on feedback and the classical capacity of a noisy quantum channel in shannon information theory the capacity of a memoryless communication channel cannot be increased by the use of feedback from receiver to sender in this correspondence the use of classical feedback is shown to provide no increase in the unassisted classical capacity of a memoryless quantum channel when feedback is used across nonentangled input states or when the channel is an entanglement breaking channel this gives a generalization of the shannon theory for certain classes of feedback protocols when transmitting through noisy quantum communication channels

global optimization and simulated annealing in this paper we are concerned with global optimization which can be defined as the problem of finding points on a bounded subset of n in which some real valued functionf assumes its optimal maximal or minimal value we present a stochastic approach which is based on the simulated annealing algorithm the approach closely follows the formulation of the simulated annealing algorithm as originally given for discrete optimization problems the mathematical formulation is extended to continuous optimization problems and we prove asymptotic convergence to the set of global optima furthermore we discuss an implementation of the algorithm and compare its performance with other well known algorithms the performance evaluation is carried out for a standard set of test functions from the literature

on quantum coding for ensembles of mixed states we consider the problem of optimal asymptotically faithful compression for ensembles of mixed quantum states although the optimal rate is unknown we prove upper and lower bounds and describe a series of illustrative examples of compression of mixed states we also discuss a classical analogue of the problem

higher order generalized invexity and duality in nondifferentiable mathematical programming in this paper we consider a number of higher order duals to a nondifferentiable programming problem and establish duality under the higher order generalized invexity conditions introduced in an earlier work by mishra and rueda

lower bounds on the quantum capacity and highest error exponent of general memoryless channels tradeoffs between the information rate and fidelity of quantum error correcting codes are discussed quantum channels to be considered are those subject to independent errors and modeled as tensor products of copies of a general completely positive cp linear map where the dimension of the underlying hilbert space is a prime number on such a quantum channel the highest fidelity of a quantum error correcting code of length n and rate r is proven to be lower bounded by 1 exp ne r o n for some function e r the e r is positive below some threshold r sub 0 a direct consequence of which is that r sub 0 is a lower bound on the quantum capacity this is an extension of the author s earlier result while the earlier work states the result for the depolarizing channel and a slight generalization of it pauli channels the result of this work applies to general discrete memoryless channels including channel models derived from a physical law of time evolution

quantum capacity under adversarial quantum noise arbitrarily varying quantum channels we investigate entanglement transmission over an unknown channel in the presence of a third party called the adversary which is enabled to choose the channel from a given set of memoryless but non stationary channels without informing the legitimate sender and receiver about the particular choice that he made this channel model is called an arbitrarily varying quantum channel avqc we derive a quantum version of ahlswede s dichotomy for classical arbitrarily varying channels this includes a regularized formula for the common randomness assisted capacity for entanglement transmission of an avqc quite surprisingly and in contrast to the classical analog of the problem involving the maximal and average error probability we find that the capacity for entanglement transmission of an avqc always equals its strong subspace transmission capacity

coordination capacity we develop elements of a theory of cooperation and coordination in networks rather than considering a communication network as a means of distributing information or of reconstructing random processes at remote nodes we ask what dependence can be established among the nodes given the communication constraints specifically in a network with communication rates ri j between the nodes we ask what is the set of all achievable joint distributions p x1 xm of actions at the nodes of the network several networks are solved including arbitrarily large cascade networks distributed cooperation can be the solution to many problems such as distributed games distributed control and establishing mutual information bounds on the influence of one part of a physical system on another

a note on higher order symmetric duality in this paper a pair of wolfe type higher order symmetric dual multiobjective programs is formulated strong and converse duality theorems are established under invexity assumptions duality relations for mond weir type dual models have also been obtained under pseudoinvexity assumptions

metamodeling radial basis functions versus polynomials abstract for many years metamodels have been used in simulation to provide approximations to the input output functions provided by a simulation model in this paper metamodels based on radial basis functions are applied to approximate test functions known from the literature these tests were conducted to gain insights into the behavior of these metamodels their ease of computation and their ability to capture the shape and minima of the test functions these metamodels are compared against polynomial metamodels by using surface and contour graphs of the error function difference between metamodel and the given function and by evaluating the numerical stability of the required computations full factorial and latin hypercube designs were used to fit the metamodels graphical and statistical methods were used to analyze the test results factorial designs were generally more successful for fitting the test functions as compared to latin hypercube designs radial basis function metamodels using factorial and latin hypercube designs provided better fit than polynomial metamodels using full factorial designs

stabilizer quantum codes over the clifford algebra the key problem for constructing a stabilizer quantum code is how to create a set of generators for the stabilizer of the stabilizer quantum code i e check matrix in this paper we suggest an approach based on the clifford algebra to create the check matrix for the stabilizer quantum codes in the proposed approach the recursive relation of the matrix transform over the clifford algebra is employed to generate the check matrix with the proposed approach a quantum code with any length can be constructed easily especially some new codes which are impossible via previous approaches are constructed

multiobjective symmetric duality involving cones abstract in this paper a pair of multiobjective symmetric dual programs over arbitrary cones are formulated for cone convex functions weak strong converse and self duality theorems are proved for these programs

the quantum capacity of channels with arbitrarily correlated noise we study optimal rates for quantum communication over a single use of a channel which itself can correspond to a finite number of uses of a channel with arbitrarily correlated noise the corresponding capacity is often referred to as the one shot quantum capacity in this paper we prove bounds on the one shot quantum capacity of an arbitrary channel this allows us to compute the quantum capacity of a channel with arbitrarily correlated noise in the limit of asymptotically many uses of the channel in the memoryless case we explicitly show that our results reduce to known expressions for the quantum capacity

multivariate adaptive regression splines a new method is presented for flexible regression modeling of high dimensional data the model takes the form of an expansion in product spline basis functions where the number of basis functions as well as the parameters associated with each one product degree and knot locations are automatically determined by the data this procedure is motivated by the recursive partitioning approach to regression and shares its attractive properties unlike recursive partitioning however this method produces continuous models with continuous derivatives it has more power and flexibility to model relationships that are nearly additive or involve interactions in at most a few variables in addition the model can be represented in a form that separately identifies the additive contributions and those associated with the different multivariable interactions

higher order symmetric duality in vector optimization problem involving generalized cone invex functions in this paper a pair of higher order symmetric dual model in vector optimization problem is formulated the higher order cone pseudoinvex and higher order strongly cone pseudoinvex functions are defined the weak strong and converse duality theorems are established using these defined functions

useful states and entanglement distillation we derive general upper bounds on the distillable entanglement of a mixed state under one way and two way local operations and classical communication locc in both cases the upper bound is based on a convex decomposition of the state into useful and useless quantum states by useful we mean a state whose distillable entanglement is non negative and equal to its coherent information and thus given by a single letter tractable formula on the other hand useless states are undistillable i e their distillable entanglement is zero we prove that in both settings the distillable entanglement is convex on such decompositions hence an upper bound on the distillable entanglement is obtained from the contributions of the useful states alone being equal to the convex combination of their coherent informations optimizing over all such decompositions of the input state yields our upper bound the useful and useless states are given by degradable and antidegradable states in the one way locc setting and by maximally correlated and positive partial transpose ppt states in the two way locc setting respectively we also illustrate how our method can be extended to quantum channels interpreting our upper bound as a convex roof extension we show that it reduces to a particularly simple non convex optimization problem for the classes of isotropic states and werner states in the one way locc setting this non convex optimization yields an upper bound on the quantum capacity of the qubit depolarizing channel that is strictly tighter than previously known bounds for large values of the depolarizing parameter in the two way locc setting the non convex optimization achieves the ppt relative entropy of entanglement for both isotropic and werner states

minimax and symmetric duality for a class of multiobjective variational mixed integer programming problems abstract in this paper we formulate a pair of multiobjective variational mixed integer programs for arbitrary cones under the separability and partial invexity assumptions on the functions involved we establish the weak strong converse and self duality theorems related to efficient solution

efficient quantum polar codes requiring no preshared entanglement we construct an explicit quantum coding scheme which achieves a communication rate not less than the coherent information when used to transmit the quantum information over a noisy quantum channel for pauli and erasure channels we also present efficient encoding and decoding algorithms for this communication scheme based on polar codes essentially linear in the blocklength but which do not require the sender and receiver to share any entanglement before the protocol begins due to the existence of degeneracies in the involved error correcting codes it is indeed possible that the rate of the scheme exceeds the coherent information we provide a simple criterion which indicates such performance finally we discuss how the scheme can be used for secret key distillation as well as private channel coding

trading classical communication quantum communication and entanglement in quantum shannon theory in this paper we give tradeoffs between classical communication quantum communication and entanglement for processing information in the shannon theoretic setting we first prove a unit resource capacity theorem that applies to the scenario where only the above three noiseless resources are available for consumption or generation the optimal strategy mixes the three fundamental protocols of teleportation superdense coding and entanglement distribution we then provide an achievable rate region and a matching multiletter converse for the direct static capacity theorem this theorem applies to the scenario where a large number of copies of a noisy bipartite state are available in addition to consumption or generation of the above three noiseless resources our coding strategy involves a protocol that we name the classically assisted state redistribution protocol and the three fundamental protocols we finally provide an achievable rate region and a matching multiletter converse for the direct dynamic capacity theorem this theorem applies to the scenario where a large number of uses of a noisy quantum channel are available in addition to the consumption or generation of the three noiseless resources our coding strategy combines the classically enhanced father protocol with the three fundamental unit protocols

higher order duality in multiobjective fractional programming with support functions abstract in this paper a new class of higher order f type i functions for a multiobjective programming problem is introduced which subsumes several known studied classes higher order mond weir and schaible type dual programs are formulated for a nondifferentiable multiobjective fractional programming problem where the objective functions and the constraints contain support functions of compact convex sets in r n weak and strong duality results are studied in both the cases assuming the involved functions to be higher order f type i a number of previously studied problems appear as special cases

fidelity and entanglement fidelity for infinite dimensional quantum systems instead of unitary freedom for finite dimensional cases bi contractive freedom in the operator sum representation for quantum channels of infinite dimensional systems is established specifically if the channel sends every pure state to a finite rank state then the isometric freedom feature holds then a method of computing entanglement fidelity and a relation between quantum fidelity and entanglement fidelity for infinite dimensional systems are obtained in addition upper and lower bounds of the quantum fidelity and their connection to the trace distance are also provided

a resource framework for quantum shannon theory quantum shannon theory is loosely defined as a collection of coding theorems such as classical and quantum source compression noisy channel coding theorems entanglement distillation etc which characterize asymptotic properties of quantum and classical channels and states in this paper we advocate a unified approach to an important class of problems in quantum shannon theory consisting of those that are bipartite unidirectional and memoryless

nonparametric fitting of aerodynamic data using smoothing thin plate splines this paper introduces a nonparametric fitting method for the interpolation of aerodynamic observations over a large range of multiple angles of attack the method is based on the employment of smoothing thin plate spline class functions a well renewed mathematical tool for multivariate data mining based on the generalization of the univariate natural cubic splines in which a roughness penalty criterion is used to produce very smooth predictive hypersurfaces compared with other methods such as parametric or even conventional nonparametric methods the use of a smoothing thin plate spline is more effective in that the predictive surface comes directly from the observed points thus minimizing any intervention of the analyst aimed at introducing model parameters this forms the basis for a very reliable fitting technique in which model construction can be relatively easy to implement an application of the method is carried out on a case study representative of some experimental data coming from a wind tunnel campaign on a typical three dimensional fuselage shaped body aimed at the acquisition of its aerodynamic coefficients over a rather extensive attitude range specifically the application is focused on the body lift coefficient as a function of both angle of attack and sideslip angle the data set is also interpolated using concurrent response surface methods namely a linear model a bivariate spline a radial basis function network a support vector regression technique a regression kriging and a moving least squares approach alternatively known as local polynomial regression results of data fitting are assessed using a cross validation approach and reveal a clear superiority of smoothing thin plate spline over the other methods leading to a more regular fitted surface and a more reliable prediction tool even when some observations are omitted this is important per se but acquires even more significance when an aerodynamic test campaign is to be planned with the minimum number of experimental observations

information rates achievable with algebraic codes on quantum discrete memoryless channels the highest information rate at which quantum error correction schemes work reliably on a channel is called the quantum capacity here this is proven to be lower bounded by the limit of coherent information maximized over the set of input density operators which are proportional to the projections onto the code spaces of symplectic stabilizer codes the quantum channels to be considered are those subject to independent errors and modeled as tensor products of copies of a completely positive linear map on a hilbert space of finite dimension the codes that are proven to have the desired performance are symplectic stabilizer codes on the depolarizing channel the bound proven here is actually the highest possible rate at which symplectic stabilizer codes work reliably

causal limit on quantum communication the capacity of a channel is known to be equivalent to the highest rate at which it can generate entanglement analogous to entanglement the notion of a causality measure characterizes the temporal aspect of quantum correlations despite holding an equally fundamental role in physics temporal quantum correlations have yet to find their operational significance in quantum communication here we uncover a connection between quantum causality and channel capacity we show the amount of temporal correlations between two ends of the noisy quantum channel as quantified by a causality measure implies a general upper bound on its channel capacity the expression of this new bound is simpler to evaluate than most previously known bounds we demonstrate the utility of this bound by applying it to a class of shifted depolarizing channels which results in improvement over previously known bounds for this class of channels

decoding quantum information via the petz recovery map we obtain a lower bound on the maximum number of qubits qn e n which can be transmitted over n uses of a quantum channel n for a given non zero error threshold e to obtain our result we first derive a bound on the one shot entanglement transmission capacity of the channel and then compute its asymptotic expansion up to the second order in our method to prove this achievability bound the decoding map used by the receiver on the output of the channel is chosen to be the petz recovery map also known as the transpose channel our result in particular shows that this choice of the decoder can be used to establish the coherent information as an achievable rate for quantum information transmission applying our achievability bound to the 50 50 erasure channel which has zero quantum capacity we find that there is a sharp error threshold above which qn e n scales as n

monotonicity under local operations linear entropic formulas all correlation measures classical and quantum must be monotonic under local operations in this paper we characterize monotonic formulas that are linear combinations of the von neumann entropies associated with the quantum state of a physical system that has n parts we show that these formulas form a polyhedral convex cone which we call the monotonicity cone and enumerate its facets we illustrate its structure and prove that it is equivalent to the cone of monotonic formulas implied by strong subadditivity we explicitly compute its extremal rays for n leq5 we also consider the symmetric monotonicity cone in which the formulas are required to be invariant under subsystem permutations we describe this cone fully for all n

multiobjective nonlinear second order symmetric duality with k f pseudoconvexity abstract the purpose of this paper is to introduce a new class of generalized cone pseudoconvex functions and strongly cone pseudoconvex functions called second order k f pseudoconvex functions and strongly second order k f pseudoconvex functions a pair of second order symmetric dual multiobjective nonlinear programs is formulated over arbitrary generalized cone pseudoconvex functions for these second order symmetric dual programs the weak strong and converse duality theorems are established using the above generalization of cone pseudoconvex functions a self duality theorem is also given by assuming the functions involved to be skew symmetric

symmetric duality for minimax mixed integer programming problems with pseudo invexity in this paper we consider the pair of symmetric dual multiobjective variational mixed integer programs proposed by chen and yang x chen j yang symmetric duality for minimax multiobjective variational mixed integer programming problems with partial invexity european journal of operational research 181 2007 76 85 and extend some of their results under the assumptions of partial pseudo invexity and separability on the functions involved these results include several results available in literature as special cases

a father protocol for quantum broadcast channels a new protocol for quantum broadcast channels based on the fully quantum slepian wolf protocol is presented the protocol yields an achievable rate region for entanglement assisted transmission of quantum information through a quantum broadcast channel that can be considered the quantum analogue of marton s region for classical broadcast channels the protocol can be adapted to yield achievable rate regions for unassisted quantum communication and for entanglement assisted classical communication in the case of unassisted transmission the region we obtain has no independent constraint on the sum rate only on the individual transmission rates regularized versions of all three rate regions are provably optimal

multiobjective second order symmetric duality with f convexity we suggest a pair of second order symmetric dual programs in multiobjective nonlinear programming for these second order symmetric dual programs we prove the weak strong and converse duality theorems under f convexity conditions

on second order symmetric duality in nondifferentiable programming this article is concerned with a pair of second order symmetric dual non differentiable programs and second order f pseudo convexity we establish the weak and the strong duality theorems for the new pair of dual models under the f pseudo convexity assumption several known results including mond and schechter as well as others are obtained as special cases

capacity theorems for quantum multiple access channels classical quantum and quantum quantum capacity regions in this paper we consider quantum channels with two senders and one receiver for an arbitrary such channel we give multiletter characterizations of two different two dimensional capacity regions the first region comprises the rates at which it is possible for one sender to send classical information while the other sends quantum information the second region consists of the rates at which each sender can send quantum information for each region we give an example of a channel for which the corresponding region has a single letter description one of our examples relies on a new result proved here perhaps of independent interest stating that the coherent information over any degradable channel is concave in the input density operator we conclude with connections to other work and a discussion on generalizations where each user simultaneously sends classical and quantum information

distillation of secret key and entanglement from quantum states we study and solve the problem of distilling a secret key from quantum states representing correlation between two parties alice and bob and an eavesdropper eve via oneway public discussion we

higher order generalized convexity and duality in nondifferentiable multiobjective mathematical programming in this paper a class of generalized convexity is introduced and a unified higher order dual model for nondifferentiable multiobjective programs is described where every component of the objective function contains a term involving the support function of a compact convex set weak duality theorems are established under generalized convexity conditions the well known case of the support function in the form of square root of a positive semidefinite quadratic form and other special cases can be readily derived from our results

the capacity of the quantum channel with general signal states it is shown that the capacity of a classical quantum channel with arbitrary possibly mixed states equals the maximum of the entropy bound with respect to all a priori distributions this completes the recent result of hausladen jozsa schumacher westmoreland and wootters 1996 who proved the equality for the pure state channel

symmetric duality in multiobjective programming involving generalized cone invex functions abstract in this paper cone pseudoinvex and strongly cone pseudoinvex functions are defined a pair of mond weir type symmetric dual multiobjective programs is formulated over arbitrary cones weak duality strong duality and converse duality theorems are established using the above defined functions a self duality theorem is also given by assuming the functions involved to be skew symmetric

second order asymptotics of visible mixed quantum source coding via universal codes the simplest example of a quantum information source with memory is a mixed source which emits signals entirely from one of two memoryless quantum sources with given a priori probabilities considering a mixed source consisting of a general one parameter family of memoryless sources we derive the second order asymptotic rate for fixed length visible source coding furthermore we specialize our main result to a mixed source consisting of two memoryless sources our results provide the first example of the second order asymptotics for a quantum information processing task employing a resource with memory for the case of a classical mixed source using a finite alphabet our results reduce to those obtained by nomura and han to prove the achievability part of our main result we introduce universal quantum source codes achieving the second order asymptotic rates these are obtained by an extension of hayashi s construction of their classical counterparts

second order symmetric duality for nonlinear multiobjective mixed integer programming we formulate two pairs of second order symmetric duality for nonlinear multiobjective mixed integer programs for arbitrary cones by using the concepts of efficiency and second order invexity we establish weak strong converse and self duality theorems for the dual models several known results are obtained as special cases

second order symmetric duality in non differentiable multiobjective programming with f convexity abstract this paper is concerned with a pair of mond weir type second order symmetric dual non differentiable multiobjective programming problems we establish the weak and strong duality theorems for the new pair of dual models under second order f convexity assumptions several results including many recent works are obtained as special cases

potential capacities of quantum channels we introduce potential capacities of quantum channels in an operational way and provide upper bounds for these quantities which quantify the ultimate limit of usefulness of a channel for a given task in the best possible context unfortunately except for a few isolated cases potential capacities seem to be as hard to compute as their plain analogues we thus study upper bounds on some potential capacities for the classical capacity we give an upper bound in terms of the entanglement of formation to establish a bound for the quantum and private capacity we first lift the channel to a hadamard channel and then prove that the quantum and private capacity of a hadamard channel is strongly additive implying that for these channels potential and plain capacity are equal employing these upper bounds we show that if a channel is noisy however close it is to the noiseless channel then it cannot be activated into the noiseless channel by any other contextual channel this conclusion holds for all the three capacities we also discuss the so called environment assisted quantum capacity because we are able to characterize its potential version

pseudo invexity and duality in nonlinear programming abstract the purpose of this paper is to study various duality results in nonlinear programming for pseudo invex functions such results were known in the literature for invex functions

minimax and symmetric duality for nonlinear multiobjective mixed integer programming abstract we formulate two pairs of symmetric duality for nonlinear multiobjective mixed integer programs for arbitrary cones by using the concept of efficiency we establish the weak strong converse and self duality theorems for our symmetric models several known results are obtained as special cases

entanglement transmission and generation under channel uncertainty universal quantum channel coding we determine the optimal rates of universal quantum codes for entanglement transmission and generation under channel uncertainty in the simplest scenario the sender and receiver are provided merely with the information that the channel they use belongs to a given set of channels so that they are forced to use quantum codes that are reliable for the whole set of channels this is precisely the quantum analog of the compound channel coding problem we determine the entanglement transmission and entanglement generating capacities of compound quantum channels and show that they are equal moreover we investigate two variants of that basic scenario namely the cases of informed decoder or informed encoder and derive corresponding capacity results

approximate degradable quantum channels degradable quantum channels are an important class of completely positive trace preserving maps among other properties they offer a single letter formula for the quantum and the private classical capacity and are characterized by the fact that a complementary channel can be obtained from the channel by applying a degrading channel in this paper we introduce the concept of approximate degradable channels which satisfy this condition up to some finite varepsilon geq 0 that is there exists a degrading channel which upon composition with the channel is varepsilon close in the diamond norm to the complementary channel we show that for any fixed channel the smallest such varepsilon can be efficiently determined via a semidefinite program moreover these approximate degradable channels also approximately inherit all other properties of degradable channels as an application we derive improved upper bounds to the quantum and private classical capacity for certain channels of interest in quantum communication

lower bound for the quantum capacity of a discrete memoryless quantum channel we generalize the random coding argument of stabilizer codes and derive a lower bound on the quantum capacity of an arbitrary discrete memoryless quantum channel for the depolarizing channel our lower bound coincides with that obtained by bennett et al we also slightly improve the quantum gilbert varshamov bound for general stabilizer codes and establish an analog of the quantum gilbert varshamov bound for linear stabilizer codes our proof is restricted to the binary quantum channels but its extension of to l adic channels is straight forward

converse duality in nonlinear programming with cone constraints abstract the purpose of this paper is to establish various converse duality results for nonlinear programming with cone constraints and its four dual models introduced by chandra and abha s chandra abha a note on pseudo invex and duality in nonlinear programming european journal of operational research 122 2000 161 165

a simple test for quantum channel capacity based on state and channel isomorphism we point out that semidefinite programming can be used as a quick test for nonzero one way quantum channel capacity this can be achieved by searching for symmetric extensions of states isomorphic to a given quantum channel with this method we provide examples of quantum channels that can lead to high entanglement transmission but still have zero one way capacity in particular regions of symmetric extendibility for isotropic states in arbitrary dimensions are presented further we derive a new entanglement parameter based on normalized relative entropy distance to the set of states that have symmetric extensions and show explicitly the symmetric extension of isotropic states being the nearest to singlets in the set of symmetrically extendible states the suitable regularization of the parameter provides a new upper bound on one way distillable entanglement

symmetric duality for multiobjective fractional variational problems involving cones in this paper a pair of multiobjective fractional variational symmetric dual problems over cones is formulated weak strong and converse duality theorems are established under generalized f convexity assumptions moreover self duality theorem is also discussed

non differentiable symmetric duality for multiobjective programming with cone constraints abstract two pairs of non differentiable multiobjective symmetric dual problems with cone constraints over arbitrary cones which are wolfe type and mond weir type are considered on the basis of weak efficiency with respect to a convex cone we obtain symmetric duality results for the two pairs of problems under cone invexity and cone pseudoinvexity assumptions on the involved functions our results extend the results in khurana s khurana symmetric duality in multiobjective programming involving generalized cone invex functions european journal of operational research 165 2005 592 597 to the non differentiable multiobjective symmetric dual problem

on the reversible extraction of classical information from a quantum source consider a source of pure quantum states with von neumann entropy s by the quantum source coding theorem arbitrarily long strings of signals may be encoded asymptotically into s qubits per signal the schumacher limit in such a way that entire strings may be recovered with arbitrarily high fidelity suppose that classical storage is free while quantum storage is expensive and suppose that the states of do not fall into two or more orthogonal subspaces we show that if can be compressed with arbitrarily high fidelity into a qubits per signal plus any amount of auxiliary classical storage then a must still be at least as large as the schumacher limit s of thus no part of the quantum information content of can be faithfully replaced by classical information if the states do fall into orthogonal subspaces then a may be less than s but only by an amount not exceeding the amount of classical information specifying the subspace for a signal from the source

on sufficiency of the kuhn tucker conditions if all the functions fo x f x f x are convex on c then these conditions are also sufficient various classes of functions have been defined for the purpose of weakening this limitation of convexity in mathematical programming mangasarian 11 has speculated that pseudo convexity of x and quasiconvexity off x are the weakest conditions that can be imposed so that the above conditions are sufficient for optimality it will be shown that there are other wide classes of functions for which the conditions are sufficient 545

the information disturbance tradeoff and the continuity of stinespring s representation stinespring s dilation theorem is the basic structure theorem for quantum channels it states that any quantum channel arises from a unitary evolution on a larger system here we prove a continuity theorem for stinespring s dilation if two quantum channels are close in cb norm then it is always possible to find unitary implementations which are close in operator norm with dimension independent bounds this result generalizes uhlmann s theorem from states to channels and allows to derive a formulation of the information disturbance tradeoff in terms of quantum channels as well as a continuity estimate for the no broadcasting theorem we briefly discuss further implications for quantum cryptography thermalization processes and the black hole information loss puzzle

non differentiable second order symmetric duality in mathematical programming with f convexity abstract a pair of wolfe type non differentiable second order symmetric primal and dual problems in mathematical programming is formulated the weak and strong duality theorems are then established under second order f convexity assumptions symmetric minimax mixed integer primal and dual problems are also investigated

higher order symmetric duality in nondifferentiable multiobjective programming problems abstract in this paper a pair of nondifferentiable multiobjective programming problems is first formulated where each of the objective functions contains a support function of a compact convex set in rn for a differentiable function h r n r n r we introduce the definitions of the higher order f convexity f pseudo convexity f quasi convexity of function f r n r with respect to h when f and h are taken certain appropriate transformations all known other generalized invexity such as invexity type i invexity and higher order type i invexity can be put into the category of the higher order f invex functions under these the higher order f convexity assumptions we prove the higher order weak higher order strong and higher order converse duality theorems related to a properly efficient solution

non differentiable higher order symmetric duality in mathematical programming with generalized invexity a pair of non differentiable higher order symmetric dual model in mathematical programming is formulated the weak and strong duality theorems are established under higher order invexity assumption symmetric minimax mixed integer primal and dual problems are also investigated

mond weir type second order symmetric duality in non differentiable minimax mixed integer programming problems abstract a pair of mond weir type non differentiable second order symmetric minimax mixed integer primal and dual problems in mathematical programming is formulated symmetric and self duality theorems are then established under second order f pseudo convexity assumptions several known results including that of gulati and ahmad eur j oper res 101 1997 122 hou and yang j math anal appl 255 2001 491 and mond and schechter bull aust math soc 53 1996 177 as well as others are obtained as special cases

communicating probability distributions a rate distortion problem is solved that is motivated by a quantum data compression problem the goal is to send information about a source string x so that a receiver can construct a second string y for which the joint empirical probability distribution of x and y is close to some desired distribution the problem differs from the usual rate distortion problems in that one must consider both remote sources and distortion functions that are not averages of per letter distortion functions

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

coding theorem and strong converse for quantum channels we present a new proof of holevo s 1973 1977 coding theorem for transmitting classical information through quantum channels and its strong converse the technique is largely inspired by wolfwitz s 1964 combinatorial approach using types of sequences as a byproduct of our approach which is independent of previous ones both in the coding theorem and the converse we can give a new proof of holevo s information bound

on quantum fidelities and channel capacities for the discrete memoryless quantum channel we show the equivalence of two different notions of quantum channel capacity that which uses the entanglement fidelity as its criterion for success in transmission and that which uses the minimum fidelity of pure states in a subspace of the input hilbert space as its criterion as a corollary any source with entropy rate less than the capacity may be transmitted with high entanglement fidelity we also show that a restricted class of encodings is sufficient to transmit any quantum source which may be transmitted on a given channel this enables us to simplify a known upper bound for the channel capacity it also enables us to show that the availability of an auxiliary classical channel from encoder to decoder does not increase the quantum capacity

second order asymptotics for source coding dense coding and pure state entanglement conversions we introduce two variants of the information spectrum relative entropy defined by tomamichel and hayashi which have the particular advantage of satisfying the data processing inequality i e monotonicity under quantum operations this property allows us to obtain one shot bounds for various information processing tasks in terms of these quantities moreover these relative entropies have a second order asymptotic expansion which in turn yields tight second order asymptotics for optimal rates of these tasks in the independent and identically distributed setting the tasks studied in this paper are fixed length quantum source coding noisy dense coding entanglement concentration pure state entanglement dilution and transmission of information through a classical quantum channel in the latter case we retrieve the second order asymptotics obtained by tomamichel and tan our results also yield the known second order asymptotics of fixed length classical source coding derived by hayashi the second order asymptotics of entanglement concentration and dilution provide a refinement of the inefficiency of these protocols a quantity which in the case of entanglement dilution was studied by harrow and lo we prove how the discrepancy between the optimal rates of these two processes in the second order implies the irreversibility of entanglement concentration established by kumagai and hayashi in addition the spectral divergence rates of the information spectrum approach isa can be retrieved from our relative entropies in the asymptotic limit this enables us to directly obtain the more general results of the isa from our one shot bounds

stationary quantum source coding in this article the quantum version of the source coding theorem is obtained for a completely ergodic source this result extends schumacher s quantum noiseless coding theorem for memoryless sources the control of the memory effects requires some earlier results of hiai and petz on high probability subspaces our result is equivalently considered as a compression theorem for noiseless stationary channels

technical note on symmetric duality in multiobjective programming some remarks on recent results abstract certain shortcomings are pointed out in some recent works of das and nanda european journal of operational research 97 1997 167 171 and kim et al european journal of operational research 107 1998 686 691 which show that these studies are highly restricted

entanglement assisted communication of classical and quantum information in this paper we consider the problem of transmitting classical and quantum information reliably over an entanglement assisted quantum eaq channel our main result is a capacity theorem that gives a 3 d achievable rate region points in the region are rate triples consisting of the classical communication rate the quantum communication rate and the entanglement consumption rate of a particular coding scheme the crucial protocol in achieving the boundary points of the capacity region is a protocol that we name the classically enhanced father cef protocol the cef protocol is more general than other protocols in the family tree of quantum shannon theoretic protocols in the sense that several previously known quantum protocols are now child protocols of it the cef protocol also shows an improvement over a timesharing strategy for the case of a qubit dephasing channel this result justifies the need for simultaneous coding of classical and quantum information over an eaq channel our capacity theorem is of a multiletter nature requiring a limit over many uses of the channel but it reduces to a single letter characterization for at least three channels the completely depolarizing channel the quantum erasure channel and the qubit dephasing channel

mixed symmetric duality in non differentiable multiobjective mathematical programming two mixed symmetric dual models for a class of non differentiable multiobjective nonlinear programming problems with multiple arguments are introduced in this paper these two mixed symmetric dual models unify the four existing multiobjective symmetric dual models in the literature weak and strong duality theorems are established for these models under some mild assumptions of generalized convexity several special cases are also obtained

symmetric and self duality in vector optimization problem abstract in this paper we present the first order symmetric and self duality programs in multiobjective nonlinear programming problems for these first order symmetric and dual programs we introduce the weak strong and converse duality theorems under convexity and concavity conditions where the pair of the symmetric dual multiobjective nonlinear programming problems in this paper different which in d s kim y b yun h kuk second order symmetric and self duality in multiobjective programming appl math lett 10 2 1997 17 22 also we prove the self duality theorem for these first order self dual programs and illustrate its example

multiobjective symmetric duality with cone constraints we formulate a pair of multiobjective symmetric dual programs for pseudo invex functions and arbitrary cones our model is unifying the wolfe vector symmetric dual and the mond weir vector symmetric dual models we establish the weak strong converse and self duality theorems for our pair of dual models nanda and das results optimization 28 1994 267 eur j oper res 88 1996 572 are obtained as special cases

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

communicating over adversarial quantum channels using quantum list codes in this correspondence we study quantum communication in the presence of adversarial noise in this setting communicating with perfect fidelity requires a quantum code of bounded minimum distance for which the best known rates are given by the quantum gilbert varshamov qgv bound asking only for arbitrarily high fidelity and letting the sender and receiver use a secret key of length logarithmic in the number of qubits sent we find a dramatic improvement over the qgv rates in fact our protocols allow high fidelity transmission at noise levels for which perfect fidelity is impossible to achieve such rates we introduce fully quantum list codes which may be of independent interest

optimality criteria in nonlinear programming involving nonconvex functions abstract in this paper a new class of functions called convex quasiconvex and pseudoconvex are defined and a number of sufficient optimality criteria are obtained for nonlinear programming problems involving these functions

higher order generalized invexity and duality in mathematical programming in this paper we introduce the concepts of higher order type i pseudo type i and quasi type i functions and establish various higher order duality results involving these functions

a note on pseudo invexity and duality in nonlinear programming abstract certain shortcomings are pointed out in the recent work of s nanda l n das european journal of operational research 88 1996 572 577 and appropriate modifications are suggested for studying duality under pseudo invexity assumptions

extrinsic and intrinsic data in quantum measurements asymptotic convex decomposition of positive operator valued measures we study the problem of separating the data produced by a given quantum measurement on states from a memoryless source which is unknown except for its average state described by a positive operator valued measure povm into a meaningful intrinsic and a not meaningful extrinsic part we are able to give an asymptotically tight separation of this form with the intrinsic data quantified by the holevo mutual information of a certain state ensemble associated to the povm and the source in a model that can be viewed as the asymptotic version of the convex decomposition of povms into extremal ones this result is applied to a similar separation therorem for quantum instruments and quantum operations in their kraus form finally we comment on links to related subjects we stress the difference between data and information in particular by pointing out that information typically is strictly less than data derive the holevo bound from our main result and look at its classical case we show that this includes the solution to the problem of extrinsic intrinsic data separation with a known source then compare with the well known notion of sufficient statistics the result on decomposition of quantum operations is used to exhibit a new aspect of the concept of entropy exchange of an open dynamics an appendix collects several estimates for mixed state fidelity and trace norm distance that seem to be new in particular a construction of canonical purification of mixed states that turns out to be valuable to analyze their fidelity

compressing quantum mixed state sources by sending classical information we consider visible compression for discrete memoryless sources of mixed quantum states when only classical information can be sent from alice to bob we assume that bob knows the source statistics and that alice and bob have access to the same source of random numbers we put in an information theoretic framework some previous results on visible compression for sources of states with commuting density operators and remove the commutativity requirement we derive a general achievable compression rate which is for the noncommutative case still higher than the known lower bound we also present several related problems of classical information theory and show how they can be used to answer some questions of the mixed state compression problem

quantum data processing we prove a data processing inequality for quantum communication channels which states that processing a received quantum state may never increase the mutual information between input and output states