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

parametric output feedback controller design abstract a parameterization of fixed gain output feedback controllers which will assign a complete set of distinct eigenvalues to a given state space system is presented the main result is a compact parametric expression for the output feedback controller gain matrix explicitly characterized by two sets of free parameters the set of n closed loop system eigenvalues and a set of mr n design parameters for n state r input m output systems the free design parameters are determined by a sequential design procedure which automatically satisfies the basic orthogonality constraints on the left and right closed loop eigenvectors under the condition m r n the principal benefits of the explicit characterization of a parametric class of output feedback controllers lie in the ability to directly accommodate various different design criteria an illustration of the parametric output feedback design procedure is given by way of approximating the optimal full state regulator response of a fifth order pilot plant evaporator model

use of the design freedom of time optimal control abstract a method for synthesizing a state feedback time optimal controller for linear n state r input discrete time systems is developed the nonuniqueness of the solution is organized in such a way as to select the controller with the minimum value of the frobenius norm of the feedback gain matrix k it is shown that among the rn design parameters in the parametric form of k only r n rp r need to be considered in the search technique where p r is the order of the smallest jordan block in the jordan form of the closed loop system

author s reply to comments on eigenstructure assignment in linear multivariable systems a parametric solution by m m fahmy and j o reilly the authors reply that klein is correct in his observation that the approaches to eigenstructure assignment in earlier articles by b c moore 1976 g klein and moore 1977 are equivalent to those of the authors they assert however that their philosophies are quite different these differences are then described

quantum data hiding we expand on our work on quantum data hiding hiding classical data among parties who are restricted to performing only local quantum operations and classical communication locc we review our scheme that hides one bit between two parties using bell 1964 states and we derive upper and lower bounds on the secrecy of the hiding scheme we provide an explicit bound showing that multiple bits can be hidden bitwise with our scheme we give a preparation of the hiding states as an efficient quantum computation that uses at most one ebit of entanglement a candidate data hiding scheme that does not use entanglement is presented we show how our scheme for quantum data hiding can be used in a conditionally secure quantum bit commitment scheme

dead beat control of linear discrete time systems the paper considers the problem of determining the various classes of state feed back dead beat controllers for linear multivariable discrete time systems unlike earlier work attention is not restricted to the special case of minimum time dead beat controllers a general dead beat control problem is posed and solved the solution is based principally on an approach of closed loop eigenstructure assignment the minimum of free parameters in each class are specified and used in an explicit parametric form for the feedback gain matrix the concept of the greatest minimum of free parameters is introduced finally the method is illustrated by a numerical example

parametric compensator design a parametrization of dynamical output feedback compensators that will assign a complete set of distinct eigenvalues to a given state space system is presented the main result is a compact parametric expression for the gain matrices of an output feedback compensator of dynamical order i n m r explicitly characterized by two sets of free parameters the set of n l closed loop system eigenvalues and a set of n mr n m r 1 effective free parameters for n state r input m output systems these latter n effective free parameters are determined by a sequential design procedure the principal benefits of the explicit characterization of a parametric class of dynamical output feedback compensators lie in the ability to directly accommodate various different design criteria

tight asymptotic bounds on local hypothesis testing between a pure bipartite state and the white noise state we consider asymptotic hypothesis testing or state discrimination with asymmetric treatment of errors between an arbitrary fixed bipartite pure state psi rangle and the white noise state the completely mixed state under one way local operations and classical communications locc two way locc and separable positive operator valued measures povms as a result we derive the hoeffding bounds under two way locc povms and separable povms further we derive stein s lemma type of optimal error exponents under one way locc two way locc and separable povms up to the third order which clarifies the difference between one way and two way locc povm our results clarify the relationship between the entanglement of renyi entropy and the hypothesis testing under locc since the entanglement of renyi entropy appears in the formula of both the hoeffding bounds and stein s lemma type of error exponents this paper gives a very rare example in which the optimal performance under the infinite round two way locc is also equal to that under separable operations and can be attained with two round communication but not with the one way locc

construction and parameterization of a class of minimum time deadbeat controllers abstract a method for constructing and parametrizing a class of minimum time deadbeat controllers mtdc for a discrete time system is presented the number of construction steps is equal to the controllability index of the controllable part of the system the method reduces the considered problem to that of solving at most r linear equations at each step where r is the input dimension the minimum number of free parameters that characterizes the constructed class of mtdc is specified and arranged in a new compact linear parametric form of mtdc contrary to many existing methods the presented method does not require the system to be controllable

minimum gain minimum time deadbeat controllers abstract this paper considers the design of minimum gain minimum time deadbeat controllers mgmtdc for linear discrete time systems a new direct method for constructing the mgmtdc of minimum frobenius norm is developed compared with many existing techniques the proposed method gives analytic expressions for the constructed mgmtdc requires less computational effort and does not require that the transition matrix be nonsingular

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

generalized killing spinors in dimension 5 we study the intrinsic geometry of hypersurfaces in calabi yau manifolds of real dimension 6 and more generally structures on 5 manifolds defined by a generalized killing spinor we prove that in the real analytic case such a 5 manifold can be isometrically embedded as a hypersurface in a calabi yau manifold in a natural way we classify nilmanifolds carrying invariant structures of this type and present examples of the associated metrics with holonomy

regulation of time invariant discrete time descriptor systems time invariant discrete time descriptor systems of the form exk 1 axk buk where e and a are n n matrices and e may be singular are considered the problem is to find a feedback law uk kxk that drives the descriptor from x 0 to the origin in less than n time steps

on eigenstructure assignment in linear multivariable systems the eigenvalue assignment approach of brogan 1 2 is generalized and extended to the assignment of the entire closed loop eigenstructure of linear multivariable systems the set of assignable eigenvectors and generalized eigenvectors emerges naturally in the solution and is given moreover in an explicit parametric form two numerical examples are worked out to demonstrate the application of the procedure

parameterization of the class of deadbeat controllers this technical note deals with the problem of parameterizing the class of deadbeat controllers for a given system through the minimum of parameters it is shown that if n and m are dimensions of the state vector and control vector respectively and the i s are the controllability indexes then almost the whole class of deadbeat controllers is explicitly parameterizable through mn mu 1 3 mu 2 2m 1 mu m parameters

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

new g _2 holonomy cones and exotic nearly kahler structures on s 6 and s 3 times s 3 there is a rich theory of so called strict nearly kaehler manifolds almost hermitian manifolds generalising the famous almost complex structure on the 6 sphere induced by octonionic multiplication nearly kaehler 6 manifolds play a distinguished role both in the general structure theory and also because of their connection with singular spaces with holonomy group the compact exceptional lie group g 2 the metric cone over a riemannian 6 manifold m has holonomy contained in g 2 if and only if m is a nearly kaehler 6 manifold a central problem in the field has been the absence of any complete inhomogeneous examples we prove the existence of the first complete inhomogeneous nearly kaehler 6 manifolds by proving the existence of at least one cohomogeneity one nearly kaehler structure on the 6 sphere and on the product of a pair of 3 spheres we conjecture that these are the only simply connected inhomogeneous cohomogeneity one nearly kaehler structures in six dimensions

parametric time optimal control of linear discrete time systems by state feedback part 2 irregular kronecker invariants in an earlier paper part 1 a parametric state feedback time optimal control law was devised for the regular kronecker invariants on the basis of parametrization of the vector companion form the present paper describes a straight forward technique for obtaining the parametric feedback matrix by exploiting the parametric vector companion forms in the case of irregular kronecker invariants hidden properties of vector companion forms are also given which result in entirely different and interesting techniques for parametrization of the control law an illustrative example is presented

real killing spinors and holonomy we give a description of all complete simply connected riemannian manifolds carrying real killing spinors furthermore we present a construction method for manifolds with the exceptional holonomy groupsg2 and spin 7

the effect of sampling period on the behaviour of systems incorporating state feedback an exposition of the effects of sampling on the controllability characteristics and the kronecker invariants of the plant and the input matrices of sampled data systems is presented in particular the effect of sampling period on the feedback matrix for time optimal control of sampled data systems is investigated in detail and it is shown that different classes of systems produce different response characteristics as the sampling period becomes large also simple expressions for a nt in terms of a t and b nt as a function of a t and b t are derived these expressions are computationally attractive and therefore facilitate the study of the effect of sampling period on system behaviour by applying these expressions the effects of sampling period on the feedback matrices for time optimal control of three classes of systems whose open loop plants are asymptotically stable marginally stable and unstable are illustrated by numerical examples

parameterization of the class of deadbeat controllers via the theory of decoupling a novel approach is presented for parameterizing the class of minimum time deadbeat controllers mtdc through the minimum number of parameters the approach is based on the theory of decoupling and the properties of square decouplable systems the main result is a compact parametric form for the class of mtdc of a discrete time system contrary to many existing techniques no special assumption on the invertibility of the transition matrix is required

a study of locc detection of a maximally entangled state using hypothesis testing we study how well we can answer the question is the given quantum state equal to a certain maximally entangled state using locc in the context of hypothesis testing under several locality and invariance conditions optimal tests will be derived for several special cases by using basic theory of group representations some optimal tests are realized by performing quantum teleportation and checking whether the state is teleported we will also give a finite process for realizing some optimal tests the performance of the tests will be numerically compared

eigenstructure assignment in linear multivariable systems a parametric solution this paper generalizes a recently reported method 1 of closed loop eigenstructure assignment via state feedback in a linear multivariable system with n states and r control inputs by introducing a lemma on the differentiation of determinants the class of assignable eigenvectors and generalized eigenvectors associated with the assigned eigenvalues is explicitly described by a complete set of n r dimensional free parameter vectors this parametric characterization conveniently organizes the nonuniqueness of the solution of the eigenvalue assignment problem and thereby provides an efficient means of further modifying the system dynamic response a numerical example is worked out to demonstrate the feasibility of the method

on the general solution of the state deadbeat control problem in this note the state deadbeat control problem is considered it is shown that after appropriate change of basis of input and state spaces the general solution of the state deadbeat control problem can be expressed completely by the rows of the powers of system matrix this result yields a very simple procedure for the calculation of a state feedback deadbeat control gain it also provides the number of free parameters which could be used for further design purposes the results are illustrated by an example at the end of the note

embedding into manifolds with torsion we introduce a class of special geometries associated to the choice of a differential graded algebra contained in lambda mathbb r n we generalize some known embedding results that effectively characterize the real analytic riemannian manifolds that can be realized as submanifolds of a riemannian manifold with special holonomy to this more general context in particular we consider the case of hypersurfaces inside nearly kahler and einstein sasaki manifolds proving that the corresponding evolution equations always admit a solution in the real analytic case

feedback gain optimization in decentralized eigenvalue assignment abstract this paper develops a new design procedure for minimizing the norm of a decentralized output feedback matrix which assigns a user specified set of eigenvalues two distinct approaches which can be meshed together as a unified design tool are derived assuming one has computed a decentralized feedback matrix which assigns a desired spectrum the first approach describes an iterative algorithm which reduces an algebraic cost function e g the frobenius norm of the feedback gains while maintaining the desired spectrum this algorithm allows for small movements in the eigenvalues the iteration step is based on the first order variational behaviour of the eigenvalue eigenvector equations the second algorithm modifies a continuation method for decentralized eigenvalue assignment to include an optimizing factor numerical considerations for the design procedures are discussed an example showing the improvement possible by the application of the procedure is also given

metrics with exceptional holonomy it is proved that there exist metrics with holonomy g2 and spin 7 thus settling the remaining cases in berger s list of possible holonomy groups we first reformulate the holonomy h condition as a set of differential equations for an associated h structure on a given manifold we collect the needed algebraic facts about g2 and spin 7 we then apply the machinery of over determined partial differential equations in the form of the cartan kahler theorem to prove the existence of solutions whose holonomy is g2 or spin 7 we also provide explicit examples and some information about the generality of the space of

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

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

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

the discrete linear time invariant time optimal control problem an overview a review of two decades of investigation into one of the fundamental problems of control theory the discrete linear time invariant time optimal control problem is presented two classes of multi input time optimal controller one based on system controllability and the other on eigenvalue assignment are considered in some detail also discussed are the dual state reconstruction problem the deadbeat control of linear systems with inaccessible state and other extensions the exposition is a unifying one and involves only that matrix algebra commonly encountered in control theory

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

parametrization of minimum time output deadbeat controllers for all classes of invertible systems this paper considers the problem of parametrizing through the minimum number of parameters the minimum time output deadbeat controller mtodc for a given linear multivariable output controllable system s a b c e having n states m inputs p outputs and a transfer function matrix h z of full rank r the main result is a new compact linear parametric form for a class of mtodc that zeros the outputs of the system s in the minimum number of control iterations 1 where 1 i 1 2 r assumed to be decreasingly ordered are equal lo the negatives of the right factorization indices at infinity of h z the developed parametric class is a linear function in effective free parameters the principal benefits of this explicit parametrization of mtodcs lie in the ability to accommodate directly various different design criteria

generalized cylinders in semi riemannian and spin geometry we use a construction which we call generalized cylinders to give a new proof of the fundamental theorem of hypersurface theory it has the advantage of being very simple and the result directly extends to semi riemannian manifolds and to embeddings into spaces of constant curvature we also give a new way to identify spinors for different metrics and to derive the variation formula for the dirac operator moreover we show that generalized killing spinors for codazzi tensors are restrictions of parallel spinors finally we study the space of lorentzian metrics and give a criterion when two lorentzian metrics on a manifold can be joined in a natural manner by a 1 parameter family of such metrics

special metrics and triality abstract we investigate a new 8 dimensional riemannian geometry defined by a generic closed and coclosed 3 form with stabiliser psu 3 and which arises as a critical point of hitchin s variational principle we give a riemannian characterisation of this structure in terms of invariant spinor valued 1 forms which are harmonic with respect to the twisted dirac operator on 1 we establish various obstructions to the existence of topological reductions to psu 3 for compact manifolds we also give sufficient conditions for topological psu 3 structures that can be lifted to topological su 3 structures we also construct the first known compact example of an integrable non symmetric psu 3 structure in the same vein we give a new riemannian characterisation for topological quaternionic kahler structures which are defined by an sp 1 sp 2 invariant self dual 4 form again we show that this form is closed if and only if the corresponding spinor valued 1 form is harmonic for and that these equivalent conditions produce constraints on the ricci tensor

cohomogeneity one einstein sasaki 5 manifolds we consider hypersurfaces in einstein sasaki 5 manifolds which are tangent to the characteristic vector field we introduce evolution equations that can be used to reconstruct the 5 dimensional metric from such a hypersurface analogous to the nearly hypo and half flat evolution equations in higher dimensions we use these equations to classify einstein sasaki 5 manifolds of cohomogeneity one

a general riccati equation solution to the deadbeat control problem it is well known that the state of a controllable system can be driven to zero in minimum time for arbitrary initial condition by the time varying kalman gain sequence computed via a singular riccati equation this paper shows how a constant deadbeat control feedback which will accomplish the same result in the same minimum time can always be found via the same riccati equation

explicit parameterization of state deadbeat controllers a general state deadbeat control problem not restricted to the controllability indexes is posed and solved a result for the explicit parameterization of deadbeat controllers is obtained with the parameterization only the genuine independent free parameters appear in the deadbeat controllers

deadbeat control and tracking of discrete time systems a new approach for forcing the state of a linear discrete time system to zero in a minimum number of steps is discussed the problem is formulated as the solution to a steady state optimal control problem with no cost on the control this problem in turn is set up as the solution to an associated eigenvalue problem no special assumption on the open loop system matrix and or the ratio of the number of states to controls is required stable numerical techniques are presented for solving for the feedback gain robust deadbeat tracking is also discussed