multiplicativity of completely bounded p norms implies a strong converse for entanglement assisted capacity the fully quantum reverse shannon theorem establishes the optimal rate of noiseless classical communication required for simulating the action of many instances of a noisy quantum channel on an arbitrary input state while also allowing for an arbitrary amount of shared entanglement of an arbitrary form turning this theorem around establishes a strong converse for the entanglement assisted classical capacity of any quantum channel this paper proves the strong converse for entanglement assisted capacity by a completely different approach and identifies a bound on the strong converse exponent for this task namely we exploit the recent entanglement assisted meta converse theorem of matthews and wehner several properties of the recently established sandwiched renyi relative entropy also referred to as the quantum renyi divergence and the multiplicativity of completely bounded p norms due to devetak et al the proof here demonstrates the extent to which the arimoto approach can be helpful in proving strong converse theorems it provides an operational relevance for the multiplicativity result of devetak et al and it adds to the growing body of evidence that the sandwiched renyi relative entropy is the correct quantum generalization of the classical concept for all 1

quantum discord for qubit qudit systems we present two formulae to calculate quantum discord a kind of quantum correlation between a qubit and a second party of arbitrary dimension d the first formula is the original entropic definition and the second is a recently proposed geometric distance measure which leads to an analytical formulation the tracing over the qubit in the entropic calculation is reduced to a very simple prescription and when the d dimensional system is a so calledx state the density matrix having non zero elements only along the diagonal and anti diagonal the entropic calculation can also be carried out analytically such states of the full bipartite qubit qudit system may be named extended x states whose density matrix is built of four block matrices each visually appearing as an x the optimization involved in the entropic calculation is generally over two parameters reducing to one for many cases and avoided altogether for an overwhelmingly large set of density matrices as our numerical investigations demonstrate in the case of n 2 extended x states encompass the entire 15 dimensional parameter space that is they represent the full qubit qubit system

remainder terms for some quantum entropy inequalities we consider three von neumann entropy inequalities subadditivity pinsker s inequality for relative entropy and the monotonicity of relative entropy for these we state conditions for equality and we prove some new error bounds away from equality including an improved version of pinsker s inequality

feasibility study of e transition prediction in navier stokes methods for airfoils when navier stokes methods are applied in the design process for laminar airfoils the prediction of the transition location still represents an unresolved problem by the acceptence of the e n method as representing a convenient transition prediction tool the requirements for coupling e n to navier stokes methods will be demonstrated in particular the possibility to determine the laminar and turbulent viscous length scales is outlined based on the knowledge of the viscous layer thickness a mesh adaption procedure can be applied the navier stokes results produced using adapted meshes are shown to be identical to boundary layer results when the computed wall pressure from the navier stokes solution is used as input for the boundary layer calculation for the validation of the necessary steps in the coupling procedure the laminar airfoil doal3 was selected this airfoil was measured in the transonic wind tunnel braunschweig facility at the dlr german aerospace research establishment the limiting n factor for that wind tunnel was determined beforehand

structure of states which satisfy strong subadditivity of quantum entropy with equality we give an explicit characterisation of the quantum states which saturate the strong subadditivity inequality for the von neumann entropy by combining a result of petz characterising the equality case for the monotonicity of relative entropy with a recent theorem by koashi and imoto we show that such states will have the form of a so called short quantum markov chain which in turn implies that two of the systems are independent conditioned on the third in a physically meaningful sense this characterisation simultaneously generalises known necessary and sufficient entropic conditions for quantum error correction as well as the conditions for the achievability of the holevo bound on accessible information

entanglement optimizing mixtures of two qubit states entanglement in incoherent mixtures of pure states of two qubits is considered via the concurrence measure a set of pure states is optimal if the concurrence for any mixture of them is the weighted sum of the concurrences of the generating states when two or three pure real states are mixed it is shown that 28 5 or 5 12 of the cases respectively are optimal conditions that are obeyed by the pure states generating such optimally entangled mixtures are derived for four or more pure states it is shown that there are no such sets of real states the implication of these on the superposition of two or more dimerized states is discussed a corollary of these results also show in how many cases rebit concurrence can be the same as that of qubit concurrence

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

a class of separable quantum states we present a sufficient condition for a bipartite state to be separable via the strong positive partial transposition structure introduced in chru ci ski et al 2008 phys rev a 77 022113 from which we obtain a class of separable states in particular we prove that any classical quantum state is a state of our class but not vice versa both finite and infinite dimensional systems are considered

correlation function and mutual information correlation function and mutual information are two powerful tools to characterize the correlations in a quantum state of a composite system widely used in many body physics and in quantum information science respectively we find that these two tools may give different conclusions about the order of the degrees of correlation in two specific two qubit states this result implies that the orderings of bipartite quantum states according to the degrees of correlation depend on which correlation measure we adopt

from log determinant inequalities to gaussian entanglement via recoverability theory many determinantal inequalities for positive definite block matrices are consequences of general entropy inequalities specialized to gaussian distributed vectors with prescribed covariances in particular strong subadditivity ssa yields ln det v ac ln det v bc ln det v abc ln det v c geq 0 for all 3 times 3 block matrices v abc where subscripts identify principal submatrices we shall refer to the above mentioned inequality as ssa of log det entropy in this paper we develop further insights on the properties of the above mentioned inequality and its applications to classical and quantum information theory in the first part of this paper we show how to find known and new necessary and sufficient conditions under which saturation with equality occurs subsequently we discuss the role of the classical transpose channel also known as petz recovery map in this problem and find its action explicitly we then prove some extensions of the saturation theorem by finding faithful lower bounds on a log det conditional mutual information in the second part we focus on quantum gaussian states whose covariance matrices are not only positive but obey additional constraints due to the uncertainty relation for gaussian states the log det entropy is equivalent to the renyi entropy of order 2 we provide a strengthening of log det ssa for quantum covariance matrices that involves the so called gaussian renyi 2 entanglement of formation a well behaved entanglement measure defined via a gaussian convex roof construction we then employ this result to define a log det entropy equivalent of the squashed entanglement measure which is remarkably shown to coincide with the gaussian renyi 2 entanglement of formation this allows us to establish useful properties of such measure s such as monogamy faithfulness and additivity on gaussian states

the geometric approach to quantum correlations computability versus reliability we propose a modified metric based on the hilbert schmidt norm and adopt it to define a rescaled version of the geometric measure of quantum discord such a measure is found not to suffer from pathological dependence on state purity although the employed metric is still non contractive under quantum operations we show that the resulting indicator of quantum correlations is in agreement with other bona fide discord measures in a number of physical examples we present a critical assessment of the requirements of reliability versus computability when approaching the task of quantifying or measuring general quantum correlations in a bipartite state

quantum game players can have advantage without discord the last two decades have witnessed a rapid development of quantum information processing a new paradigm which studies the power and limit of quantum advantages in various information processing tasks problems such as when quantum advantage exists and if existing how much it could be are at a central position of these studies in a broad class of scenarios there are implicitly or explicitly at least two parties involved who share a state and the correlation in this shared state is the key factor to the efficiency under concern in these scenarios the shared entanglement or discord is usually what accounts for quantum advantage in this paper we examine a fundamental problem of this nature from the perspective of game theory a branch of applied mathematics studying selfish behaviors of two or more players we exhibit a natural zero sum game in which the chance for any player to win the game depends only on the ending correlation we show that in a certain classical equilibrium a situation in which no player can further increase her payoff by any local classical operation whoever first uses a quantum computer has a big advantage over its classical opponent the equilibrium is fair to both players and as a shared correlation it does not contain any discord yet a quantum advantage still exists this indicates that at least in game theory the previous notion of discord as a measure of non classical correlation needs to be reexamined when there are two players with different objectives

on the quantum renyi relative entropies and related capacity formulas following csiszar s approach in classical information theory it is shown that the quantum relative entropies with parameter 0 1 can be represented as generalized cutoff rates and hence a direct operational interpretation of the quantum relative entropies are provided it is also shown that various generalizations of the holevo capacity defined in terms of the relative entropies coincide for the parameter range 0 2 and an upper bound on the one shot e capacity of a classical quantum channel in terms of these capacities is given

faithful squashed entanglement squashed entanglement is a measure for the entanglement of bipartite quantum states in this paper we present a lower bound for squashed entanglement in terms of a distance to the set of separable states this implies that squashed entanglement is faithful that is it is strictly positive if and only if the state is entangled we derive the lower bound on squashed entanglement from a lower bound on the quantum conditional mutual information which is used to define squashed entanglement the quantum conditional mutual information corresponds to the amount by which strong subadditivity of von neumann entropy fails to be saturated our result therefore sheds light on the structure of states that almost satisfy strong subadditivity with equality the proof is based on two recent results from quantum information theory the operational interpretation of the quantum mutual information as the optimal rate for state redistribution and the interpretation of the regularised relative entropy of entanglement as an error exponent in hypothesis testing the distance to the set of separable states is measured in terms of the locc norm an operationally motivated norm giving the optimal probability of distinguishing two bipartite quantum states each shared by two parties using any protocol formed by local quantum operations and classical communication locc between the parties a similar result for the frobenius or euclidean norm follows as an immediate consequence the result has two applications in complexity theory the first application is a quasipolynomial time algorithm solving the weak membership problem for the set of separable states in locc or euclidean norm the second application concerns quantum merlin arthur games here we show that multiple provers are not more powerful than a single prover when the verifier is restricted to locc operations thereby providing a new characterisation of the complexity class qma

characterizing nonclassical correlations via local quantum uncertainty quantum mechanics predicts that measurements of incompatible observables carry a minimum uncertainty which is independent of technical deficiencies of the measurement apparatus or incomplete knowledge of the state of the system nothing yet seems to prevent a single physical quantity such as one spin component from being measured with arbitrary precision here we show that an intrinsic quantum uncertainty on a single observable is ineludible in a number of physical situations when revealed on local observables of a bipartite system such uncertainty defines an entire class of bona fide measures of nonclassical correlations for the case of 2 ifmmode times else texttimes fi d systems we find that a unique measure is defined which we evaluate in closed form we then discuss the role that these correlations which are of the discord type can play in the context of quantum metrology we show in particular that the amount of discord present in a bipartite mixed probe state guarantees a minimum precision as quantified by the quantum fisher information in the optimal phase estimation protocol

renyi squashed entanglement discord and relative entropy differences the squashed entanglement quantifies the amount of entanglement in a bipartite quantum state and it satisfies all of the axioms desired for an entanglement measure the quantum discord is a measure of quantum correlations that are different from those due to entanglement what these two measures have in common is that they are both based upon the conditional quantum mutual information in berta et al 2015 j math phys 56 022205 we recently proposed renyi generalizations of the conditional quantum mutual information of a tripartite state on abc with c being the conditioning system which were shown to satisfy some properties that hold for the original quantity such as non negativity duality and monotonicity with respect to local operations on the system b with it being left open to show that the renyi quantity is monotone with respect to local operations on system a here we define a renyi squashed entanglement and a renyi quantum discord based on a renyi conditional quantum mutual information and investigate these quantities in detail taking as a conjecture that the renyi conditional quantum mutual information is monotone with respect to local operations on both systems a and b we prove that the renyi squashed entanglement and the renyi quantum discord satisfy many of the properties of the respective original von neumann entropy based quantities in our prior work berta et al 2015 phys rev a 91 022333 we also detailed a procedure to obtain renyi generalizations of any quantum information measure that is equal to a linear combination of von neumann entropies with coefficients chosen from the set 1 0 1 here we extend this procedure to include differences of relative entropies using the extended procedure and a conjectured monotonicity of the renyi generalizations in the renyi parameter we discuss potential remainder terms for well known inequalities such as monotonicity of the relative entropy joint convexity of the relative entropy and the holevo bound

conditional decoupling of quantum information insights from quantum information theory show that correlation measures based on quantum entropy are fundamental tools that reveal the entanglement structure of multipartite states in that spirit groisman popescu and winter phys rev a 72 032317 2005 showed that the quantum mutual information i a b quantifies the minimal rate of noise needed to erase the correlations in a bipartite state of quantum systems ab here we investigate correlations in tripartite systems abe in particular we are interested in the minimal rate of noise needed to apply to the systems ae in order to erase the correlations between a and b given the information in system e in such a way that there is only negligible disturbance on the marginal be we present two such models of conditional decoupling called deconstruction and conditional erasure cost of tripartite states abe our main result is that both are equal to the conditional quantum mutual information i a b e establishing it as an operational measure for tripartite quantum correlations

the role of coherence entropy of physical twin observables in entanglement the concept of physical twin observables pto for bipartite quantum states introduced and proved relevant for quantum information theory in recent work is substantially simplified the relation of observable and state is studied in detail from the point of view of coherence entropy properties of this quantity are further explored it is shown that besides for pure states also for a class of mixed states quantum discord measure of entanglement can be expressed through the coherence entropy of a pto complete in relation to the state

correlative capacity of composite quantum states we characterize the optimal correlative capacity of entangled separable and classically correlated states introducing the notions of the infimum and supremum within majorization theory we construct the least disordered separable state compatible with a set of marginals the maximum separable correlation information supportable by the marginals of a multiqubit pure state is shown to be a local operations and classical communication monotone the least disordered composite of a pair of qubits is found for the above classes with classically correlated states defined as diagonal in the product of marginal bases

new features of quantum discord uncovered by q entropies the notion of quantum discord introduced by ollivier and zurek phys rev lett 88 2001 017901 see also henderson and vedral j phys a 34 2001 6899 has attracted increasing attention in recent years as an entropic quantifier of non classical features pertaining to the correlations exhibited by bipartite quantum systems here we generalize the notion so as to encompass power law q entropies that reduce to the standard shannon entropy in the limit q 1 and study the concomitant consequences the ensuing new discord like measures we advance describe aspects of non classicality that are different from those associated with the standard quantum discord a particular manifestation of this difference concerns a feature related to order let d1 stand for the standard shannon based discord measure and dq for the q 1 one if two quantum states a b are such that d1 a d1 b this order relation does not remain invariant under a change from d1 to dq

varieties of iteration theories the equational properties of iteration when combined with composition and pairing are captured by the notion of iteration theory which was introduced in siam j comput 9 1980 pp 26 45 9 1980 pp 525 540 we believe although all of our evidence will not be exhibited here that every iterative construction satisfies at least the properties of iteration theories in this paper axiomatizations are given for several varieties of iteration theories which occur naturally in the semantics of programming languages i e those generated by theories of trees j comput sys sci 16 1978 pp 362 399 theories of sequacious functions proc 1973 colloquium vol 80 studies in logic north holland amsterdam 1975 pp 175 230 theories of partial functions and theories of both sequacious and partial functions with distinguished predicates we show which additional equations must be added to the axioms for iteration theories comput ling comput lang 14 1980 pp 183 207 in order to

quantum conditional mutual information and approximate markov chains a state on a tripartite quantum system a otimes b otimes c forms a markov chain if it can be reconstructed from its marginal on a otimes b by a quantum operation from b to b otimes c we show that the quantum conditional mutual information i a c b of an arbitrary state is an upper bound on its distance to the closest reconstructed state it thus quantifies how well the markov chain property is approximated

quantum channels with polytopic images and image additivity we study quantum channels with respect to their image i e the image of the set of density operators under the action of the channel we first characterize the set of quantum channels having polytopic images and show that additivity of the minimal output entropy can be violated in this class we then provide a complete characterization of quantum channels t that are universally image additive in the sense that for any quantum channel s the image of t otimes s is the convex hull of the tensor product of the images of t and s these channels turn out to form a strict subset of entanglement breaking channels with polytopic images and a strict superset of classical quantum channels

continuity of quantum conditional information we prove continuity of quantum conditional information s 12 2 with respect to the uniform convergence of states and obtain a bound which is independent of the dimension of the second party this can e g be used to prove the continuity of squashed entanglement

equational logic of circular data type specification abstract iteration theories introduced by bloom elgot and wright in 1980 formalize the equational properties of the strong behaviors of flowchart algorithms we show that the same equational properties are shared by the functors used to specify circular data types lehmann and smyth 1981 have shown how to specify circular data types such as stacks as fixed points of certain functors the called gw functors for example the set of stacks of elements in the set a is a solution to the equation in the variable x x f a x where f x x 1 a x is the functor on set taking the pair a x to the disjoint union of the singleton set 1 and the product a x such equations have initial solutions f a which in turn determine a solution functor f the equational properties of the operation f f are precisely captured by the axioms for iteration theories more precisely we show how the structure th c of all functors c n c p n p 0 on the category c forms an iteration theory and conversely any identity valid in all such structures is valid in the class of all iteration theories

monogamy of measurement induced nonlocality measurement induced nonlocality was introduced by luo and fu 2011 phys rev lett 106 120401 as a measure of nonlocality in a bipartite state in this paper we will discuss the monogamy property of measurement induced nonlocality for some three and four qubit classes of states unlike discord we find quite surprising results in this situation both the ghz and w states satisfy monogamy relations in the three qubit case however in general there are violations of monogamy relations in both the ghz class and w class states in the case of the four qubit system monogamy holds for most of the states in the generic class the four qubit ghz state does not satisfy the monogamy relation but the w state does we provide several numerical results including counterexamples regarding the monogamy nature of measurement induced nonlocality we will also extend our results of the generalized w class to n qubit systems

quantum discord a measure of the quantumness of correlations two classically identical expressions for the mutual information generally differ when the systems involved are quantum this difference defines the quantum discord it can be used as a measure of the quantumness of correlations separability of the density matrix describing a pair of systems does not guarantee vanishing of the discord thus showing that absence of entanglement does not imply classicality we relate this to the quantum superposition principle and consider the vanishing of discord as a criterion for the preferred effectively classical states of a system i e the pointer states

transition prediction for three dimensional boundary layers in computational fluid dynamics applications a method is presented for estimating the laminar turbulent transition location in three dimensional boundary layers for computational fluid dynamics cfd applications requiring numerous transition estimates with no user intervention given the reynolds number and the cp distribution the location of transition is estimated based on the attachment line state the potential for relaminarization the occurrence of laminar separation and the growth of instabilities transition caused by instability is estimated based on n factors calculated for tollmien schlichting waves and for stationary crossflow instabilities a neural network is used in place of solving the orr sommerfeld stability equation for determining the instability growth rates the current version of the method assumes incompressible flow the boundary layer flow and instabilities are calculated based on an infinite sweep strip boundary layer approximation the instability calculations also employ the parallel flow approximation

quantum discord discord between the whole and its constituent quantum discord a measure of quantum correlation beyond entanglement is initially defined as the discord between two classically equivalent while quantum discordant definitions of mutual information in this paper we report some new interpretations of discord which rely on the differences between measurement induced effects on the local measured system and the whole system specifically with proper quantitative definitions introduced in buscemi et al 2008 phys rev lett 100 210504 we find that quantum discord can be interpreted as the differences of measurement induced disturbance or information gain on the local measured system and on the whole system combined with previous similar results based on measurement induced entanglement and decoherence our results provide a unified view on quantum discord

geometry of two qubit states with negative conditional entropy we review the geometric features of negative conditional entropy and the properties of the conditional amplitude operator proposed by cerf and adami for two qubit states in comparison with entanglement and nonlocality of the states we identify the region of negative conditional entropy in the tetrahedron of locally maximally mixed two qubit states within this set of states negative conditional entropy implies nonlocality and entanglement but not vice versa and we show that the cerf adami conditional amplitude operator provides an entanglement witness equivalent to the peres horodecki criterion outside of the tetrahedron this equivalence is generally not true

multipartite generalization of quantum discord a generalization of quantum discord to multipartite systems is proposed a key feature of our formulation is its consistency with the conventional definition of discord in bipartite systems it is by construction zero only for systems with classically correlated subsystems and is a non negative quantity giving a measure of the total nonclassical correlations in the multipartite system with respect to a fixed measurement ordering for the tripartite case we show that the discord can be decomposed into contributions resulting from changes induced by nonclassical correlation breaking measurements in the conditional mutual information and tripartite mutual information the former gives a measure of the bipartite nonclassical correlations and is a non negative quantity while the latter is related to the monogamy of the nonclassical correlations

on quantum renyi entropies a new generalization and some properties the renyi entropies constitute a family of information measures that generalizes the well known shannon entropy inheriting many of its properties they appear in the form of unconditional and conditional entropies relative entropies or mutual information and have found many applications in information theory and beyond various generalizations of renyi entropies to the quantum setting have been proposed most prominently petz s quasi entropies and renner s conditional min max and collision entropy however these quantum extensions are incompatible and thus unsatisfactory we propose a new quantum generalization of the family of renyi entropies that contains the von neumann entropy min entropy collision entropy and the max entropy as special cases thus encompassing most quantum entropies in use today we show several natural properties for this definition including data processing inequalities a duality relation and an entropic uncertainty relation

multipartite quantum correlations and local recoverability characterizing genuine multipartite quantum correlations in quantum physical systems has historically been a challenging problem in quantum information theory more recently however the total correlation or multipartite information measure has been helpful in accomplishing this goal especially with the multipartite symmetric quantum msq discord piani et al 2008 phys rev lett 100 090502 doi 10 1103 physrevlett 100 090502 1 and the conditional entanglement of multipartite information cemi yang et al 2008 phys rev lett 101 140501 doi 10 1103 physrevlett 101 140501 2 here we apply a recent and significant improvement of strong subadditivity of quantum entropy fawzi renner 2014 in order to develop these quantities further in particular we prove that the msq discord is nearly equal to zero if and only if the multipartite state for which it is evaluated is approximately locally recoverable after performing measurements on each of its systems furthermore we prove that the cemi is a faithful entanglement measure i e it vanishes if and only if the multipartite state for which it is evaluated is a fully separable state along the way we provide an operational interpretation of the msq discord in terms of the partial state distribution protocol which in turn as a special case gives an interpretation for the original discord quantity finally we prove an inequality that could potentially improve upon the fawzi renner inequality in the multipartite context but it remains an open question to determine whether this is so 1 http dx doi org 10 1103 physrevlett 100 090502 2 http dx doi org 10 1103 physrevlett 101 140501

optimal quantum source coding with quantum side information at the encoder and decoder consider many instances of an arbitrary quadripartite pure state of four quantum systems abcd alice holds the ac part of each state bob holds b while r represents all other parties correlated with abc alice is required to redistribute the c systems to bob while asymptotically preserving the overall purity we prove that this is possible using q qubits of communication and e ebits of shared entanglement between alice and bob provided that q ges 1 2i c d b and q e ges h c b proving the optimality of the luo devetak outer bound the optimal qubit rate provides the first known operational interpretation of quantum conditional mutual information we also show how our protocol leads to a fully operational proof of strong subaddivity and uncover a general organizing principle in analogy to thermodynamics that underlies the optimal rates

squashed entanglement an additive entanglement measure in this paper we present a new entanglement monotone for bipartite quantum states its definition is inspired by the so called intrinsic information of classical cryptography and is given by the halved minimum quantum conditional mutual information over all tripartite state extensions we derive certain properties of the new measure which we call squashed entanglement it is a lower bound on entanglement of formation and an upper bound on distillable entanglement furthermore it is convex additive on tensor products and superadditive in general continuity in the state is the only property of our entanglement measure which we cannot provide a proof for we present some evidence however that our quantity has this property the strongest indication being a conjectured fannes type inequality for the conditional von neumann entropy this inequality is proved in the classical case

direct scheme for measuring the geometric quantum discord we propose a scheme to directly measure the exact value of the geometric quantum discord of an arbitrary two qubit state we need only to perform the projective measurement in all the anti symmetric subspace and our scheme is parametrically efficient in contrast to the widely adopted quantum state tomography scheme in the sense of less parameter estimations and projectors moreover the present scheme can be easily realized with the current experimental techniques

a fully quantum asymptotic equipartition property the classical asymptotic equipartition property is the statement that in the limit of a large number of identical repetitions of a random experiment the output sequence is virtually certain to come from the typical set each member of which is almost equally likely in this paper a fully quantum generalization of this property is shown where both the output of the experiment and side information are quantum an explicit bound on the convergence is given which is independent of the dimensionality of the side information this naturally leads to a family of reacutenyi like quantum conditional entropies for which the von neumann entropy emerges as a special case

iteration theories of synchronization trees synchronization trees are shown to form an iteration theory in a natural way the class of grove iteration theories is introduced the regular synchronization trees are shown to be the free theories in the subclass of synchronization theories moreover the bisimulation equivalence classes of regular synchronization trees are shown to be the free synchronization theories satisfying an infinite idempotency law

quantum markov chains sufficiency of quantum channels and renyi information measures a short quantum markov chain is a tripartite state such that system a can be recovered perfectly by acting on system c of the reduced state such states have conditional mutual information equal to zero and are the only states with this property a quantum channel is sufficient for two states and if there exists a recovery channel using which one can perfectly recover from and from the relative entropy difference is equal to zero if and only if is sufficient for and in this paper we show that these properties extend to renyi generalizations of these information measures which were proposed in berta et al 2015 j math phys 56 022205 seshadreesan et al 2015 j phys a math theor 48 395303 thus providing an alternate characterization of short quantum markov chains and sufficient quantum channels these results give further support to these quantities as being legitimate renyi generalizations of the conditional mutual information and the relative entropy difference along the way we solve some open questions of ruskai and zhang regarding the trace of particular matrices that arise in the study of monotonicity of relative entropy under quantum operations and strong subadditivity of the von neumann entropy

quantumness of bipartite states in terms of conditional entropies quantum discord as defined by olliver and zurek 2002 phys rev lett 88 017901 as the difference of two natural quantum extensions of the classical mutual information plays an interesting role in characterizing quantumness of correlations inspired by this idea we will study quantumness of bipartite states arising from different quantum analogs of the classical conditional entropy our approach is intrinsic in contrast to the olliver zurek method that involves extrinsic local measurements for this purpose we introduce two alternative variants of quantum conditional entropies via conditional density operators which in turn are intuitive quantum extensions of equivalent classical expressions for the conditional probability the significance of these quantum conditional entropies in characterizing quantumness of bipartite states is illustrated through several examples

on matrix inequalities between the power means counterexamples abstract we prove that the known sufficient conditions on the real parameters p q for which the matrix power mean inequality a p b p 2 1 p a q b q 2 1 q holds for every pair of matrices a b 0 are indeed best possible the proof proceeds by constructing 2 2 counterexamples the best possible conditions on p q for which a p 1 p a q 1 q holds for every unital positive linear map and a 0 are also clarified

min and max relative entropies and a new entanglement monotone two new relative entropy quantities called the min and max relative entropies are introduced and their properties are investigated the well known min and max entropies introduced by renner are obtained from these we define a new entanglement monotone which we refer to as the max relative entropy of entanglement and which is an upper bound to the relative entropy of entanglement we also generalize the min and max relative entropies to obtain smooth min and max relative entropies these act as parent quantities for the smooth renyi entropies eth zurich ph d dissertation 2005 and allow us to define the analogues of the mutual information in the smooth renyi entropy framework further the spectral divergence rates of the information spectrum approach are shown to be obtained from the smooth min and max relative entropies in the asymptotic limit

viscous inviscid analysis of transonic and low reynolds number airfoils a method of accurately calculating transonic and low reynolds number airfoil flows implemented in the viscous inviscid design analysis code ises is presented the euler equations are discretized on a conservative streamline grid and are strongly coupled to a two equation integral boundary layer formulation using the displacement thickness concept a transition prediction formulation of the e type is derived and incorporated into the viscous formulation the entire discrete equation set including the viscous and transition formulations is solved as a fully coupled nonlinear system by a global newton method this is a rapid and reliable method for dealing with strong viscous inviscid interactions which invariably occur in transonic and low reynolds number airfoil flows the results presented demonstrate the ability of the ises code to predict transitioning separation bubbles and their associated losses the rapid airfoil performance degradation with decreasing reynolds number is thus accurately predicted also presented is a transonic airfoil calculation involving shock induced separation showing the robustness of the global newton solution procedure good agreement with experiment is obtained further demonstrating the performance of the present integral boundary layer formulation

a lower bound of quantum conditional mutual information in this paper a lower bound of quantum conditional mutual information is obtained by employing the peierls bogoliubov inequality and the golden thompson inequality comparison with the bounds obtained by other researchers indicates that our result is independent of any measurements it may give some new insights into squashed entanglement and perturbations of markov chain states

strong converse for the classical capacity of entanglement breaking and hadamard channels via a sandwiched renyi relative entropy a strong converse theorem for the classical capacity of a quantum channel states that the probability of correctly decoding a classical message converges exponentially fast to zero in the limit of many channel uses if the rate of communication exceeds the classical capacity of the channel along with a corresponding achievability statement for rates below the capacity such a strong converse theorem enhances our understanding of the capacity as a very sharp dividing line between achievable and unachievable rates of communication here we show that such a strong converse theorem holds for the classical capacity of all entanglement breaking channels and all hadamard channels the complementary channels of the former these results follow by bounding the success probability in terms of a sandwiched renyi relative entropy by showing that this quantity is subadditive for all entanglement breaking and hadamard channels and by relating this quantity to the holevo capacity prior results regarding strong converse theorems for particular covariant channels emerge as a special case of our results

distillability and ppt entanglement of low rank quantum states the bipartite quantum states with rank strictly smaller than the maximum of the ranks of the reduced states a and b are distillable by local operations and classical communication horodecki p smolin j a terhal b m and thapliyal a v 2003 theor comput sci 292 589 96 1999 arxiv quant ph 9910122 our first main result is that this is also true for npt states with rank equal to this maximum a state is ppt if the partial transpose of its density matrix is positive semidefinite and otherwise it is npt this was conjectured first in 1999 in the special case when the ranks of a and b are equal see horodecki p smolin j a terhal b m and thapliyal a v 2003 theor comput sci 292 589 96 1999 arxiv quant ph 9910122 our second main result provides a complete solution of the separability problem for bipartite states of rank 4 namely we show that such a state is separable if and only if it is ppt and its range contains at least one product state we also prove that the so called checkerboard states are distillable if and only if they are npt

diagonal quantum discord quantum discord measures quantum correlation by comparing the quantum mutual information with the maximal amount of mutual information accessible to a quantum measurement this paper analyzes the properties of diagonal discord a simplified version of discord that compares quantum mutual information with the mutual information revealed by a measurement that correspond to the eigenstates of the local density matrices in contrast to the optimized discord diagonal discord is easily computable it also finds connections to thermodynamics and resource theory here we further show that for the generic case of non degenerate local density matrices diagonal discord exhibits desirable properties as a preferable discord measure we employ the theory of resource destroying maps liu z w et al 2017 phys rev lett 118 060502 to prove that diagonal discord is monotonically nonincreasing under the operation of local discord nongenerating qudit channels d 2 and provide numerical evidence that such monotonicity holds for qubit channels as well we also show that it is continuous and derive a fannes like continuity bound our results hold for a variety of simple discord measures generalized from diagonal discord