second order initial value problems with non absolute integrals in ordered banach spaces abstract in this paper we derive the existence and comparison results for second order initial value problems in ordered banach spaces the considered problems can be implicit singular functional discontinuous and nonlocal the main tools are fixed point results in ordered spaces and the theory of locally hl integrable vector valued functions

existence results for urysohn integral inclusions involving the henstock integral this paper presents two existence results for urysohn integral inclusions in banach spaces the set valued integral involved being the henstock integral in particular the existence of continuous solutions for integral inclusions of volterra and of hammerstein type is obtained our results extend the existence theorems given in literature in the single or set valued case under bochner or pettis integrability hypothesis the compactness of solutions set is also studied

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

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

an anhomomorphic logic for quantum mechanics although various schemes for anhomomorphic logics for quantum mechanics have been considered in the past we shall mainly concentrate on the quadratic or grade 2 scheme in this scheme the grade 2 truth functions are called coevents we discuss properties of coevents projections on the space of coevents and the master observable we show that the set of projections forms an orthomodular poset we introduce the concept of precluding coevents and show that this is stronger than the previously studied concept of preclusive coevents precluding coevents are defined naturally in terms of the master observable a result that exhibits a duality between preclusive and precluding coevents is given some simple examples are presented

characterizing locally indistinguishable orthogonal product states bennett physical review a vol 59 no 2 p 1070 1999 identified a set of orthogonal product states in the hilbert space bbc 3 otimes bbc 3 such that reliably distinguishing those states requires nonlocal quantum operations while more examples have been found for this counterintuitive ldquononlocality without entanglementrdquo phenomenon a complete and computationally verifiable characterization for all such sets of states remains unknown in this paper we give such a characterization for both bbc 3 otimes bbc 3 and bbc 2 otimes bbc 2 otimes bbc 2 as a consequence we show that in both spaces there is no additional set of a fundamentally different structure than those of the known instances

monotone measures and universal integrals in a uniform framework for the scientific impact assessment problem the choquet sugeno and shilkret integrals with respect to monotone measures as well as their generalization the universal integral stand for a useful tool in decision support systems in this paper we propose a general construction method for aggregation operators that may be used in assessing output of scientists we show that the most often currently used indices of bibliometric impact like hirsch s h woeginger s w egghe s g kosmulski s maxprod and similar constructions may be obtained by means of our framework moreover the model easily leads to some new very interesting functions

on state versus channel quantum extension problems exact results for u otimes u otimes u symmetry we develop a framework which unifies seemingly different extension or joinability problems for bipartite quantum states and channels this includes known extension problems such as optimal quantum cloning and quantum marginal problems as special instances central to our generalization is a variant of the jamiolkowski isomorphism between bipartite states and linear transformations which we term the homocorrelation map in contrast to the better known choi isomorphism which emphasizes the preservation of the positivity constraint use of the jamiolkowski isomorphism allows one to characterize the preservation of the statistical correlations of bipartite states and quantum channels the resulting homocorrelation map thus acquires a natural operational interpretation we define and analyze state joining channel joining and local positive joining problems in three party settings with collective symmetry obtaining exact analytical characterizations in low dimensions we find that bipartite quantum states are limited in the degree to which their measurement outcomes may agree whereas quantum channels are limited in the degree to which their measurement outcomes may disagree loosely speaking quantum mechanics enforces an upper bound on the strength of positive correlation across two subsystems at a single time as well as on the strength of negative correlation between the state of a single system across two instants of time we argue that these general statistical bounds inform the quantum joinability limitations and show that they are in fact sufficient for the three party invariant setting

continuous time and consistent histories we discuss the use of histories labelled by a continuous time in the approach to consistent histories quantum theory in which propositions about the history of the system are represented by projection operators on a hilbert space this extends earlier work by two of us c j isham and n linden j math phys 36 5392 5408 1995 where we showed how a continuous time parameter leads to a history algebra that is isomorphic to the canonical algebra of a quantum field theory we describe how the appropriate representation of the history algebra may be chosen by requiring the existence of projection operators that represent propositions about the time average of the energy we also show that the history description of quantum mechanics contains an operator corresponding to velocity that is quite distinct from the momentum operator finally the discussion is extended to give a preliminary account of quantum field theory in this approach to the consistent histories formalism

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

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

asymptotic state discrimination and a strict hierarchy in distinguishability norms in this paper we consider the problem of discriminating quantum states by local operations and classical communication locc when an arbitrarily small amount of error is permitted this paradigm is known as asymptotic state discrimination and we derive necessary conditions for when two multipartite states of any size can be discriminated perfectly by asymptotic locc we use this new criterion to prove a gap in the locc and separable distinguishability norms we then turn to the operational advantage of using two way classical communication over one way communication in locc processing with a simple two qubit product state ensemble we demonstrate a strict majorization of the two way locc norm over the one way norm

poincare invariance for continuous time histories we show that the relativistic analog of the two types of time translation in a nonrelativistic history theory is the existence of two distinct poincare groups the internal poincare group is analogous to the one that arises in the standard canonical quantization scheme the external poincare group is similar to the group that arises in a lagrangian description of the standard theory in particular it performs explicit changes of the space time foliation that is implicitly assumed in standard canonical field theory

quantum integrals and anhomomorphic logics the basic arena for a probabilistic structure is a set a of events corresponding to a is a dual structure a of coevents we call a an anhomomorphic logic and the coevents are given by truth functions from a to the two element boolean algebra z2 0 1 one of the main goals of a physical theory is to describe physical reality and a coevent a z2 provides such a description in the sense that an event a a actually occurs if and only if a 1 the quantum integral over an event a with respect to a coevent is defined and its properties are treated integrals with respect to various coevents are computed quantum systems are frequently described by a quantum measure which gives the propensity a that an event a occurs for a if a 0 whenever a 0 we say that is preclusive preclusivity is a reality filter because it eliminates coevents that do not describe a possible reality for the system a quantum measure that can be represented as a quantum integral with respect to a coevent i

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

are there realistically interpretable local theories although it rests on strongly established proofs the statement that no realistically interpretable local theory is compatible with some experimentally testable predictions of quantum mechanics seems at first sight to be incompatible with a few general ideas and clear cut statements occurring in recent theoretical work by griffiths omnes and ballentine and jarrett it is shown here that in fact none of the developments due to these authors can be considered as a realistically interpretable local theory so that there is no valid reason for suspecting that the existing proofs of the statement in question are all flawed

symmetry and history quantum theory an analog of wigner s theorem the basic ingredients of the consistent histories approach to quantum theory are a space up of history propositions and a space d of decoherence functionals in this article we consider such history quantum theories in the case where up is given by the set of projectors p v on some hilbert space v we define the notion of a physical symmetry of a history quantum theory pshqt and specify such objects exhaustively with the aid of an analog of wigner s theorem in order to prove this theorem we investigate the structure of d define the notion of an elementary decoherence functional and show that each decoherence functional can be expanded as a certain combination of these functionals we call two history quantum theories that are related by a pshqt physically equivalent and show explicitly in the case of history quantum mechanics how this notion is compatible with one that has appeared previously

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

consistent quantum realism a reply to bassi and ghirardi a recent claim by bassi and ghirardi that the consistent decoherent histories approach cannot provide a realistic interpretation of quantum theory is shown to be based upon a misunderstanding of the single framework rule they have replaced the correct rule with a principle which directly contradicts it it is their assumptions not those of the consistent histories approach which lead to a logical contradiction

quantum measure and integration theory this article begins with a review of quantum measure spaces quantum forms and indefinite inner product spaces are then discussed the main part of the paper introduces a quantum integral and derives some of its properties the quantum integral s form for simple functions is characterized and it is shown that the quantum integral generalizes the lebesgue integral a bounded monotone convergence theorem for quantum integrals is obtained and it is shown that a radon nikodym type theorem does not hold for quantum measures as an example a quantum lebesgue integral on the real line is considered

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

initial value problems for nonlinear second order impulsive integro differential equations in banach spaces in this paper the fixed point theory is used to investigate the existence and uniqueness of solutions of initial value problems for nonlinear second order impulsive integro differential equations in banach spaces

realizing a 2 d positive operator valued measure by local operations and classical communication we study the realization of a 2 d positive operator valued measure povm by local operations and classical communication locc we derive that any povm on a 2 d hilbert space in which each party s space is finite dimensional can be realized by one way locc this implies that any optimal discrimination of quantum states spanning such a 2 d hilbert space is possible by one way locc regardless of the optimality criterion used and how entangled the states are

convergence theorems for hl integrable vector valued functions with applications abstract in this paper we prove dominated and monotone convergence theorems for hl integrable banach valued functions these results and a fixed point theorem in ordered spaces are then applied to prove existence and comparison results for integral equations of fredholm type in ordered banach spaces involving kurzweil integrals or improper integrals results are used also to solve concrete second order functional boundary value problems involving discontinuities and singularities

solution tube method for impulsive periodic differential inclusions of first order abstract the aim of this paper is to obtain an existence result for impulsive differential inclusions of first order with boundary conditions in hilbert spaces under a hypothesis of integrability in the henstock lebesgue sense for the multifunction on the right hand side the proof is based on the assumption that there exists a solution tube for the inclusion taken under consideration this novel concept which generalizes the extensively used notions of upper and lower solution was adapted to the present setting finally a compactness property is proved

stochastic description for open quantum systems abstract a linear quantum brownian motion model with a general spectral density function is considered in the framework of the influence functional formalism a langevin equation can be introduced to describe the system s fully quantum properties even beyond the semiclassical regime in particular we show that the reduced wigner function for the system can be formally written as a double average over both the initial conditions and the stochastic source of the langevin equation this is exploited to provide a derivation of the master equation for the reduced density matrix alternative to those existing in the literature furthermore we prove that all the correlation functions obtained in the context of the stochastic description associated to the langevin equation actually correspond to quantum correlation functions for system observables in doing so we also compute the closed time path generating functional of the open system

symmetries of history quantum theories and decoherence functionals recently schreckenberg investigated symmetries in the context of history quantum theories in the case that the space of histories is given by the set of projectors on some finite dimensional hilbert space he obtained first a complete characterization of all physical symmetries of history quantum theories an analog of wigner s theorem and second a complete mathematical characterization of symmetries of single decoherence functionals in this paper we extend schreckenberg s results to the case where the underlying space of histories is given by the set of projectors on some infinite dimensional hilbert space

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

generalizations of k order additive discrete fuzzy measures abstract two types of generalizations of k order additive discrete fuzzy measures recently introduced by grabisch are shown first a special type of discrete fuzzy measures generalizing the pseudo additive measures with respect to a pan addition is introduced following the ideas of grabisch a mobius like transformation of discrete fuzzy measures is presented and an evaluation formula for the corresponding choquet like integral is given including the sugeno integral next k order additive fuzzy measures on general spaces are introduced combination of both generalizations is discussed and several open problems are addressed

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

generalized schmidt decomposition and classification of three quantum bit states we prove for any pure three quantum bit state the existence of local bases which allow one to build a set of five orthogonal product states in terms of which the state can be written in a unique form this leads to a canonical form which generalizes the two quantum bit schmidt decomposition it is uniquely characterized by the five entanglement parameters it leads to a complete classification of the three quantum bit states it shows that the right outcome of an adequate local measurement always erases all entanglement between the other two parties

impulsive retarded differential equations in banach spaces via bochner lebesgue and henstock integrals t f t xt xt0 1 1 where is a given continuous function from r 0 r 0 to a banach space x and f is a continuous map from an open set r c r 0 x to x given a continuous function x t0 r t0 a x a 0 t0 r we follow 11 to deane xt r 0 x by xt x t r 0 t t0 t0 a the initial value problem 1 1 is equivalent to the integral equation

quantum chaos an entropy approach a new definition of the entropy of a given dynamical system and of an instrument describing the measurement process is proposed within the operational approach to quantum mechanics it generalizes other definitions of entropy in both the classical and quantum cases the kolmogorov sinai ks entropy is obtained for a classical system and the sharp measurement instrument for a quantum system and a coherent states instrument a new quantity coherent states entropy is defined it may be used to measure chaos in quantum mechanics the following correspondence principle is proved the upper limit of the coherent states entropy of a quantum map as 0 is less than or equal to the ks entropy of the corresponding classical map chaos umpire sits and by decision more imbroils the fray by which he reigns next him high arbiter chance governs all john milton paradise lost book ii

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

two derivations of the master equation of quantum brownian motion central to many discussion of decoherence is a master equation for the reduced density matrix of a massive particle experiencing scattering from its surrounding environment such as that of joos and zeh such master equations enjoy a close relationship with spontaneous localization models like the grw model the aim of this paper is to present two derivations of the master equation the first derivation is a pedagogical model designed to illustrate the origins of the master equation as simply as possible focusing on physical principles and without the complications of s matrix theory this derivation may serve as a useful tutorial example for students attempting to learn this subject area the second is the opposite a very general derivation using non relativistic many body field theory it reduces to the equation of the type given by joos and zeh in the one particle sector but correcting certain numerical factors which have recently become significant in connection with experimental tests of decoherence this master equation also emphasizes the role of local number density as the preferred basis for decoherence in this model

atoms of weakly null additive monotone measures and integrals in this paper we prove some properties of atoms of weakly null additive monotone measures by using the regularity and weak null additivity a sin gleton characterization of atoms of monotone measures on a metric space is shown it is a generalization of previous results obtained by pap the calculation of the sugeno integral and the choquet integral over an atom is also presented respectively similar results for recently introduced universal integral are also given following these results it is shown that the sugeno integral and the choquet integral over an atom of monotone measure is maxitive linear and standard linear respectively convergence theorems for the sugeno integral and the choquet integral over an atom of a monotone measure are also shown

logical reformulation of quantum mechanics iv projectors in semiclassical physics this is a technical paper providing the proofs of three useful theorems playing a central role in two kinds of physical applications an explicit logical and mathematical formulation of the interpretation of quantum mechanics and the corresponding description of irreversibility the appendix contains a brief mathematical introduction to microlocal analysis three theorems are derived in the text a associating a projector in hilbert space with a macroscopic regular cell in classical phase space b specifying the algebra of the projectors associated with different cells c showing the connection between the classical motion of cells and the schrodinger evolution of projectors for a class of regular hamiltonians corresponding approximately to deterministic systems as described within the framework of quantum mechanics applications to the interpretation of quantum mechanics are given and the consequences for irreversibility will be given later

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

quantum dynamics without the wavefunction when suitably generalized and interpreted the path integral offers an alternative to the more familiar quantal formalism based on state vectors self adjoint operators and external observers mathematically one generalizes the path integral as propagator to a quantal measure on the space of all conceivable worlds and this generalized measure expresses the dynamics or law of motion of the theory much as wiener measure expresses the dynamics of brownian motion within such histories based schemes new and more realistic possibilities open up for resolving the philosophical problems of the state vector formalism in particular one can dispense with the need for external agents by locating the predictive content of in its sets of measure zero such sets are to be precluded but unrestricted application of this rule engenders contradictions one possible response would remove the contradictions by circumscribing the application of the preclusion concept another response more in the tradition of quantum logic would accommodate the contradictions by dualizing to a space of co events and effectively identifying reality with an element of this dual space

linearly positive histories probabilities for a robust family of sequences of quantum events non negative probabilities that obey the sum rules may be assigned to a much wider family of sets of histories than decohering histories the resulting linearly positive histories avoid the highly restrictive decoherence conditions and yet give the same probabilities when those conditions apply thus linearly positive histories are a broad extension of decohering histories moreover the resulting theory is manifestly time reversal invariant

the action operator for continuous time histories we define the action operator for the consistent histories formalism as the quantum analog of the classical action functional for the simple harmonic oscillator case we conclude that the action operator is the generator of time transformations and is associated with the two types of time evolution of the standard quantum theory the wave packet reduction and the unitary time evolution we construct the corresponding classical histories and demonstrate the relevance with the quantum histories finally we show the relation of the action operator to the decoherence functional

rank two bipartite bound entangled states do not exist we explore the relation between the rank of a bipartite density matrix and the existence of bound entanglement we show a relation between the rank marginal ranks and distillability of a mixed state and use this to prove that any rank n bound entangled state must have support on no more than an n n hilbert space a direct consequence of this result is that there are no bipartite bound entangled states of rank two we also show that a separability condition in terms of a quantum entropy inequality is associated with the above results we explore the idea of how many pure states are needed in a mixture to cancel the distillable entanglement of a schmidt rank n pure state and provide a lower bound of n 1 we also prove that a mixture of a non zero amount of any pure entangled state with a pure product state is distillable

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

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

a new result on impulsive differential equations involving non absolutely convergent integrals in this paper we obtain as an application of a darbo type theorem global solutions for differential equations with impulse effects under the assumption that the function on the right hand side is integrable in the henstock sense we thus generalize several previously given results in literature for ordinary or impulsive equations

unextendible product bases uncompletable product bases and bound entanglement we report new results and generalizations of our work on unextendible product bases upb uncompletable product bases and bound entanglement we present a new construction for bound entangled states based on product bases which are only completable in a locally extended hilbert space we introduce a very useful representation of a product basis an orthogonality graph using this representation we give a complete characterization of unextendible product bases for two qutrits we present several generalizations of upbs to arbitrary high dimensions and multipartite systems we present a sufficient condition for sets of orthogonal product states to be distinguishable by separable superoperators we prove that bound entangled states cannot help increase the distillable entanglement of a state beyond its regularized entanglement of formation assisted by bound entanglement

impulsive nonlocal differential equations through differential equations on time scales abstract we propose a non standard approach to impulsive differential equations in banach spaces by embedding this type of problems into differential dynamic problems on time scales we give an existence result for dynamic equations and as a consequence we obtain an existence result for impulsive differential equations

k order additive discrete fuzzy measures and their representation abstract in order to face with the complexity of discrete fuzzy measures we propose the concept of k orderadditive fuzzy measure including usual additive measures and fuzzy measures every discrete fuzzy measure is a k order additive fuzzy measure for a unique k a related topic of the paper is to introduce an alternative representation of fuzzy measures called the interaction representation which sets and extends in a common framework the shapley value and the interaction index proposed by murofushi and soneda

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

super quantum measures on effect algebras with the riesz decomposition properties we give one basis of the space of super quantum measures on finite effect algebras with the riesz decomposition properties rdp for short then we prove that the super quantum measures and quantum interference functions on finite effect algebras with the rdp are determined each other at last we investigate the relationships between the super quantum measures and the diagonally positive signed measures on finite effect algebras with the rdp in detail

on the structure of the k additive fuzzy measures in this paper we present some results concerning the vertices of the set of fuzzy measures being at most k additive we provide an algorithm to compute them we give some examples of the results obtained with this algorithm and give lower bounds on the number of vertices for the n 1 additive case proving that it grows much faster than the number of vertices of the general fuzzy measures the results in the paper suggest that the structure of k additive measures might be more complex than expected from their definition and in particular that they are more complex than general fuzzy measures

on the solution of dydx ap f x y abstract we prove a substantial extension of picard s theorem on the solvability of the ordinary differential equation dy dx f x y and also obtain a generalization of the result in terms of approximate derivative dy dx ap the results are illustrated by suitable examples

can a quantum state over time resemble a quantum state at a single time the standard formalism of quantum theory treats space and time in fundamentally different ways in particular a composite system at a given time is represented by a joint state but the formalism does not prescribe a joint state for a composite of systems at different times if there were a way of defining such a joint state this would potentially permit a more even handed treatment of space and time and would strengthen the existing analogy between quantum states and classical probability distributions under the assumption that the joint state over time is an operator on the tensor product of single time hilbert spaces we analyse various proposals for such a joint state including one due to leifer and spekkens one due to fitzsimons jones and vedral and another based on discrete wigner functions finding various problems with each we identify five criteria for a quantum joint state over time to satisfy if it is to play a role similar to the standard joint state for a composite system that it is a hermitian operator on the tensor product of the single time hilbert spaces that it represents probabilistic mixing appropriately that it has the appropriate classical limit that it has the appropriate single time marginals that composing over multiple time steps is associative we show that no construction satisfies all these requirements if hermiticity is dropped then there is an essentially unique construction that satisfies the remaining four criteria

complex probabilities on r n as real probabilities on c n and an application to path integrals we establish a necessary and sufficient condition for averages over complex valued weight functions on r n to be represented as statistical averages over real non negative probability weights on c n using this result we show that many path integrals for time ordered expectation values of bosonic degrees of freedom in real valued time can be expressed as statistical averages over ensembles of paths with complex valued coordinates and then speculate on possible consequences of this result for the relation between quantum and classical mechanics

logical reformulation of quantum mechanics i foundations the basic rules of quantum mechanics are reformulated they deal primarily with individual systems and do not assume that every ket may represent a physical state the customary kinematic and dynamic rules then allow to construct consistent boolean logics describing the history of a system following essentially griffiths proposal logical implication is defined within these logics the multiplicity of which reflects the complementary principle only one interpretative rule of quantum mechanics is necessary in such a framework it states that these logics providebona fide foundations for the description of a quantum system and for reasoning about it one attempts to build up classical physics including classical logic on these quantum foundations the resulting theory of measurement needs not to statea priori that the eigenvalues of an observable have to be the results of individual measurements nor to assume wave packet reduction both these properties can be obtained as consequences of the basic rules one also needs not to postulate that every observable is measurable even in principle a proposition calculus is obtained allowing in principle the replacement of the discussion of problems concerned with the practical interpretation of experiments by due calculations

consistent histories and the interpretation of quantum mechanics the usual formula for transition probabilities in nonrelativistic quantum mechanics is generalized to yield conditional probabilities for selected sequences of events at several different times called consistent histories through a criterion which ensures that within limits which are explicitly defined within the formalism classical rules for probabilities are satisfied the interpretive scheme which results is applicable to closed isolated quantum systems is explicitly independent of the sense of time i e past and future can be interchanged has no need for wave function collapse makes no reference to processes of measurement though it can be used to analyze such processes and can be applied to sequences of microscopic or macroscopic events or both as long as the mathematical condition of consistency is satisfied when applied to appropriate macroscopic events it appears to yield the same answers as other interpretative schemes for standard quantum mechanics though from a different point of view which avoids the conceptual difficulties which are sometimes thought to require reference to conscious observers or classical apparatus

contrary quantum histories and contrary inferences abstract in the context of the quantum histories approach to quantum mechanics we define a contrary relation between quantum histories generalizing the standard definition of contrary quantum properties using this contrary relation we study the possibility of inferring contrary quantum histories we consider the quantum histories approach with three different consistency conditions weak medium and global consistency conditions for the first two conditions we show that it is possible to infer contrary histories from different families of histories in accordance with previous results for global consistency condition we prove that it is not possible to infer contrary histories

how to calculate decoherence matrices numerically abstract a central object in the interpretation of quantum mechanics of closed systems is the decoherence matrix but only for a very small number of models one is able to give explicit expressions for its elements so numerical methods are required unfortunately the dimensions of these matrices are usually very high which makes also a direct numerical calculation impossible in this paper i will develop an algorithm that combines the numerical calculation of the elements of the decoherence matrix with a permanent estimation if the chosen histories are almost decoherent the algorithm will provide the diagonal and maybe some near to diagonal elements only in this case within numerical errors we can assume that all not calculated elements are smaller than a given threshold if the histories are coherent the algorithm has to calculate too much data there exist too much non vanishing elements and the success depends mainly on the available computer time as an example i apply this procedure to the caldeira leggett model

everything you always wanted to know about locc but were afraid to ask in this paper we study the subset of generalized quantum measurements on finite dimensional systems known as local operations and classical communication locc while locc emerges as the natural class of operations in many important quantum information tasks its mathematical structure is complex and difficult to characterize here we provide a precise description of locc and related operational classes in terms of quantum instruments our formalism captures both finite round protocols as well as those that utilize an unbounded number of communication rounds while the set of locc is not topologically closed we show that finite round locc constitutes a compact subset of quantum operations additionally we show the existence of an open ball around the completely depolarizing map that consists entirely of locc implementable maps finally we demonstrate a two qubit map whose action can be approached arbitrarily close using locc but nevertheless cannot be implemented perfectly

separability problem for multipartite states of rank at most 4 one of the most important problems in quantum information is the separability problem which asks whether a given quantum state is separable we investigate multipartite states of rank at most 4 which are ppt i e all their partial transposes are positive semidefinite we show that any ppt state of rank 2 or 3 is separable and has length at most 4 for separable states of rank 4 we show that they have length at most 6 it is six only for some qubit qutrit or multiqubit states it turns out that any ppt entangled state of rank 4 is necessarily supported on a 3 3 or a 2 2 2 subsystem we obtain a very simple criterion for the separability problem of the ppt states of rank at most 4 such a state is entangled if and only if its range contains no product vectors this criterion can be easily applied since a four dimensional subspace in the 3 3 or 2 2 2 system contains a product vector if and only if its plucker coordinates satisfy a homogeneous polynomial equation the chow form of the corresponding segre variety we have computed an explicit determinantal expression for the chow form in the former case while such an expression was already known in the latter case

unextendible product bases and bound entanglement an unextendible product basis upb for a multipartite quantum system is an incomplete orthogonal product basis whose complementary subspace contains no product state we give examples of upbs and show that the uniform mixed state over the subspace complementary to any upb is a bound entangled state we exhibit a tripartite 2 3 2 3 2 upb whose complementary mixed state has tripartite entanglement but no bipartite entanglement i e all three corresponding 2 3 4 bipartite mixed states are unentangled we show that members of a upb are not perfectly distinguishable by local positive operator valued measurements and classical communication s0031 9007 99 09360 6

from classical to quantum mechanics how to translate physical ideas into mathematical language following previous works by e prugovecki physica a 91a 202 1978 and stochastic quantum mechanics and quantum space time reidel dordrecht 1986 on common features of classical and quantum mechanics we develop a unified mathematical framework for classical and quantum mechanics based on l2 spaces over classical phase space in order to investigate to what extent quantum mechanics can be obtained as a simple modification of classical mechanics on both logical and analytical levels to obtain this unified framework we split quantum theory in two parts i general quantum axiomatics a system is described by a state in a hilbert space observables are self adjoints operators and so on and ii quantum mechanics proper that specifies the hilbert space as l2 rn the heisenberg rule pi qj i ij with p i the free hamiltonian h 2 2m and so on we show that general quantum axiomatics up to a supplementary axiom of classicity can be used as a nonstandard mathematical ground to formula

decoherent histories and realism we reconsider the decoherent histories approach to quantum mechanics and analyze some problems related to its interpretation which we believe have not been adequately clarified by its proponents we put forward some assumptions which in our opinion are necessary for a realistic interpretation of the probabilities that the formalism attaches to decoherent histories we prove that such assumptions unless one limits the set of the decoherent families which can be taken into account lead to a logical contradiction the line of reasoning we follow is conceptually different from other arguments which have been presented and which have been rejected by the supporters of the decoherent histories approach the conclusion is that the decoherent histories approach to be considered as an interesting realistic alternative to the orthodox interpretation of quantum mechanics requires the identification of a mathematically precise criterion to characterize an appropriate set of decoherent families which does not give rise to any problem

a topos formulation of history quantum theory topos theory has been suggested by doring and isham as an alternative mathematical structure with which to formulate physical theories in particular it has been used to reformulate standard quantum mechanics in such a way that a novel type of logic is used to represent propositions in this paper we extend this formulation to include temporally ordered collections of propositions as opposed to single time propositions that is to say we have developed a quantum history formalism in the language of topos theory where truth values can be assigned to temporal propositions we analyze the extent to which such truth values can be derived from the truth values of the constituent single time propositions

about the notion of truth in quantum mechanics the meaning of truth in quantum mechanics is considered in order to respond to some objections raised by b d espagnat against a logical interpretation of quantum mechanics recently proposed by the author a complete answer is given it is shown that not only can factual data be said to be true but also some of their logical consequences so that the definition of truth given by heisenberg is both extended and refined some nontrue but reliable propositions may also be used but they are somewhat arbitrary because of the complementarity principle for instance the propositions expressing wave packet reduction can be either true or reliable according to the case under study separability is also discussed as far as the true properties of an individual system are concerned quantum mechanics is separable