binary hypothesis chernoff distance which was originally proved by audenaert et al

asymptotic distinguishability measures for shift invariant quasifree states of fermionic lattice systems we apply the recent results of hiai et al j math phys 49 032112 2008 to the asymptotic hypothesis testing problem of locally faithful shift invariant quasifree states on a car algebra we use a multivariate extension of szeg s theorem to show the existence of the mean chernoff and hoeffding bounds and the mean relative entropy and show that these quantities arise as the optimal error exponents in suitable settings

entropy densities for algebraic states abstract algebraic or finitely correlated states are translation invariant states on an infinite tensor product c algebra whose construction is rather general including quantum markov chains for a strongly mixing algebraic state we obtain the relation between the mean entropy and another entropy density which means the macroscopic uniformity under the relevant state in the statistical mechanical sense for this purpose an outstanding property of approximately product type is shown for strongly mixing algebraic states we also obtain similar relations of the mean relative entropy to other entropy densities for two translation invariant states when the reference one is a strongly mixing algebraic state

control of systems integrating logic dynamics and constraints this paper proposes a framework for modeling and controlling systems described by interdependent physical laws logic rules and operating constraints denoted as mixed logical dynamical mld systems these are described by linear dynamic equations subject to linear inequalities involving real and integer variables mld systems include linear hybrid systems finite state machines some classes of discrete event systems constrained linear systems and nonlinear systems which can be approximated by piecewise linear functions a predictive control scheme is proposed which is able to stabilize mld systems on desired reference trajectories while fulfilling operating constraints and possibly take into account previous qualitative knowledge in the form of heuristic rules due to the presence of integer variables the resulting on line optimization procedures are solved through mixed integer quadratic programming miqp for which efficient solvers have been recently developed some examples and a simulation case study on a complex gas supply system are reported

upper bounds on the error probabilities and asymptotic error exponents in quantum multiple state discrimination we consider the multiple hypothesis testing problem for symmetric quantum state discrimination between r given states 1 r by splitting up the overall test into multiple binary tests in various ways we obtain a number of upper bounds on the optimal error probability in terms of the binary error probabilities these upper bounds allow us to deduce various bounds on the asymptotic error rate for which it has been hypothesized that it is given by the multi hypothesis quantum chernoff bound or chernoff divergence c 1 r as recently introduced by nussbaum and szkola in analogy with salikhov s classical multi hypothesis chernoff bound this quantity is defined as the minimum of the pairwise binary chernoff divergences minj kc j k it was known already that the optimal asymptotic rate must lie between c 3 and c and that for certain classes of sets of states the bound is actually achieved it was known to be achieved in particular when the state pair that is closest together in chernoff dive

second order asymptotics for quantum hypothesis testing in settings beyond i i d quantum lattice systems and more quantum stein s lemma is a cornerstone of quantum statistics and concerns the problem of correctly identifying a quantum state given the knowledge that it is one of two specific states or it was originally derived in the asymptotic i i d setting in which arbitrarily many say n identical copies of the state n or n are considered to be available in this setting the lemma states that for any given upper bound on the probability n of erroneously inferring the state to be the probability n of erroneously inferring the state to be decays exponentially in n with the rate of decay converging to the relative entropy of the two states the second order asymptotics for quantum hypothesis testing which establishes the speed of convergence of this rate of decay to its limiting value was derived in the i i d setting independently by tomamichel and hayashi and li we extend this result to settings beyond i i d examples of these include gibbs states of quantum spin systems with finite

asymptotic convertibility of entanglement an information spectrum approach to entanglement concentration and dilution we consider asymptotic convertibility of an arbitrary sequence of bipartite pure states into another by local operations and classical communication locc we adopt an information spectrum approach to address cases where each element of the sequences is not necessarily a tensor power of a bipartite pure state we derive necessary and sufficient conditions for the locc convertibility of one sequence to another in terms of spectral entropy rates of entanglement of the sequences based on these results we also provide simple proofs for previously known results on the optimal rates of entanglement concentration and dilution of general sequences of bipartite pure states

coding theorems for compound problems via quantum renyi divergences recently a new notion of quantum renyi divergences has been introduced by muller lennert dupuis szehr fehr and tomamichel and wilde winter and yang which found a number of applications in strong converse theorems here we show that these new renyi divergences are also useful tools to obtain coding theorems in the direct domain of various problems we demonstrate this by giving new and considerably simplified proofs for the achievability parts of stein s lemma with composite null hypothesis universal state compression and the classical capacity of compound classical quantum channels based on single shot error bounds already available in the literature and simple properties of the quantum renyi divergences the novelty of our proofs is that the composite compound coding theorems can be almost directly obtained from the single shot error bounds essentially with the same effort as for the case of simple null hypothesis single source single channel

trajectory tracking control of bimodal piecewise affine systems this paper deals with a trajectory tracking problem for a class of bimodal piecewise affine systems which is inherently difficult because of the discontinuous changes of their vector fields first we introduce an error variable and an error system as a generalization of the tracking error and its system as an error variable a function switched by the mode of a piecewise affine system is adopted to overcome the inherent difficulty in trajectory tracking control of piecewise affine systems next we design a tracking controller which stabilizes the error system using a lyapunov like function which can be applied to systems including state jumps furthermore the feasibility condition of tracking for siso piecewise linear systems is simplified finally a numerical example is given to illustrate the effectiveness of the proposed method

two approaches to obtain the strong converse exponent of quantum hypothesis testing for general sequences of quantum states we present two general approaches to obtain the strong converse exponent of simple quantum hypothesis testing for correlated quantum states one approach requires that the states satisfy a certain factorization property typical examples of such states are the temperature states of translation invariant finite range interactions on a spin chain the other approach requires the differentiability of a regularized renyi alpha divergence in the parameter alpha typical examples of such states include temperature states of non interacting fermionic lattice systems and classical irreducible markov chains in all cases we get that the strong converse exponent is equal to the hoeffding anti divergence which in turn is obtained from the regularized renyi divergences of the two states

hypothesis testing for gaussian states on bosonic lattices the asymptotic state discrimination problem with simple hypotheses is considered for a cubic lattice of bosons a complete solution is provided for the problems of the chernoff and the hoeffding bounds and stein s lemma in the case when both hypotheses are gaussian states with gauge and translation invariant quasifree parts

the chernoff lower bound for symmetric quantum hypothesis testing we consider symmetric hypothesis testing in quantum statistics where the hypotheses are density operators on a finite dimensional complex hilbert space representing states of a finite quantum system we prove a lower bound on the asymptotic rate exponents of bayesian error probabilities the bound represents a quantum extension of the chernoff bound which gives the best asymptotically achievable error exponent in classical discrimination between two probability measures on a finite set in our framework the classical result is reproduced if the two hypothetic density operators commute recently it has been shown elsewhere phys rev lett 98 2007 160504 that the lower bound is achievable also in the generic quantum noncommutative case this implies that our result is one part of the definitive quantum chernoff bound

the structure of renyi entropic inequalities we investigate the universal inequalities relating the rnyi entropies of the marginals of a multi partite quantum state this is in analogy to the same question for the shannon and von neumann ent

error exponents in hypothesis testing for correlated states on a spin chain we study various error exponents in a binary hypothesis testing problem and extend recent results on the quantum chernoff and hoeffding bounds for product states to a setting when both the null hypothesis and the alternative hypothesis can be correlated states on a spin chain our results apply to states satisfying a certain factorization property typical examples are the global gibbs states of translation invariant finite range interactions as well as certain finitely correlated states