logarithmic corrections and finite size scaling in the two dimensional 4 state potts model we analyze the scaling and finite size scaling behavior of the two dimensional 4 state potts model we find new multiplicative logarithmic corrections for the susceptibility in addition to the already known ones for the specific heat we also find additive logarithmic corrections to scaling some of which are universal we have checked the theoretical predictions at criticality and off criticality by means of high precision monte carlo data

avoidance of many pursuers in the simple motion case on presente une condition suffisante d existence d une strategie d evasion dans un jeu a n poursuivants dans le plan en considerant le cas d un mouvement simple

avoidance of many pursuers in differential games governed by kth order differential equations abstract an evasion game with many pursuers governed by k th order differential equations on the plane is considered a sufficient condition for evasion along each trajectory of a certain set is established this result generalizes the main result of w rzymowski j differential equations 62 1986 334 356 and shows the connection between evasion in the simple motion case and that in the case when k 2 the method used here is analogous to that of w rzymowski above and w rzymowski dissertationes math rozprawy mat ccxlvii 1986 the paper summarizes the main results of p borowko and w rzymowski j math anal appl 111 1985 535 546 w rzymowski above and w rzymowski j math anal appl 120 1986 89 94

an analysis of completely positive trace preserving maps on m2 abstract we give a useful new characterization of the set of all completely positive trace preserving maps m 2 m 2 from which one can easily check any trace preserving map for complete positivity we also determine explicitly all extreme points of this set and give a useful parameterization after reduction to a certain canonical form this allows a detailed examination of an important class of non unital extreme points that can be characterized as having exactly two images on the bloch sphere we also discuss a number of related issues about the images and the geometry of the set of stochastic maps and show that any stochastic map on m 2 can be written as a convex combination of two generalized extreme points

entanglement breaking indices we study a set of new functionals called entanglement breaking indices which characterize how many local iterations of a given local quantum channel are needed in order to completely destroy the entanglement between the system of interest over which the transformation is defined and an external ancilla the possibility of contrasting the noisy effects introduced by the channel iterations via the action of intermediate filtering transformations is analyzed we provide some examples in which our functionals can be exactly calculated the differences between unitary and non unitary filtering operations are analyzed showing that at least for systems of dimension d larger than or equal to 3 the non unitary choice is preferable the gap between the performances of the two cases being divergent in some cases for d 2 qubit case on the contrary no evidences of the presence of such gap is revealed we conjecture that for this special case unitary filtering transformations are optimal the scenario in which more general filtering protocols are allowed is also discussed in some detail the case of a depolarizing noise acting on a two qubit system is exactly solved in a general case

avoidance of one pursuer abstract using the method of w rzymowski dissertationes math ccxlvii 1986 we give a sufficient condition for the existence of the evasion strategy in differential games with one pursuer

genuine multipartite entanglement criteria based on positive maps positive maps applied to a subsystem of a bipartite quantum state constitute a central tool in characterising entanglement in the multipartite case however the direct application of a positive but not completely positive map cannot distinguish if a state is genuinely multipartite entangled or just entangled across some bipartition we thus generalise this bipartite concept to the multipartite setting by introducing non positive maps that are positive on the subset of biseparable states but can map to a non positive element if applied to a genuine multipartite entangled state we explicitly construct examples of multipartite non positive maps obtained from positive maps via a lifting procedure that in this fashion can reveal genuine multipartite entanglement in a robust way

high precision renormalization group study of the roughening transition abstract we confirm the kosterlitz thouless scenario of the roughening transition for three different solid on solid models the discrete gaussian model the absolute value solid on solid model and the dual transform of the xy model with standard cosine action the method is based on a matching of the renormalization group flow of the candidate models with the flow of a bona fide kt model the exactly solvable bcsos model the monte carlo simulations are performed using efficient cluster algorithms we obtain high precision estimates for the critical couplings and other non universal quantities for the xy model with cosine action our critical coupling estimate is xyr 1 1197 5 for the roughening coupling of the discrete gaussian and the absolute value solid on solid model we find kdgr 0 6645 6 and kasosr 0 8061 3 respectively

optimal entanglement witnesses from generalized reduction and robertson maps we provide a generalization of the reduction and robertson positive maps in matrix algebras they give rise to a new class of optimal entanglement witnesses their structural physical approximation is analyzed as a byproduct we provide new examples of ppt positive partial transpose entangled states

optimal entanglement criterion for mixed quantum states we develop a strong and computationally simple entanglement criterion the criterion is based on an elementary positive map phi which operates on state spaces with even dimension n or 4 it is shown that phi detects many entangled states with a positive partial transposition ppt and that it leads to a class of optimal entanglement witnesses this implies that there are no other witnesses which can detect more entangled ppt states the map phi yields a systematic method for the explicit construction of high dimensional manifolds of bound entangled states

entanglement of positive definite functions on compact groups we define and study entanglement of continuous positive definite functions on products of compact groups we formulate and prove an infinite dimensional analog of the horodecki theorem giving a necessary and sufficient criterion for separability of such functions the resulting characterisation is given in terms of mappings of the space of continuous functions preserving positive definiteness a relation between the developed group theoretical formalism and the conventional one given in terms of density matrices is established through the non commutative fourier analysis it shows that the presented method plays the role of a generating function formalism for the theory of entanglement

a new criterion for indecomposability of positive maps we give a criterion for a positive mapping on the space of operators on a hilbert space to be indecomposable we show that this criterion can be applied to two families of positive maps these families of maps can then be used to form separability criteria for bipartite quantum states that can detect the entanglement of bound entangled quantum states

bipartite depolarizing maps we introduce a 3 parameter class of maps 1 acting on a bipartite system which are a natural generalisation of the depolarizing channel and include it as a special case then we find the exact regions of the parameter space that alternatively determine a positive completely positive entanglement breaking or entanglement annihilating map this model displays a much richer behaviour than the one shown by a simple depolarizing channel yet it stays exactly solvable as an example of this richness positive partial transposition but not entanglement breaking maps is found in theorem 2 a simple example of a positive yet indecomposable map is provided see the remark at the end of section iv the study of the entanglement annihilating property is fully addressed by theorem 7 finally we apply our results to solve the problem of the entanglement annihilation caused in a bipartite system by a tensor product of local depolarizing channels in this context a conjecture posed in the work of filippov j russ laser res 35 484 2014 is affirmatively answered and the gaps that the imperfect bounds of filippov and ziman phys rev a 88 032316 2013 left open are closed to arrive at this result we furthermore show how the hadamard product between quantum states can be implemented via local operations

additivity for unital qubit channels additivity of the holevo capacity is proved for product channels under the condition that one of the channels is a unital qubit channel with the other completely arbitrary as a byproduct this proves that the holevo bound is the classical information capacity of such qubit channels and provides an explicit formula for this classical capacity additivity of minimal entropy and multiplicativity of p norms are also proved under the same assumptions the proof relies on a new bound for the p norm of an output state from the half noisy phase damping channel

separability criteria and bounds for entanglement measures employing a recently proposed separability criterion we develop analytical lower bounds for the concurrence and for the entanglement of formation of bipartite quantum systems the separability criterion is based on a nondecomposable positive map which operates on state spaces with even dimension n 4 and leads to a class of nondecomposable optimal entanglement witnesses it is shown that the bounds derived here complement and improve the existing bounds obtained from the criterion of positive partial transposition and from the realignment criterion

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

a norm compression inequality for block partitioned positive semidefinite matrices abstract let a be a positive semidefinite matrix block partitioned as a b c c d where b and d are square blocks we prove the following inequalities for the schatten q norm q a q q 2 q 2 c q q b q q d q q 1 q 2 and a q q 2 q 2 c q q b q q d q q 2 q we show that these bounds obey a strong sharpness condition when the blocks are of size at least 2 2 and b q d q c q finally our bounds can be extended to symmetric partitionings into larger numbers of blocks for a aij a q q i a ii q q 2 q 2 i j a ij q q 1 q 2 while for 2 q the inequality is reversed

boundary correlation functions of the six vertex model we consider the six vertex model on an n n square lattice with the domain wall boundary conditions boundary one point correlation functions of the model are expressed as determinants of n n matrices generalizing the known result for the partition function in the free fermion case explicit answers are obtained the introduced correlation functions are closely related to the problem of enumeration of alternating sign matrices and domino tilings

generalized choi maps in three dimensional matrix algebra we consider a class of positive linear maps in the three dimensional matrix algebra which are generalizations of the positive linear map constructed by choi in the relation with positive semidefinite biquadratic forms we find conditions for which such maps are completely positive completely copositive decomposable and two positive

bounds on action of local quantum channels we derive an upper bound on the action of a direct product of two quantum maps channels acting on bi partite quantum states we assume that the individual channelsj affect single particle states so that for an arbitrary input j the distance dj j j j between the input j and the outputj j of the channel is less than given this assumption we show that for an arbitrary separable two partite state 12 the distance between the input 12 and the output 1 2 12 fulfils the bound d12 1 2 12 12 2 2 1 1 d 1 1 1 d2 where d1 and d2 are the dimensions of the first and second quantum system respectively in contrast entangled states are transformed in such a way that the bound on the action of the local channels is d12 1 2 12 12 2 2 1 d where d is the dimension of the smaller of the two quantum systems passing through the channels our results show that the fundamental distinction between the set of separable and the set of entangled states results in two different bounds which in turn can be exploited for discrimination between the two sets of states we generalize our results to multi partite channels

remarks on additivity of the holevo channel capacity and of the entanglement of formation the purpose of this article is to discuss the relation between the additivity questions regarding the quantities holevo capacityofaquantumchannelt and entanglementofformationofabipartitestate in particular using the stinespring dilation theorem we give a formula for the channel capacity involving entanglement of formation this can be used to show that additivity of the latter for some states can be inferred from the additivity of capacity for certain channels we demonstrate this connection for some families of channels allowing us to calculate the entanglement cost for many states including some where a strictly smaller upper bound on the distillable entanglement is known group symmetry is used for more sophisticated analysis giving formulas valid for a class of channels this is presented in a general framework extending recent findings of vidal dur and cirac we also discuss the property of superadditivity of the entanglement of formation which would imply both the general additivity of this function under tensor products and of the holevo capacity with or without linear cost constraints

extended reduction criterion and lattice states we study a particular class of states of a bipartite system consisting of two four level parties by means of an adapted extended reduction criterion we associate their entanglement properties to the geometric patterns of a planar lattice consisting of 16 points

cones of positive maps and their duality relations the structure of cones of positive and k positive maps acting on a finite dimensional hilbert space is investigated special emphasis is given to their duality relations to the sets of superpositive and k superpositive maps we characterize k positive and k superpositive maps with regard to their properties under taking compositions a number of results obtained for maps are also rephrased for the corresponding cones of block positive k block positive separable and k entangled operators due to the jamiolkowski choi isomorphism generalizations to a situation where no such simple isomorphism is available are also made employing the idea of mapping cones as a side result to our discussion we show that extreme entanglement witnesses which are optimal should be of special interest in entanglement studies

inequalities for quantum entropy a review with conditions for equality this article presents self contained proofs of the strong subadditivity inequality for von neumann s quantum entropy s and some related inequalities for the quantum relative entropy most notably its convexity and its monotonicity under stochastic maps moreover the approach presented here which is based on klein s inequality and lieb s theorem that the function a tr ek log a is concave allows one to obtain conditions for equality in the case of strong subadditivity which states that s 123 s 2 s 12 s 23 where the subscripts denote subsystems of a composite system equality holds if and only if log 123 log 12 log 2 log 23 using the fact that the holevo bound on the accessible information in a quantum ensemble can be obtained as a consequence of the monotonicity of relative entropy we show that equality can be attained for that bound only when the states in the ensemble commute the article concludes with an appendix giving a short description of epstein s elegant proof of lieb s the

a series of absolutely indecomposable positive maps in matrix algebras abstract we provide examples of positive maps in m n c n 4 which cannot be decomposed into a sum of a 2 positive map and a 2 copositive map

the structural physical approximation conjecture it was conjectured that the structural physical approximation spa of an optimal entanglement witness is separable or equivalently that the spa of an optimal positive map is entanglement breaking this conjecture was disproved first for indecomposable maps and more recently for decomposable maps the arguments in both cases are sketched along with important related results this review includes background material on topics including entanglement witnesses optimality duality of cones decomposability and the statement and motivation for the spa conjecture so that it should be accessible for a broad audience

concurrence of arbitrary dimensional bipartite quantum states we derive an analytical lower bound for the concurrence of a bipartite quantum state in arbitrary dimension a functional relation is established relating concurrence the peres horodecki criterion and the realignment criterion we demonstrate that our bound is exact for some mixed quantum states the significance of our method is illustrated by giving a quantitative evaluation of entanglement for many bound entangled states some of which fail to be identified by the usual concurrence estimation method

evasion along each trajectory in differential games with many pursuers a method of evasion for linear differential games was established by pontryagin in his work 6 he considered there an evasion game governed by a linear differential equation in r with a linear subspace m of r as a terminal set the game was assumed to end when the solution to the equation reached coincidence with the subspace m the evader s aim was to prevent the termination of the game the method of evasion applied in 6 was based on the projection of the trajectory onto suitably chosen two dimensional subspace l laying in the orthogonal complement of m in r and thereby reduced the evasion problem to the problem of avoidance of the origin in the subspace l it was assumed as usually in such a case that dim m iz 2 next this method has been extended by many authors to the nonlinear case see e g c4 7 31 when more than one pursuer takes part in the game some additional assumptions like dim m n 3 as it was made in 3 are necessary in order that pontryagin s method be applicable to such an evasion problem there are however examples of games with several pursuers that do not satisfy these extra assumptions but nevertheless can be solved directly see 2 10 11 91 in this paper we treat the problem of evasion for games with many pursuers governed by kth order differential equations on the plane using a method closely related to the one given in 9 this problem resembles the above mentioned general evasion problems in spirit and simultaneously allows us to incorporate many special examples we limit ourselves here to considering the case of games described by kth order differential equations instead of more general situations in which the operator v see 7 might be used as the expense of being able to assert the possibility of evasion along each trajectory in these games the assumption that the players move on the plane is not essential we have made it for convenience they could move in any space r with m 3 2 334 0022 0396 86 3 00

constructing positive maps from block matrices positive maps are useful for detecting entanglement in quantum information theory any entangled state can be detected by some positive map in this paper the relation between positive block matrices and completely positive trace preserving maps is characterized consequently a new method for constructing decomposable maps from positive block matrices is derived in addition a method for constructing positive but not completely positive maps from hermitian block matrices is also obtained

equation of motion for multiqubit entanglement in multiple independent noisy channels we investigate the possibility and conditions to factorize the entanglement evolution of a multiqubit system passing through multi sided noisy channels by means of a lower bound of concurrence lbc as an entanglement measure we derive an explicit formula of the lbc evolution of the n qubit generalized greenberger horne zeilinger gghz state under some typical noisy channels based on which two kinds of factorizing conditions for the lbc evolution are presented in this case the time dependent lbc can be determined by a product of initial lbc of the system and the lbc evolution of a maximally entangled gghz state under the same multi sided noisy channels we analyze the realistic situations where these two kinds of factorizing conditions can be satisfied in addition we also discuss the dependence of entanglement robustness on the number of qubits and that of the noisy channels

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

the square lattice f model revisited a loop cluster update scaling study the six vertex f model on the square lattice constitutes the unique example of an exactly solved model exhibiting an infinite order phase transition of the kosterlitz thouless type as one of the few non trivial exactly solved models it provides a welcome gauge for new numerical simulation methods and scaling techniques in view of the notorious problems of clearly resolving the kosterlitz thouless scenario in the two dimensional xy model numerically the f model in particular constitutes an instructive reference case for the simulational description of this type of phase transition we present a loop cluster update monte carlo study of the square lattice f model with a focus on the properties not exactly known such as the polarizability or the scaling dimension in the critical phase for the analysis of the simulation data finite size scaling is explicitly derived from the exact solution and plausible assumptions guided by the available exact results the careful inclusion of correction terms in the scaling formulae allows for a reliable determination of the asymptotic behaviour

generalising wigner s theorem we analyse linear maps of operator algebras mapping the set of rank k projectors onto the set of rank l projectors surjectively a complete characterisation of such maps for prime is provided a particular case corresponding to is well known as wigner s theorem hence our result may be considered as a generalisation of this celebrated wigner s result

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

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

inequalities for trace norms of 2 2 block matrices this paper derives an inequality relating the p norm of a positive 2 2 block matrix to the p norm of the 2 2 matrix obtained by replacing each block by its p norm the inequality had been known for integer values of p so the main contribution here is the extension to all values p 1 in a special case the result reproduces hanner s inequality a weaker inequality which applies also to non positive matrices is presented as an application in quantum information theory the inequality is used to obtain some results concerning maximal p norms of product channels

maximization of capacity and lp norms for some product channels it is conjectured that the holevo capacity of a product channel is achieved when product states are used as input amosov holevo and werner have also conjectured that the maximal lp norm of a product channel is achieved with product input states in this article we establish both of these conjectures in the case that is arbitrary and is a cq or qc channel as defined by holevo we also establish the amosov holevo and werner conjecture when is arbitrary and either is a qubit channel and p 2 or is a unital qubit channel and p is integer our proofs involve a new conjecture for the norm of an output state of the half noisy channel i when is a qubit channel we show that this conjecture in some cases also implies additivity of the holevo capacity

bulk and surface properties in the critical phase of the two dimensional xy model monte carlo simulations of the two dimensional xy model are performed in a square geometry with various boundary conditions bc using conformal mappings we deduce the exponent t of the order parameter correlation function and its surface analogue t as a function of the temperature in the critical low temperature phase of the model the temperature dependence of both exponents is obtained numerically with a good accuracy up to the kosterlitz thouless transition temperature the bulk exponent follows from simulations of correlation functions with periodic boundary conditions or order parameter profiles with open boundary conditions and with symmetry breaking surface fields at very low temperatures t is found in pretty good agreement with the linear temperature dependence of berezinskii s spin wave approximation we also show some evidence that there are no noticeable logarithmic corrections to the behaviour of the order parameter density profile at the kosterlitz thouless kt transition temperature while these corrections exist for the correlation function at the kt transition the value tkt 1 4 is accurately recovered the exponent associated with the surface correlations is similarly obtained after a slight modification of the boundary conditions the correlation function is computed with free bc and the profile with mixed fixed free bc it exhibits a monotonic behaviour with temperature starting linearly according to the spin wave approximation and increasing up to a value tkt 1 2 at the kosterlitz thouless transition temperature the thermal exponent e t is also computed and we give some evidence that it keeps a constant value in agreement with the marginality condition of the temperature field below the kt transition

characterizing entanglement via uncertainty relations we derive a family of necessary separability criteria for finite dimensional systems based on inequalities for variances of observables we show that every pure bipartite entangled state violates some of these inequalities furthermore a family of bound entangled states and true multipartite entangled states can be detected the inequalities also allow us to distinguish between different classes of true tripartite entanglement for qubits we formulate an equivalent criterion in terms of covariance matrices this allows us to apply criteria known from the regime of continuous variables to finite dimensional systems

tensor powers of 2 positive maps by studying tensor powers n of a positive map of b k into b h for finite dimensional hilbert spaces k and h we give conditions for a map such that n 2 positive for all n to be nondistillable and completely positive

on a characterization of positive maps drawing on results of choi stormer and woronowicz we present a nearly complete characterization of certain important classes of positive maps in particular we construct a general class of positive linear maps acting between two matrix algebras b h and b k where h and k are finite dimensional hilbert spaces it turns out that elements of this class are characterized by operators from the dual cone of the set of all separable states on b h k subsequently the relation between entanglements and positive maps is described finally a new characterization of the cone b h b k is given

decomposability of linear maps under tensor powers both completely positive and completely copositive maps stay decomposable under tensor powers i e under tensoring the linear map with itself but are there other examples of maps with this property we show that this is not the case any decomposable map that is neither completely positive nor completely copositive will lose decomposability eventually after taking enough tensor powers moreover we establish explicit bounds to quantify when this happens to prove these results we use a symmetrization technique from the theory of entanglement distillation and analyze when certain symmetric maps become non decomposable after taking tensor powers finally we apply our results to construct new examples of non decomposable positive maps and establish a connection to the positive partial transpose squared conjecture

generation of mapping cones from small sets we answer in the affirmative a recently posed question that asked if there exists an untypical convex mapping cone i e one that does not arise from the transpose map and the cones of k positive and k superpositive maps we explicitly construct such a cone based on atomic positive maps our general technique is to consider the smallest convex mapping cone generated by a single map and we derive several results on such mapping cones we use this technique to also present several other examples of untypical mapping cones including a family of cones generated by spin factors we also provide a full characterization of mapping cones generated by single elements in the qubit case in terms of their typicality

a class of atomic positive linear maps in matrix algebras we find a large class of atomic positive linear maps between n dimensional matrix algebras and study their properties in connection with complete positivity 2 positivity and schwarz inequality

differential games of evasion with many pursuers abstract we extend the method of w rzymowski method of construction of the evasion strategy for differential games with many pursuers dissertationes math ccxlvii 1986 to the general case i e to games governed by an equation of the form z f t z u v where the terminal set is a finite union of linear subspaces of the state space we prove a theorem providing a new sufficient condition for avoidance of many pursuers that is more general than previous ones to apply this method to such a general case we introduce a new strategy for the evader however use of similar strategies from rzymowski is also possible after obtaining this result we find a similar condition concerning games governed by many differential equations last we consider games described by kth order differential inclusions for such games with many pursuers we give a new sufficient condition for evasion along each trajectory of a certain set

counterexample to an additivity conjecture for output purity of quantum channels a conjecture arising naturally in the investigation of additivity of classical information capacity of quantum channels states that the maximal purity of outputs from a quantum channel as measured by the p norm should be multiplicative with respect to the tensor product of channels we disprove this conjecture for p 4 79 the same example with p also disproves a conjecture for the multiplicativity of the injective norm of hilbert space tensor products

a note on the optimality of decomposable entanglement witnesses and completely entangled subspaces entanglement witnesses ews constitute one of the most important entanglement detectors in quantum systems nevertheless their complete characterization in particular with respect to the notion of optimality is still missing even in the decomposable case here we show that for any qubit qunit decomposable ew dew w the three statements are equivalent i the set of product vectors obeying e f w e f 0 spans the corresponding hilbert space ii w is optimal and iii w q with q denoting a positive operator supported on a completely entangled subspace ces and standing for the partial transposition while implications i ii and ii iii are known here we prove that iii implies i this is a consequence of a more general fact saying that product vectors orthogonal to any ces in span after partial conjugation the whole space on the other hand already in the case of the hilbert space there exist dews for which iii does not imply i consequently either i does not imply ii or ii does not imply iii and the above transparent characterization obeyed by qubit qunit dews does not hold in general

on structural physical approximations and entanglement breaking maps very recently a conjecture saying that the so called structural physical approximations spas to optimal positive maps optimal entanglement witnesses give entanglement breaking eb maps separable states has been posed korbicz et al 2008 phys rev a 78 062105 the main purpose of this contribution is to explore this subject first we extend the set of entanglement witnesses supporting the conjecture then we ask whether spas constructed from other than the depolarizing channel maps also lead to eb maps and show that in general this is not the case on the other hand we prove an interesting fact that for any positive map there exists an eb channel such that the spa of constructed with the aid of is again an eb channel finally we ask similar questions in the case of continuous variable systems we provide a simple way of constructing spa and prove that in the case of the transposition map it gives the eb channel

distinguishing separable and entangled states we show how to design families of operational criteria that distinguish entangled from separable quantum states the simplest of these tests corresponds to the well known peres horodecki positive partial transpose ppt criterion and the more complicated tests are strictly stronger the new criteria are tractable due to powerful computational and theoretical methods for the class of convex optimization problems known as semidefinite programs we successfully applied the results to many low dimensional states from the literature where the ppt test fails as a by product of the criteria we provide an explicit construction of the corresponding entanglement witnesses

on positive linear maps between matrix algebras abstract there is a concrete example of a positive linear map from m 2 to m 4 which is not decomposable modification of this map gives an explicit counterexample to a conjecture of woronowicz on the strong kadison inequality

directed loop monte carlo simulations of vertex models we show how the directed loop monte carlo algorithm can be applied to study vertex models the algorithm is employed to calculate the arrow polarization in the six vertex model with the domain wall boundary conditions the model exhibits spatially separated ordered and disordered regions we show how the boundary between these regions depends on parameters of the model we give some predictions on the behavior of the polarization in the thermodynamic limit and discuss the relation to the arctic circle theorem

counterexamples to the maximal p norm multiplicativity conjecture for all p 1 for all p 1 we demonstrate the existence of quantum channels with non multiplicative maximal output p norms equivalently for all p 1 the minimum output renyi entropy of order p of a quantum channel is not additive the violations found are large in all cases the minimum output renyi entropy of order p for a product channel need not be significantly greater than the minimum output entropy of its individual factors since p 1 corresponds to the von neumann entropy these counterexamples demonstrate that if the additivity conjecture of quantum information theory is true it cannot be proved as a consequence of any channel independent guarantee of maximal p norm multiplicativity we also show that a class of channels previously studied in the context of approximate encryption lead to counterexamples for all p 2

state space structure and entanglement of rotationally invariant spin systems we investigate the structure of so 3 invariant quantum systems which are composed of two particles with spins j1 and j2 the states of the composite spin system are represented by means of two complete sets of rotationally invariant operators namely by the projections pj onto the eigenspaces of the total angular momentum j and by certain invariant operators qk which are built out of spherical tensor operators of rank k it is shown that these representations are connected by an orthogonal matrix whose elements are expressible in terms of wigner s 6 j symbols the operation of the partial time reversal of the combined spin system is demonstrated to be diagonal in the qk representation these results are employed to obtain a complete characterization of spin systems with j1 1 and arbitrary j2 1 we prove that the peres horodecki criterion of positive partial transposition ppt is necessary and sufficient for separability if j2 is an integer while for half integer spins j2 there always exist entangled ppt states bound entanglement we construct an optimal entanglement witness for the case of half integer spins and design a protocol for the detection of entangled ppt states through measurements of the total angular momentum

capacity of quantum channels using product measurements the capacity of a quantum channel for transmission of classical information depends in principle on whether product states or entangled states are used at the input and whether product or entangled measurements are used at the output we show that when product measurements are used the capacity of the channel is achieved with product input states so that entangled inputs do not increase capacity we show that this result continues to hold if sequential measurements are allowed whereby the choice of successive measurements may depend on the results of previous measurements we also present a new simplified expression which gives an upper bound for the shannon capacity of a channel and which bears a striking resemblance to the well known holevo bound

magnetic fluctuations in the classical xy model the origin of an exponential tail in a complex system we study the probability density function for the fluctuations of the magnetic order parameter in the low temperature phase of the mathrm xy model of finite size in two dimensions this system is critical over the whole of the low temperature phase it is shown analytically and without recourse to the scaling hypothesis that in this case the distribution is non gaussian and of universal form independent of both system size and critical exponent ensuremath eta an exact expression for the generating function of the distribution is obtained which is transformed and compared with numerical data from high resolution molecular dynamics and monte carlo simulations the asymptotes of the distribution are calculated and found to be of exponential and double exponential form the calculated distribution is fitted to three standard functions a generalization of gumbel s first asymptote distribution from the theory of extremal statistics a generalized log normal distribution and a ensuremath chi 2 distribution the calculation is extended to general dimension and an exponential tail is found in all dimensions less than 4 despite the fact that critical fluctuations are limited to d 2 these results are discussed in the light of similar behavior observed in models of interface growth and for dissipative systems driven into a nonequilibrium steady state

multiplicativity properties of entrywise positive maps abstract multiplicativity of certain maximal p q norms of a tensor product of linear maps on matrix algebras is proved in situations in which the condition of complete positivity cp is either augmented by or replaced by the requirement that the entries of a matrix representative of the map are non negative ep in particular for integer t multiplicativity holds for the maximal 2 2t norm of a product of two maps whenever one of the pair is ep for the maximal 1 t norm for pairs of cp maps when one of them is also ep and for the maximal 1 2t norm for the product of an ep and a 2 positive map similar results are shown in the infinite dimensional setting of convolution operators on l 2 r with the pointwise positivity of an integral kernel replacing entrywise positivity of a matrix these results apply in particular to gaussian bosonic channels

separable states are more disordered globally than locally a remarkable feature of quantum entanglement is that an entangled state of two parties alice a and bob b may be more disordered locally than globally that is s a s a b where s is the von neumann entropy it is known that satisfaction of this inequality implies that a state is nonseparable in this paper we prove the stronger result that for separable states the vector of eigenvalues of the density matrix of system ab is majorized by the vector of eigenvalues of the density matrix of system a alone this gives a strong sense in which a separable state is more disordered globally than locally and a new necessary condition for separability of bipartite states in arbitrary dimensions

quantum states with a positive partial transpose are useful for metrology we show that multipartite quantum states that have a positive partial transpose with respect to all bipartitions of the particles can outperform separable states in linear interferometers we introduce a powerful iterative method to find such states we present some examples for multipartite states and examine the scaling of the precision with the particle number some bipartite examples are also shown that possess an entanglement very robust to noise we also discuss the relation of metrological usefulness to bell inequality violation we find that quantum states that do not violate any bell inequality can outperform separable states metrologically we present such states with a positive partial transpose as well as with a nonpositive partial transpose

a family of indecomposable positive linear maps based on entangled quantum states abstract we introduce a new family of indecomposable positive linear maps based on entangled quantum states central to our construction is the notion of an unextendible product basis the construction lets us create indecomposable positive linear maps in matrix algebras of arbitrary high dimension

indecomposable positive maps in low dimensional matrix algebras abstract we classify a series of positive maps in low dimensional matrix algebras with respect to the degree of indecomposability and provide stronger indecomposable maps in m n we also present a basic result about the atomic property

on bipartite operators defined by sets of completely different permutations we introduce a class of bipartite operators acting on h h h being an n dimensional hilbert space defined by a set of n completely different permutations cdps bipartite operators are of particular importance in quantum information theory to represent states and observables of composite quantum systems it turns out that any set of cdps gives rise to a certain direct sum decomposition of the total hilbert space which enables one simple construction of the corresponding bipartite operator interestingly if set of cdps defines an abelian group then the corresponding bipartite operator displays an additional property the partially transposed operator again corresponds to in general different set of cdps therefore our technique may be used to construct new classes of the so called ppt positive under partial transposition states which are of great importance for quantum information using well known relation between bipartite operators and linear maps one can use also construct linear maps related to cdps we introduce a class of bipartite operators acting on h h h being an n dimensional hilbert space defined by a set of n completely different permutations cdps bipartite operators are of particular importance in quantum information theory to represent states and observables of composite quantum systems it turns out that any set of cdps gives rise to a certain direct sum decomposition of the total hilbert space which enables one simple construction of the corresponding bipartite operator interestingly if set of cdps defines an abelian group then the corresponding bipartite operator displays an additional property the partially transposed operator again corresponds to in general different set of cdps therefore our technique may be used to construct new classes of the so called ppt positive under partial transposition states which are of great importance for quantum information using well known relation between bipartite operators and linear maps one can use also construct linear maps relate

conditions for multiplicativity of maximal lp norms of channels for fixed integer p we introduce a condition for memoryless quantum channels which when satisfied guarantees the multiplicativity of the maximal lp norm with p a fixed integer by applying the condition to qubit channels it can be shown that it is not a necessary condition although some known results for qubits can be recovered when applied to the werner holevo channel which is known to violate multiplicativity when p is large relative to the dimension d the condition suggests that multiplicativity holds when d 2p 1 this conjecture is proved explicitly for p 2 3 4 finally a new class of channels is considered which generalizes the depolarizing channel to maps which are combinations of the identity channel and a noisy one whose image is an arbitrary density matrix it is shown that these channels are multiplicative for p 2

additivity of the classical capacity of entanglement breaking quantum channels we show that for the tensor product of an entanglement breaking quantum channel with an arbitrary quantum channel both the minimum entropy of an output of the channel and the holevo schumacher westmoreland capacity are additive in addition for the tensor product of two arbitrary quantum channels we give a bound involving entanglement of formation for the amount of subadditivity for minimum entropy output or superadditivity for classical capacity that can occur

a class of positive atomic maps we construct a new class of positive indecomposable maps in the algebra of d d complex matrices these maps are characterized by the weakest positivity property and for this reason they are called atomic this class provides a new rich family of atomic entanglement witnesses which define an important tool for investigating quantum entanglement it turns out that they are able to detect states with the weakest quantum entanglement

positivity of linear maps under tensor powers we investigate linear maps between matrix algebras that remain positive under tensor powers i e under tensoring with n copies of themselves completely positive and completely co positive maps are trivial examples of this kind we show that for every n there exist non trivial maps with this property and that for two dimensional hilbert spaces there is no non trivial map for which this holds for all n for higher dimensions we reduce the existence question of such non trivial tensor stable positive maps to a one parameter family of maps and show that an affirmative answer would imply the existence of non positive partial transpose bound entanglement as an application we show that any tensor stable positive map that is not completely positive yields an upper bound on the quantum channel capacity which for the transposition map gives the well known cb norm bound we furthermore show that the latter is an upper bound even for the local operations and classical communications assisted quantum capacity and that moreover it is a strong converse rate for this task

avoidance of many pursuers in differential games described by differential inclusions abstract an evasion game with many pursuers described by differential inclusions on the plane is considered a sufficient condition for the existence of an evasion strategy is established the paper generalizes the result of p borowko and w rzymoski j math anal appl 111 1985 535 546 and partially that of v l zak a piecewise program strategy of evasion from many pursuers preprint institut problem mekhaniki an sssr moscow 1982

new multiplicativity results for qubit maps let be a trace preserving positivity preserving but not necessarily completely positive linear map on the algebra of complex 2 2 matrices and let be any finite dimensional completely positive map for p 2 and p 4 we prove that the maximal p norm of the product map is the product of the maximal p norms of and restricting to the class of completely positive maps this settles the multiplicativity question for all qubit channels in the range of values p 4