joint estimation of real squeezing and displacement we study the problem of joint estimation of real squeezing and amplitude of the radiation field deriving the measurement that maximizes the probability density of detecting the true value of the unknown parameters more generally we provide a solution for the problem of estimating the unknown unitary action of a nonunimodular group in the maximum likelihood approach remarkably in this case the optimal measurements do not coincide with the so called square root measurements in the case of squeezing and displacement we analyse in detail the sensitivity of estimation for coherent states and displaced squeezed states deriving the asymptotic relation between the uncertainties in the joint estimation and the corresponding uncertainties in the optimal separate measurements of squeezing and displacement a two mode set up is also analysed showing how entanglement between optical modes can be used to approximate perfect estimation

the monge metric on the sphere and geometry of quantum states topological and geometrical properties of the set of mixed quantum states in the n dimensional hilbert space are analysed assuming that the corresponding classical dynamics takes place on the sphere we use the vector su 2 coherent states and the generalized husimi distributions to define the monge distance between two arbitrary density matrices the monge metric has a simple semiclassical interpretation and induces a non trivial geometry among all pure states the distance from the maximally mixed state proportional to the identity matrix admits the largest value for the coherent states while the delocalized chaotic states are close to this contrasts the geometry induced by the standard trace hilbert schmidt or bures metrics for which the distance from is the same for all pure states we discuss possible physical consequences including unitary time evolution and the process of decoherence we introduce also a simplified monge metric defined in the space of pure quantum states and more suitable for numerical computation

on quantum detection and the square root measurement we consider the problem of constructing measurements optimized to distinguish between a collection of possibly nonorthogonal quantum states we consider a collection of pure states and seek a positive operator valued measure povm consisting of rank one operators with measurement vectors closest in squared norm to the given states we compare our results to previous measurements suggested by peres and wootters 1991 and hausladen et al 1996 where we refer to the latter as the square root measurement srm we obtain a new characterization of the srm and prove that it is optimal in a least squares sense in addition we show that for a geometrically uniform state set the srm minimizes the probability of a detection error this generalizes a similar result of ban et al see int j theor phys vol 36 p 1269 88 1997

quantum correlations and distinguishability of quantum states a survey of various concepts in quantum information is given with a main emphasis on the distinguishability of quantum states and quantum correlations covered topics include generalized and least square measurements state discrimination quantum relative entropies the bures distance on the set of quantum states the quantum fisher information the quantum chernoff bound bipartite entanglement the quantum discord and geometrical measures of quantum correlations the article is intended both for physicists interested not only by collections of results but also by the mathematical methods justifying them and for mathematicians looking for an up to date introductory course on these subjects which are mainly developed in the physics literature

interferometric visibility and coherence recently the basic concept of quantum coherence or superposition has gained a lot of renewed attention after baumgratz et al phys rev lett 113 140401 doi 10 1103 physrevlett 113 140401 following aberg http arxiv org abs quant ph 0612146 have proposed a resource theoretic approach to quantify it this has resulted in a large number of papers and preprints exploring various coherence monotones and debating possible forms for the resource theory here we take the view that the operational foundation of coherence in a state be it quantum or otherwise wave mechanical lies in the observation of interference effects our approach here is to consider an idealized multi path interferometer with a suitable detector in such a way that the visibility of the interference pattern provides a quantitative expression of the amount of coherence in a given probe state we present a general framework of deriving coherence measures from visibility and demonstrate it by analysing several concrete visibility parameters recovering some known coherence measures and obtaining some new ones

a mixed integer programming model for multiple stage adaptive testing abstract the last decade has seen paper and pencil p p tests being replaced by computerized adaptive tests cats within many testing programs a cat may yield several advantages relative to a conventional p p test a cat can determine the questions or test items to administer allowing each test form to be tailored to a test taker s skill level subsequent items can be chosen to match the capability of the test taker by adapting to a test taker s ability a cat can acquire more information about a test taker while administering fewer items a multiple stage adaptive test mst provides a means to implement a cat that allows review before the administration the mst format is a hybrid between the conventional p p and cat formats this paper presents mixed integer programming models for mst assembly problems computational results with commercial optimization software will be given and advantages of the models evaluated

optimal tight frames and quantum measurement tight frames and rank one quantum measurements are shown to be intimately related in fact the family of normalized tight frames for the space in which a quantum mechanical system lies is precisely the family of rank one generalized quantum measurements on that space using this relationship frame theoretical analogs of various quantum mechanical concepts and results are developed the analog of a least squares quantum measurement is a tight frame that is closest in a least squares sense to a given set of vectors the least squares tight frame is found for both the case in which the scaling of the frame is specified constrained least squares frame clsf and the case in which the scaling is chosen to minimize the least squares error unconstrained least squares frame ulsf the well known canonical frame is shown to be proportional to the ulsf and to coincide with the clsf with a certain scaling

implementation of group covariant positive operator valued measures by orthogonal measurements we consider group covariant positive operator valued measures povms on a finite dimensional quantum system following neumark s theorem a povm can be implemented by an orthogonal measurement on a larger system accordingly our goal is to find a quantum circuit implementation of a given group covariant povm which uses the symmetry of the povm based on representation theory of the symmetry group we develop a general approach for the implementation of group covariant povms which consist of rank one operators the construction relies on a method to decompose matrices that intertwine two representations of a finite group we give several examples for which the resulting quantum circuits are efficient in particular we obtain efficient quantum circuits for a class of povms generated by weyl heisenberg groups these circuits allow to implement an approximative simultaneous measurement of the position and crystal momentum of a particle moving on a cyclic chain

probability measure generated by the superfidelity we study the probability measure on the set of density matrices induced by the metric defined by using superfidelity we give the formula for the probability density of eigenvalues we also study some statistical properties of the set of density matrices equipped with the introduced measure and provide a method for generating density matrices according to the introduced measure

cutoff rate for the m ary psk modulation channel with optimal quantum detection the cutoff rate r sub 0 of an optical channel transmitting m ary phase shift keyed coherent states is calculated for a receiver using the optimum quantum detector this is shown to be nearly equivalent when m 1 to a system that measures the phase of the received signal a closed form expression yielding a good approximation to r sub 0 is derived

on the relations between electre tri b and electre tri c and on a new variant of electre tri b electre tri is a set of methods designed to sort alternatives evaluated on several criteria into ordered categories the original method uses limiting profiles a recently introduced method uses central profiles we study the relations between these two methods we do so by investigating if an ordered partition obtained with one method can also be obtained with the other method after a suitable redefinition of the profiles we also investigate a number of situations in which the original method using limiting profiles gives results that do not fit well our intuition this leads us to propose a variant of electre tri that uses limiting profiles we show that this variant may have some advantages over the original method

multiaccess quantum channels shared communication channels are subject to multiple access interference transmitter and receiver design techniques that explicitly deal with this interference have been shown to improve substantially the performance of communication systems over radio frequency and other classical channels quantum multiple access communication channels on the other hand have received comparatively little attention in this paper an input output model for multiple access quantum channels relevant to optical communications is proposed the model accounts for multiaccess interference signal attenuation and random noise and can be used in the analysis and design of communication systems using a result from optimization a perturbation method is developed to find the minimum achievable error probability in small interference channels it is shown that the quantum measurement that minimizes the error probability in a no interference channel is robust in the presence of small multiaccess interference the results are illustrated with numerical examples which show that optimal quantum detectors can significantly outperform conventional detectors even for moderate levels of crosstalk

minimum error discrimination between self symmetric mixed quantum state signals we derive some properties of minimum error measurements for mixed quantum state signals where a density operator itself has a certain symmetry in the first case we show that if there exists a regular normal operator that commutes with each density operator of mixed state signals then there exists an optimal measurement that consists of detection operators expressed as the direct sum of positive operators with supports in the eigenspaces of the regular normal operator in the second case we show that for abelian geometrically uniform state signals if a matrix which represents one of the signals in a certain basis has all real elements then the matrix which represents the corresponding detection operator of an optimal measurement in that basis also has all real elements in addition we discuss some examples of applications of these properties and derive analytical solutions of optimal measurements for special cases

least squares orthogonalization using semidefinite programming we consider the problem of constructing an optimal set of orthogonal vectors from a given set of vectors in a real hilbert space the vectors are chosen to minimize the sum of the squared norms of the errors between the constructed vectors and the given vectors we show that the design of the optimal vectors referred to as the least squares ls orthogonal vectors can be formulated as a semidefinite programming sdp problem using the many well known algorithms for solving sdps which are guaranteed to converge to the global optimum the ls vectors can be computed very efficiently in polynomial time within any desired accuracy by exploiting the connection between our problem and a quantum detection problem we derive a closed form analytical expression for the ls orthogonal vectors for vector sets with a broad class of symmetry properties specifically we consider geometrically uniform gu sets with a possibly non abelian generating group and compound gu sets which consist of subsets that are gu

a multiple criteria sorting method where each category is characterized by several reference actions the electre tri nc method this paper presents electre tri nc a new sorting method which takes into account several reference actions for characterizing each category this new method gives a particular freedom to the decision maker in the co construction decision aiding process with the analyst to characterize the set of categories while there is no constraint for introducing only one reference action as typical of each category like in electre tri c almeida dias et al 2010 as in such a sorting method this new sorting method is composed of two joint rules electre tri nc also fulfills a certain number of natural requirements additional results on the behavior of the new method are also provided in this paper namely the ones with respect to the addition or removal of the reference actions used for characterizing a certain category a numerical example illustrates the manner in which electre tri nc can be used by a decision maker a comparison with some related sorting procedures is presented and it allows to conclude that the new method is appropriate to deal with sorting problems

on the distinguishability of random quantum states we develop two analytic lower bounds on the probability of success p of identifying a state picked from a known ensemble of pure states a bound based on the pairwise inner products of the states and a bound based on the eigenvalues of their gram matrix we use the latter and results from random matrix theory to lower bound the asymptotic distinguishability of ensembles of n random quantum states in d dimensions where n d approaches a constant in particular for almost all ensembles of n states in n dimensions p 0 72 an application to distinguishing boolean functions the oracle identification problem in quantum computation is given

multicriteria assignment method proaftn methodology and medical application abstract this paper presents a new fuzzy multicriteria classification method called proaftn for assigning alternatives to predefined categories this method belongs to the class of supervised learning algorithms and enables to determine the fuzzy indifference relations by generalising the indices concordance and discordance used in the electre iii method then it assigns the fuzzy belonging degree of the alternatives to the categories we also present a clinical application of the proposed method in the cytopathological diagnosis of acute leukaemia

a generalized wave particle duality relation for finite groups wave particle duality relations express the fact that knowledge about the path a particle took suppresses information about its wave like properties in particular its ability to generate an interference pattern recently duality relations in which the wave like properties are quantified by using measures of quantum coherence have been proposed quantum coherence can be generalized to a property called group asymmetry here we derive a generalized duality relation involving group asymmetry which is closely related to the success probability of discriminating between the actions of the elements of a group the second quantity in the duality relation the one generalizing which path information is related to information about the irreducible representations that make up the group representation

reference based preferences aggregation procedures in multi criteria decision making this paper aims at introducing and investigating a new family of merely qualitative models for multicriteria decision making such models do not require any numerical representation within this family we will focus on decision rules using reference levels in order to help comparing several alternatives we will investigate both the descriptive potential of such rules and their axiomatic foundations after recalling the descriptive and prescriptive limitations of merely ordinal rules that do not use reference points we will introduce a new axiom requiring that the decision maker s preference between two alternatives depends on the respective positions of their consequences relatively to reference levels under this assumption we will determine the only possible form for the decision rule and characterize some particular instances of this rule under transitivity constraints our results show that introducing reference points overcomes the usual limitations of purely ordinal aggregation methods by moving the application point of arrow s theorem

performance of quantum data transmission systems in the presence of thermal noise in the literature the performance of quantum data transmission systems is usually evaluated in the absence of thermal noise a more realistic approach taking into account the thermal noise is intrinsically more difficult because it requires dealing with glauber coherent states in an infinite dimensional space in particular the exact evaluation of the optimal measurement operators is a very difficult task and numerical approximation is unavoidable the paper faces the problem by approximating the p representation of the noisy quantum states with a large but finite numbers of terms and applying to them the square root measurement srm approach comparisons with cases where the exact solution are known show that the srm approach gives quite accurate results as application the performance of quadrature amplitude modulation qam and phase shift keying psk systems is considered in spite of the fact that the srm approach is not optimal and overestimates the error probability also in these cases the quantum detection maintains its superiority with respect to the classical homodyne detection

bayes cost reduction algorithm in quantum hypothesis testing corresp an iterative procedure is described for reducing the bayes cost in decisions among m 2 quantum hypotheses by minimizing the average cost in binary decisions between all possible pairs of hypotheses the resulting decision strategy is a projection valued measure and yields an upper bound to the minimum attainable bayes cost from it is derived an algorithm for finding the optimum measurement states for choosing among m linearly independent pure states with minimum probability of error the method is also applied to decisions among m unimodal coherent quantum signals in thermal noise

a new approach to multi criteria sorting based on fuzzy outranking relations the theseus method abstract in this paper we propose the theseus method a new approach based on fuzzy outranking relations to multi criteria sorting problems compared with other outranking based methods theseus is inspired by another view of multi criteria classification problems it utilizes a new way of evaluating the assignment of an object to an element of the set of ordered categories that were previously defined this way is based on comparing every possible assignment with the information from various preference relations that are derived from a fuzzy outranking relation defined on the universe of objects the appropriate assignment is determined by solving a simple selection problem the capacity of a reference set for making appropriate assignments is related to a good characterization of the categories a single reference action characterizing a category may be insufficient to achieve well determined assignments in this paper the reference set capacity to perform appropriate assignments is characterized by some new concepts this capacity may be increased when more objects are added to the reference set theseus is a method for handling the preference information contained in such larger reference sets

geometrically uniform frames we introduce a new class of finite dimensional frames with strong symmetry properties called geometrically uniform gu frames that are defined over a finite abelian group of unitary matrices and are generated by a single generating vector the notion of gu frames is then extended to compound gu cgu frames which are generated by a finite abelian group of unitary matrices using multiple generating vectors the dual frame vectors and canonical tight frame vectors associated with gu frames are shown to be gu and therefore also generated by a single generating vector which can be computed very efficiently using a fourier transform ft defined over the generating group of the frame similarly the dual frame vectors and canonical tight frame vectors associated with cgu frames are shown to be cgu the impact of removing single or multiple elements from a gu frame is considered a systematic method for constructing optimal gu frames from a given set of frame vectors that are not gu is also developed finally the euclidean distance properties of gu frames are discussed and conditions are derived on the abelian group of unitary matrices to yield gu frames with strictly positive distance spectrum irrespective of the generating vector

an evolutionary approach to construction of outranking models for multicriteria classification the case of the electre tri method outranking methods constitute an important class of multicriteria classification models often however their implementation is cumbersome due to the large number of parameters that the decision maker must specify past studies tried to address this issue using linear and nonlinear programming to elicit the necessary preferential information from assignment examples in this study an evolutionary approach based on the differential evolution algorithm is proposed in the context of the electre tri method computational results are given to test the effectiveness of the methodology and the quality of the obtained models

fidelity and the communication of quantum information we compare and contrast the error probability and fidelity as measures of the quality of the receiver s measurement strategy for a quantum communications system the error probability is a measure of the ability to retrieve classical information and the fidelity measures the retrieval of quantum information we present the optimal measurement strategies for maximizing the fidelity given a source that encodes information on the symmetric qubit states

multiple criteria hierarchy process for electre tri methods abstract sorting methods in particular electre tri methods are widely used in multiple criteria decision aiding to deal with ordinal classification problems problems of this kind encountered in practice involve the evaluation of different alternatives actions on several evaluation criteria that are structured in a hierarchical way in order to deal with a hierarchical structure of criteria in decision problems multiple criteria hierarchy process mchp has been recently proposed in this paper we apply the mchp to the electre tri methods in particular we extend electre tri b electre tri c and electre tri nc methods we also adapt the mchp concept to the case where interaction among evaluation criteria has either strengthening or weakening or antagonistic effect finally we present an extension of the srf method to determine the weights of criteria in case they are hierarchically structured

entropic measures of joint uncertainty effects of lack of majorization we compute renyi entropies for the statistics of a noisy simultaneous observation of two complementary observables in two dimensional quantum systems the relative amount of uncertainty between two states depends on the uncertainty measure used these results are not reproduced by a more standard duality relation we show that these behaviors are consistent with the lack of majorization relation between the corresponding statistics

mmse whitening and subspace whitening this correspondence develops a linear whitening transformation that minimizes the mean squared error mse between the original and whitened data i e one that results in a white output that is as close as possible to the input in an mse sense when the covariance matrix of the data is not invertible the whitening transformation is designed to optimally whiten the data on a subspace in which it is contained the optimal whitening transformation is developed both for the case of finite length data vectors and infinite length signals

on interferometric duality in multibeam experiments we critically analyse the problem of formulating duality between fringe visibility and which way information in multibeam interference experiments we show that the traditional notion of visibility is incompatible with any intuitive idea of complementarity but for the two beam case we derive a number of new inequalities not present in the two beam case one of them coinciding with a recently proposed multibeam generalization of the inequality found by greenberger and yasin we show by an explicit procedure of optimization in a three beam case that suggested generalizations of englert s inequality do not convey differently from the two beam case the idea of complementarity according to which an increase of visibility is at the cost of a loss in path information and vice versa

universal bounds for the holevo quantity coherent information and the jensen shannon divergence the mutual information between the sender of a classical message encoded in quantum carriers and a receiver is fundamentally limited by the holevo quantity using strong subadditivity of entropy we prove that the holevo quantity is not larger than an exchange entropy this implies an upper bound for coherent information moreover restricting our attention to classical information we bound the transmission distance between probability distributions by their entropic distance which is a concave function of their hellinger distance

minimal entropy of states emerging from noisy quantum channels we consider the minimal entropy of qubit states transmitted through two uses of a noisy quantum channel which is modeled by the action of a completely positive trace preserving or stochastic map we provide strong support for the conjecture that this minimal entropy is additive namely that the minimum entropy can be achieved when product states are transmitted explicitly we prove that for a tensor product of two unital stochastic maps on qubit states using an entanglement that involves only states which emerge with minimal entropy cannot decrease the entropy below the minimum achievable using product states we give a separate argument based on the geometry of the image of the set of density matrices under stochastic maps which suggests that the minimal entropy conjecture holds for nonunital as well as for unital maps we also show that the maximal norm of the output states is multiplicative for most product maps on n qubit states including all those for which at least one map is unital for the class of unital channels on c sup 2 we show that additivity of minimal entropy implies that the holevo see ieee trans inform theory vol 44 p 269 73 1998 and russian math surv p 1295 1331 1999 capacity of the channel is additive over two inputs achievable with orthogonal states and equal to the shannon capacity this implies that superadditivity of the capacity is possible only for nonunital channels

no signaling principle can determine optimal quantum state discrimination we provide a general framework of utilizing the no signaling principle in derivation of the guessing probability in the minimum error quantum state discrimination we show that remarkably the guessing probability can be determined by the no signaling principle this is shown by proving that in the semidefinite programing for the discrimination the optimality condition corresponds to the constraint that quantum theory cannot be used for a superluminal communication finally a general bound to the guessing probability is presented in a closed form

svd iterative decision feedback demodulation and detection of coded space time unitary differential modulation a new suboptimal demodulator based on iterative decision feedback demodulation dfd and a singular value decomposition svd for estimation of unitary matrices is introduced noncoherent communication over the rayleigh flat fading channel with multiple transmit and receive antennas where no channel state information csi is available at the receiver is investigated with four transmit antennas codes achieving bit error rate ber lower than 10 sup 4 at bit energy over the noise spectral density ratio e sub b n sub o of 0 25 db up to 3 5 db with coding rates of 1 6875 to 5 06 bits per channel use were found the performance is compared to the mutual information upper bound of the capacity attaining isotropically random ir unitary transmit matrices the codes achieve ber lower than 10 sup 4 at e sub b n sub o of 3 2 db to 5 8 db from this bound system performance including the iterative dfd algorithm is compared to the one using euclidean distance as a reliability measure for demodulation the dfd system presents a performance gain of up to 1 5 db uncoded systems doing iterative dfd demodulation and idealized pilot sequence assisted modulation psam detection are compared iterative dfd introduces a gain of more than 1 2 db the coded system comprises a serial concatenation of turbo code and a unitary matrix differential modulation code the receiver employs the high performance coupled iterative decoding of the turbo code and the modulation code information theoretic arguments are harnessed to form guidelines for code design and to evaluate performance of the iterative decoder

two sided estimates of minimum error distinguishability of mixed quantum states via generalized holevo curlander bounds we prove a concise factor of 2 estimate for the failure rate of optimally distinguishing an arbitrary ensemble of mixed quantum states generalizing work of holevo theor probab appl 23 411 1978 and curlander ph d thesis mit 1979 a modification to the minimal principle of cocha and poor proceedings of the 6th international conference on quantum communication measurement and computing rinton princeton nj 2003 is used to derive a suboptimal measurement which has an error rate within a factor of 2 of the optimal by construction this measurement is quadratically weighted and has appeared as the first iterate of a sequence of measurements proposed by je ek et al phys rev a 65 060301 2002 unlike the so called pretty good measurement it coincides with holevo s asymptotically optimal measurement in the case of nonequiprobable pure states a quadratically weighted version of the measurement bound by barnum and knill j math phys 43 2097 2002 is proven bounds on the distingu

svd iterative detection of turbo coded multiantenna unitary differential modulation a new suboptimal demodulator based on a singular value decomposition for estimation of unitary matrices is introduced noncoherent communication over the rayleigh flat fading channel with multiple transmit and receive antennas where no channel state information is available at the receiver is investigated codes achieving bit error rate ber lower than 10 sup 4 at bit energy over the noise spectral density ratio e sub b n sub 0 of 1 6 1 9 db from code restricted capacity limit were found at higher data rates computation of code restricted capacity is impractical therefore the mutual information upper bound of the capacity attaining isotropically random unitary transmit matrices was used the codes achieve ber lower than 10 sup 4 at e sub b n sub 0 of 3 2 6 db from this bound with coding rates of 1 125 5 06 bits per channel use and different modulation decoding complexities the codes comprise a serial concatenation of turbo code and a unitary matrix differential modulation code the receiver employs the high performance coupled iterative decoding of the turbo code and the modulation code information theoretic arguments are harnessed to form guidelines for code design and to evaluate performance of the iterative decoder

a semidefinite programming approach to optimal unambiguous discrimination of quantum states we consider the problem of unambiguous discrimination between a set of linearly independent pure quantum states we show that the design of the optimal measurement that minimizes the probability of an inconclusive result can be formulated as a semidefinite programming problem based on this formulation we develop a set of necessary and sufficient conditions for an optimal quantum measurement we show that the optimal measurement can be computed very efficiently in polynomial time by exploiting the many well known algorithms for solving semidefinite programs which are guaranteed to converge to the global optimum using the general conditions for optimality we derive necessary and sufficient conditions so that the measurement that results in an equal probability of an inconclusive result for each one of the quantum states is optimal we refer to this measurement as the equal probability measurement epm we then show that for any state set the prior probabilities of the states can be chosen such that the epm is optimal finally we consider state sets with strong symmetry properties and equal prior probabilities for which the epm is optimal we first consider geometrically uniform gu state sets that are defined over a group of unitary matrices and are generated by a single generating vector we then consider compound gu state sets which are generated by a group of unitary matrices using multiple generating vectors where the generating vectors satisfy a certain weighted norm constraint

square root measurement for quantum symmetric mixed state signals a certain class of mixed states artificially constructed that is used in quantum cryptography is crucial for representation of signals this correspondence shows that the square root measurement gives the optimal measurement for such a class of mixed states

determining targets for multi stage adaptive tests using integer programming this paper considers a multi stage adaptive test mst where the testlets at each stage are determined prior to the administration the assembly of a mst requires target information and target response functions for the mst design the targets are chosen to create tests with accurate scoring and high utilization of items in an operational pool forcing all msts to have information and response function plots to be within an interval about the targets will yield parallel msts in the sense that standardized paper and pencil tests are considered parallel the objective of this paper is to present a method to determine targets for the mst design based on an item pool and an assumed distribution of examinee ability the approach is applied to a skills readiness inventory test designed to identify logical reasoning deficiencies of examinees this method can be applied to obtain item response theory targets for a linear test as this is a special case of a mst

least squares inner product shaping we develop methods that construct an optimal set of vectors with a specified inner product structure from a given set of vectors in a complex hilbert space the optimal vectors are chosen to minimize the sum of the squared norms of the errors between the constructed vectors and the given vectors four special cases are considered in the first the constructed vectors are orthonormal in the second they are orthogonal in the third the gram matrix of inner products of the constructed vectors is a circulant matrix as we show the vectors form a cyclic set in the fourth the gram matrix has the property that the rows are all permutations of each other the constructed vectors are shown to be geometrically uniform

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

dominance based rough set approach for group decisions the objective of this paper is to propose an approach to support group multicriteria classification the approach is composed of three phases the first phase exploits the knowledge provided by each decision maker to individually approximate the decision classes using rough approximation the second phase seeks to combine the outputs of individual approximation phase into a collective decision table by using an appropriate aggregation procedure the third phase uses the collective decision table in order to infer a set of collective decision rules which synthesize the judgements and perspectives of the different decision makers and to permit the classification of all decision objects the proposed approach relies on the dominance based rough set approach drsa which is used at two different levels first the drsa is used during the first phase to approximate the input data relative to each decision maker second the drsa is used during the third phase to approximate the collective decision table and generate the collective decision rules this paper presents the theoretical foundation of the proposed approach three case studies using real world data and a comparative study of recent similar proposals

a group decision making approach based on evidential reasoning for multiple criteria sorting problem with uncertainty a new group decision making approach is developed to address a multiple criteria sorting problem with uncertainty the uncertainty in this paper refers to imprecise evaluations of alternatives with respect to the considered criteria the belief structure and the evidential reasoning approach are employed to represent and aggregate the uncertain evaluations in our approach the preference information elicited from a group of decision makers is composed of the assignment examples of some reference alternatives the disaggregation aggregation paradigm is utilized to infer compatible preference models from these assignment examples to help the group reach an agreement on the assignment of alternatives we propose a consensus reaching process in this process a consensus degree is defined to measure the agreement among the decision makers opinions when the decision makers are not satisfied with the consensus degree possible solutions are explored to help them adjust assignment examples in order to improve the consensus level if the consensus degree arrives at a satisfactory level a linear program is built to determine the collective assignment of alternatives the application of the proposed approach to a customer satisfaction analysis is presented at the end of the paper

quantum detection and mutual information for qam and psk signals we analyze the performance of the error probability and the mutual information for quadrature amplitude modulation qam and phase shift keying systems based on quantum detection theory it is shown that the quantum receiver called square root measurement gives about 5 7 db improvement in power in comparison with the classical one furthermore we show that the quantum qam system can achieve the same reliability as the conventional intensity modulation direct detection im dd system with almost equal power compressing the required bandwidth while the reliability is degraded in general

designing optimal quantum detectors via semidefinite programming we consider the problem of designing an optimal quantum detector to minimize the probability of a detection error when distinguishing among a collection of quantum states represented by a set of density operators we show that the design of the optimal detector can be formulated as a semidefinite programming problem based on this formulation we derive a set of necessary and sufficient conditions for an optimal quantum measurement we then show that the optimal measurement can be found by solving a standard convex semidefinite program by exploiting the many well known algorithms for solving semidefinite programs which are guaranteed to converge to the global optimum the optimal measurement can be computed very efficiently in polynomial time within any desired accuracy using the semidefinite programming formulation we also show that the rank of each optimal measurement operator is no larger than the rank of the corresponding density operator in particular if the quantum state ensemble is a pure state ensemble consisting of not necessarily independent rank one density operators then we show that the optimal measurement is a pure state measurement consisting of rank one measurement operators

residual and destroyed accessible information after measurements when quantum states are used to send classical information the receiver performs a measurement on the signal states the amount of information extracted is often not optimal due to the receiver s measurement scheme and experimental apparatus for quantum nondemolition measurements there is potentially some residual information in the postmeasurement state while part of the information has been extracted and the rest is destroyed here we propose a framework to characterize a quantum measurement by how much information it extracts and destroys and how much information it leaves in the residual postmeasurement state the concept is illustrated for several receivers discriminating coherent states

electre tri nb a new multiple criteria ordinal classification method abstract this paper presents a new method for multiple criteria ordinal classification sorting problems in an ordinal classification problem the categories also called classes in related literature are pre defined and ordered from the best to the worst or from the worst to the best the actions not necessarily known a priori are assigned to the different ordered categories several electre type methods were designed to deal with this kind of problem however none of them proposes a characterization of the categories through a set of limiting profiles this is the novelty of the current method which may be considered as an extension of electre tri b it fulfills a set of structural requirements uniqueness of the assignments independence monotonicity homogeneity conformity and stability with respect to merging and splitting operations all these features will be presented in the current paper and illustrated through three examples

electre tri c a multiple criteria sorting method based on characteristic reference actions in this paper a new sorting method following a decision aiding constructive approach is proposed this method is called electre tri c as a sorting method a set of categories must be defined to represent the way in which the actions that are going to be assigned to each of them should further be processed this method is appropriate to deal with decision aiding contexts where the categories are completely ordered and each of them is defined through a single characteristic reference action the set of characteristic actions should be co constructed through an interactive process between the analyst and the decision maker electre tri c has been conceived to verify a set of natural structural requirements conformity homogeneity monotonicity and stability which can be viewed as its fundamental properties this method is composed of two joint rules called descending rule and ascending rule which must be used conjointly and not separately each one of these rules selects only one category or a range of possible categories for a possible assignment of an action this assignment depends on the comparison of such an action to the characteristic actions according to a chosen credibility level numerical examples are also presented in order to illustrate the main theoretical results provided by the method

multicriteria sorting using a valued preference closeness relation abstract to define a metric or a similarity relation with good properties is a crucial issue in most analogy and rule induction oriented methods for multicriteria sorting here we propose a valued indifference closeness relation which is inspired on concordance and discordance measures the criterion weights are obtained from the preferential information embedded in a reference set this proposal performs very well in several practical problems

two sided bounds on minimum error quantum measurement on the reversibility of quantum dynamics and on maximum overlap using directional iterates in a unified framework we estimate the following quantities of interest in quantum information theory 1 the minimum error distinguishability of arbitrary ensembles of mixed quantum states 2 the approximate reversibility of quantum dynamics in terms of entanglement fidelity this is referred to as channel adapted quantum error recovery when applied to the composition of an encoding operation and a noise channel 3 the maximum overlap between a bipartite pure quantum state and a bipartite mixed state that may be achieved by applying a local quantum operation to one part of the mixed state and 4 the conditional min entropy of bipartite quantum states a refined version of the author s techniques j tyson j math phys 50 032016 2009 for bounding the first quantity is employed to give two sided estimates of the remaining three quantities we obtain a closed form approximate reversal channel using a state dependent kraus decomposition our reversal may be interpreted as a quadratically

theory of quantum pulse position modulation and related numerical problems the paper deals with quantum pulse position modulation ppm both in the absence pure states and in the presence mixed states of thermal noise using the glauber representation of coherent laser radiation the objective is to find optimal or suboptimal measurement operators and to evaluate the corresponding error probability for ppm the correct formulation of quantum states is given by the tensorial product of m identical hilbert spaces where m is the ppm order the presence of mixed states due to thermal noise generates an optimization problem involving matrices of huge dimensions which already for 4 ppm are of the order of ten thousand to overcome this computational complexity the currently available methods of quantum detection which are based on explicit results convex linear programming and square root measurement are compared to find the computationally less expensive one in this paper a fundamental role is played by the geometrically uniform symmetry of the quantum ppm format the evaluation of error probability confirms the vast superiority of the quantum detection over its classical counterpart

geometrically uniform codes a signal space code c is defined as geometrically uniform if for any two code sequences in c there exists an isometry that maps one sequence into the other while leaving the code c invariant geometrical uniformity a strong kind of symmetry implies such properties as a the distance profiles from code sequences in c to all other code sequences are all the same and b all voronoi regions of code sequences in c have the same shape it is stronger than ungerboeck zehavi wolf symmetry or calderbank sloane regularity nonetheless most known good classes of signal space codes are shown to be generalized coset codes and therefore geometrically uniform including a lattice type trellis codes based on lattice partitions lambda lambda such that z sup n lambda lambda 4z sup n is a lattice partition chain and b phase shift keying psk type trellis codes based on up to four way partitions of a 2 sup n psk signal set

a new decision making approach for multiple criteria sorting with an imbalanced set of assignment examples abstract we propose a novel approach to address a multiple criteria sorting mcs problem with an imbalanced set of assignment examples the approach employs a piecewise linear additive value function as the preference model and adopts the disaggregation aggregation paradigm to infer a sorting model from provided assignment examples on a set of reference alternatives we utilize a hierarchical clustering algorithm and several linear programming models to identify reference alternatives that are active to develop the sorting model so that inactive ones are eliminated from the whole set of reference alternatives then in order to construct a balanced set of assignment examples a balancing algorithm is proposed to balance active reference alternatives across categories finally the sorting model is obtained by minimizing the sum of violations between values of active reference alternatives and corresponding category thresholds furthermore the performance of the proposed approach is investigated on a hypothetical problem and several real data sets the experimental results show that our approach is efficient to address the mcs problem with an imbalanced set of assignment examples

cryptographic distinguishability measures for quantum mechanical states this paper mostly expository in nature surveys four measures of distinguishability for quantum mechanical states this is done from the point of view of the cryptographer with a particular eye on applications in quantum cryptography each of the measures considered is rooted in an analogous classical measure of distinguishability for probability distributions namely the probability of an identification error the kolmogorov distance the bhattacharyya coefficient and the shannon 1948 distinguishability as defined through mutual information these measures have a long history of use in statistical pattern recognition and classical cryptography we obtain several inequalities that relate the quantum distinguishability measures to each other one of which may be crucial for proving the security of quantum cryptographic key distribution in another vein these measures and their connecting inequalities are used to define a single notion of cryptographic exponential indistinguishability for two families of quantum states this is a tool that may prove useful in the analysis of various quantum cryptographic protocols

an optimal whitening approach to linear multiuser detection we propose a new linear multiuser receiver for synchronous code division multiple access cdma systems referred to as the orthogonal multiuser omu receiver unlike the linear minimum mean squared error mmse receiver the omu receiver depends only on the signature vectors and does not require knowledge of the received amplitudes or the channel signal to noise ratio snr several equivalent representations of the receiver are developed with different implications in terms of implementation in the first the receiver consists of a decorrelator demodulator followed by an optimal whitening transformation on a space formed by the signatures in the second the receiver consists of a bank of correlators with correlating vectors that are projections of a set of orthogonal vectors and are closest in a least squares sense to the decorrelator vectors and also closest in a least squares sense to the signature vectors in the third the receiver consists of a single user matched filter mf followed by an optimal whitening transformation on a space formed by the signatures we derive exact and approximate expressions for the probability of bit error as well as the asymptotic signal to interference noise ratio sinr in the large system limit the analysis suggests that over a wide range of channel parameters the omu receiver can outperform both the decorrelator and the single user mf and perform similarly to the linear mmse receiver despite not knowing the channel parameters

state discrimination with post measurement information we introduce a new state discrimination problem in which we are given additional information about the state after the measurement or more generally after a quantum memory bound applies the following special case plays an important role in quantum cryptographic protocols in the bounded storage model given a string x encoded in an unknown basis chosen from a set of mutually unbiased bases mubs you may perform any measurement but then store at most q qubits of quantum information and an unlimited amount of classical information later on you learn which basis was used how well can you compute a function f x of x given the initial measurement outcome the q qubits and the additional basis information we first show a lower bound on the success probability for any balanced function and any number of mutually unbiased bases beating the naive strategy of simply guessing the basis we then show that for two bases any boolean function f x can be computed perfectly if you are allowed to store just a single qubit independent of the number of possible input strings x however we show how to construct three bases such that you need to store all qubits in order to compute f x perfectly we then investigate how much advantage the additional basis information can give for a boolean function to this end we prove optimal bounds for the success probability for the and and the xor function for up to three mutually unbiased bases our result shows that the gap in success probability can be maximal without the basis information you can never do better than guessing the basis but with this information you can compute f x perfectly we also give an example where the extra information does not give any advantage at all

relational systems of preference with one or more pseudo criteria some new concepts and results this paper proposes new concepts and new results which could lead to a more realistic preference modeling than in classical decision theory sections 1 3 present four fundamental situations of preferences their combinations and the concept of relational system of preferences in 4 a particular case of relational system of preference is studied it is associated with the concept of pseudo criterion derived from the classical concept of criterion by adjunction of two thresholds some results are given generalizing the properties of such well known structures as complete preorders and semiorders sections 5 and 6 emphasize the possibilities given by the preceding concepts to take the imprecisions irresolutions and incomparabilities appearing in every concrete problem where several criteria must be considered into account

a multicriteria classification approach based on pairwise comparisons abstract classification refers to the assignment of a set of alternatives into predefined homogenous classes most of the existing classification methodologies are based on absolute comparisons among the alternatives and some reference profiles cut off points that discriminate the classes this paper proposes a new approach that involves pairwise comparisons based on the multicriteria decision aid mcda paradigm the basis of the methodology is a preference relation that is used to perform pairwise comparisons among the alternatives the criteria weights used to construct the preference relation are specified using a reference set of alternatives training sample on the basis of linear programming techniques

optimal detection of symmetric mixed quantum states we develop a sufficient condition for the least squares measurement lsm or the square root measurement to minimize the probability of a detection error when distinguishing between a collection of mixed quantum states using this condition we derive the optimal measurement for state sets with a broad class of symmetries we first consider geometrically uniform gu state sets with a possibly non abelian generating group and show that if the generator satisfies a weighted norm constraint then the lsm is optimal in particular for pure state gu ensembles the lsm is shown to be optimal for arbitrary gu state sets we show that the optimal measurement operators are gu with generator that can be computed very efficiently in polynomial time within any desired accuracy we then consider compound gu cgu state sets which consist of subsets that are gu when the generators satisfy a certain constraint the lsm is again optimal for arbitrary cgu state sets the optimal measurement operators are shown to be cgu with generators that can be computed efficiently in polynomial time

finding optimal solutions for generalized quantum state discrimination problems we study an optimal quantum measurement for generalized quantum state discrimination problems which include the problem of finding an optimal measurement maximizing the average success probability with and without a fixed rate of inconclusive results and the problem of finding an optimal measurement in the neyman pearson strategy we show that for any generalized quantum state discrimination problem there is a corresponding minimum error discrimination problem sharing the same optimal measurement we propose an approach in which the optimal measurement is obtained by solving the corresponding minimum error discrimination problem and clarify the relationship between optimal solutions to the original and the corresponding problems with which one can obtain an optimal solution to the original problem in some cases moreover as an example of application of our approach we present an algorithm for numerically obtaining optimal solutions to generalized quantum state discrimination problems

fringe visibility and which way information an inequality an inequality is derived according to which the fringe visibility in a two way interferometer sets an absolute upper bound on the amount of which way information that is potentially stored in a which way detector in some sense this inequality can be regarded as quantifying the notion of wave particle duality the derivation of the inequality does not make use of heisenberg s uncertainty relation in any form

achievement test construction using 0 1 linear programming in educational testing the work of professional test agencies has shown a trend towards item banking achievement test construction is viewed as selecting items from a test item bank such that certain specifications are met as the number of possible tests is large and practice usually imposes various constraints on the selection process a mathematical programming approach is obvious in this paper it is shown how to formulate achievement test construction as a 0 1 linear programming problem a heuristic for solving the problem is proposed and two examples are given it is concluded that a 0 1 linear programming approach fits the problem of test construction in an appropriate way and offers test agencies the possibility of computerizing their services

quantum speed limits and optimal hamiltonians for driven systems in mixed states inequalities of mandelstam tamm mt and margolus levitin ml type provide lower bounds on the time that it takes for a quantum system to evolve from one state into another knowledge of such bounds called quantum speed limits is of utmost importance in virtually all areas of physics where determination of the minimum time required for a quantum process is of interest most mt and ml inequalities found in the literature have been derived from growth estimates for the bures length which is a statistical distance measure in this paper we derive such inequalities by differential geometric methods and we compare the quantum speed limits obtained with those involving the bures length we also characterize the hamiltonians which optimize the evolution time for generic finite level quantum systems

maximum fidelity for a mirror symmetric set of qubit states in this paper we address the problem of optimal reconstruction of a quantum state from the result of a single measurement when the original quantum state is known to be a member of some specified set this process provides both classical information about the state and a reproduction of that state a suitable figure of merit for this process is the fidelity which is the probability that the state we construct on the basis of the measurement result is found by a subsequent test to match the original state we consider the maximization of the fidelity for a mirror symmetric set of three pure qubit states but find that our results are more generally applicable in contrast to previous examples we find that the strategy which minimizes the probability of erroneously identifying the state does not generally maximize the fidelity

minimum error state discrimination constrained by the no signaling principle we provide a bound on the minimum error when discriminating among quantum states using the no signaling principle the bound is general in that it depends on neither dimensions nor specific structures of given quantum states to be discriminated among we show that the bound is tight for the minimum error state discrimination between symmetric both pure and mixed qubit states moreover the bound can be applied to a set of quantum states for which the minimum error state discrimination is not known yet finally our results strengthen the quantitative connection between two no go theorems the no signaling principle and the no perfect state estimation

electre methods with interaction between criteria an extension of the concordance index this paper presents an extension of the comprehensive overall concordance index of electre methods which takes the interaction between criteria into account in real world decision aiding situations it is reasonable to consider only the interaction between a small number of criterion pairs three types of interaction have been considered mutual strengthening mutual weakening and antagonistic the new concordance index correctly takes into account such types of interactions by imposing such conditions as boundary monotonicity and continuity we demonstrate that the generalized index is able to take the three types of interaction or dependencies between criteria into account satisfactorily first using quasi criteria and then using pseudo criteria we also examine the links between the new concordance index and the choquet integral

integrated framework for preference modeling and robustness analysis for outranking based multiple criteria sorting with electre and promethee a novel framework for preference modeling and robustness analysis is proposed we apply a sorting rule deriving from the semantic meaning of an outranking relation we ensure input output correspondence with respect to three sorting perspectives the generality of our framework is illustrated with its two specific implementations preference modeling can be simplified when using model instances providing precise assignments we introduce an integrated framework for preference modeling and robustness analysis in outranking based multiple criteria sorting the preference information supplied by the decision maker dm is composed of parts of desired recommendation and imprecise requirements that the delivered outcomes should satisfy its allowed forms are imprecise assignment examples desired class cardinalities and assignment based pairwise comparisons the exploitation of all instances of the outranking model compatible with these preferences results in three types of outcomes these raise robustness concerns in terms of the stability of a suggested assignment for each alternative an observed size of each class and a comparison between recommendation delivered for pairs of alternatives the correspondence between different types of inputs and outputs facilitates the dialogue with the dm and enhances her his confidence in the suggested recommendation while referring only to a semantic meaning of an outranking relation we present the procedures for translating the preference information into parameters of compatible outranking model instances and for deriving various kinds of sorting results then we implement this general framework in the context of outranking models specific for electre and promethee finally we show how preference modeling and robustness analysis can be performed and greatly simplified with a set of preference model instances providing precise assignments for the alternatives the framework proposed for this case is based on mixed integer linear programming milp being independent of the underlying model and method application of the approaches is demonstrated on the case of classifying polish research units into four quality classes