parasupercoherent states and color supergroups parabosonic coherent states are illustrated from the displacement operator point of view such a construction requires the use of the green cusson ansatze a specific representation of parastatistics leading to color supergroups a comparison with a previous result is shown through the annihilation operator and the minimum uncertainty contexts the extension to the parasupersymmetric case is also considered

unconditional security from noisy quantum storage we consider the implementation of two party cryptographic primitives based on the sole assumption that no large scale reliable quantum storage is available to the cheating party we construct novel protocols for oblivious transfer and bit commitment and prove that realistic noise levels provide security even against the most general attack such unconditional results were previously only known in the so called bounded storage model which is a special case of our setting our protocols can be implemented with present day hardware used for quantum key distribution in particular no quantum storage is required for the honest parties

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

comments on hastings additivity counterexamples hastings 12 recently provided a proof of the existence of channels which violate the additivity conjecture for minimal output entropy in this paper we present an expanded version of hastings proof in addition to a careful elucidation of the details of the proof we also present bounds for the minimal dimensions needed to obtain a counterexample

robust stability and control of uncertain linear discrete time periodic systems with time delay this paper deals with the problems of robust stability analysis and robust control of linear discrete time periodic systems with a delayed state and subject to polytopic type parameter uncertainty in the state space matrices a robust stability criterion independent of the time delay length as well as a delay dependent criterion is proposed where the former applies to the case of a constant time delay and the latter allows for a time varying delay lying in a given interval the developed robust stability criteria are based on affinely uncertainty dependent lyapunov krasovskii functionals and are given in terms of linear matrix inequalities these stability conditions are then applied to solve the problems of robust stabilization and robust h control via static periodic state feedback numerical examples illustrate the potentials of the proposed robust stability and control methods

on weyl channels being covariant with respect to the maximum commutative group of unitaries we investigate the weyl channels being covariant with respect to the maximum commutative group of unitary operators this class includes the quantum depolarizing channel and the two pauli channel as well then we show that our estimation of the output entropy for a tensor product of the phase damping channel and the identity channel based upon the decreasing property of the relative entropy allows to prove the additivity conjecture for the minimal output entropy for the quantum depolarizing channel in any prime dimension and for the two pauli channel in the qubit case

control of linear discrete time periodic systems a decentralized control approach a decentralized control technique is applied to the problem of periodic output feedback stabilization or pole assignment for a periodically time varying discrete time system it is shown that the problem can be reduced to that of stabilizing or pole assigning a general proper multichannel system by static output feedback on the basis of the equivalence between periodic systems and a class of linear time invariant systems the notion of periodic fixed mode is introduced for a periodic system similar to the notion of uncontrollable or unobservable modes in terms of this notion both necessary conditions and sufficient conditions for the solvability of the problem are obtained

continuity of quantum channel capacities we prove that a broad array of capacities of a quantum channel are continuous that is two channels that are close with respect to the diamond norm have correspondingly similar communication capabilities we first show that the classical capacity quantum capacity and private classical capacity are continuous with the variation on arguments varepsilon apart bounded by a simple function of varepsilon and the channel s output dimension our main tool is an upper bound of the variation of output entropies of many copies of two nearby channels given the same initial state the bound is linear in the number of copies our second proof is concerned with the quantum capacities in the presence of free backward or two way public classical communication these capacities are proved continuous on the interior of the set of non zero capacity channels by considering mutual simulation between similar channels

capacities of quantum channels and how to find them we survey what is known about the information transmitting capacities of quantum channels and give a proposal for how to calculate some of these capacities using linear programming

a note on quantum entropy inequalities and channel capacities quantum entropy inequalities are studied some quantum entropy inequalities are obtained by several methods for an entanglement breaking channel we show that the entanglement assisted classical capacity is upper bounded by log d a relationship between entanglement assisted and one shot unassisted capacities is obtained this relationship shows the entanglement assisted channel capacity is upper bounded by the sum of log d and the one shot unassisted classical capacity

on a general framework for q particles paraparticles and q paraparticles through deformations the authors propose a unification of deformations associated with the descriptions of q para and q para bosons and fermions for complex values of q

additive bounds of minimum output entropies for unital channels and an exact qubit formula we find an upper bound for the minimum output entropy of a unital quantum channel and obtain an exact formula for general qubit channels our techniques incorporate the renyi entropies particularly with renyi parameter alpha 2 moreover since our upper bound is additive under tensor product we get as a corollary an upper bound for the classical capacity of unital quantum channels interestingly our upper bound for the classical capacity depends only on the operator norm of matrix representations of channels on the space of traceless hermitian operators and is tight in the sense that it gives the precise quantity of classical capacity of the werner holevo channel as an example we study quantum channels with operator sum representation that is made of the discrete weyl operators generalized pauli operators and explain how our formula works in this case finally we find new examples for which the minimum output renyi 2 entropy is additive

gradient based approach to solve optimal periodic output feedback control problems we discuss the numerical solution of the output feedback optimal periodic control problem by using a gradient search based optimization approach extension of this approach to the simultaneous stabilization of periodic multimodels is also considered for the evaluation of the function and its gradient explicit expressions are derived which involve the numerical solution of a pair of discrete time periodic lyapunov equations numerically reliable algorithms based on the periodic schur decomposition are used for the efficient solution of these equations a satellite positioning example illustrates the effectiveness of the presented approach to solve a practical periodic control problem

additivity and distinguishability of random unitary channels a random unitary channel is one that is given by a convex combination of unitary channels it is shown that the conjectures on the additivity of the minimum output entropy and the multiplicativity of the maximum output p norm can be equivalently restated in terms of random unitary channels this is done by constructing a random unitary approximation to a general quantum channel this approximation can be constructed efficiently and so it is also applied to the computational problem of distinguishing quantum circuits it is shown that the problem of distinguishing random unitary circuits is as hard as the problem of distinguishing general mixed state circuits which is complete for the class of problems having quantum interactive proof systems

an lp newton method nonsmooth equations kkt systems and nonisolated solutions we define a new newton type method for the solution of constrained systems of equations and analyze in detail its properties under suitable conditions that do not include differentiability or local uniqueness of solutions the method converges locally quadratically to a solution of the system thus filling an important gap in the existing theory the new algorithm improves on known methods and when particularized to kkt systems derived from optimality conditions for constrained optimization or variational inequalities it has theoretical advantages even over methods specifically designed to solve such systems

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

double smoothing technique for large scale linearly constrained convex optimization in this paper we propose an efficient approach for solving a class of large scale convex optimization problems the problem we consider is the minimization of a convex function over a simple possibly infinite dimensional convex set under the additional constraint mathcal a u in t where mathcal a is a linear operator and t is a convex set whose dimension is small compared to the dimension of the feasible region in our approach we dualize the linear constraints solve the resulting dual problem with a purely dual gradient type method and show how to reconstruct an approximate primal solution because the linear constraints have been dualized the dual objective function typically becomes separable and therefore easy to compute in order to accelerate our scheme we introduce a novel double smoothing technique that involves regularization of the dual problem to allow the use of a fast gradient method as a result we obtain a method with complexity o 1 over epsilon ln 1 over epsilo

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

the capacity of the quantum depolarizing channel the information carrying capacity of the d dimensional depolarizing channel is computed it is shown that this capacity can be achieved by encoding messages as products of pure states belonging to an orthonormal basis of the state space and using measurements which are products of projections onto this same orthonormal basis in other words neither entangled signal states nor entangled measurements give any advantage for information capacity the result follows from an additivity theorem for the product channel spl delta spl ominus spl psi where spl delta is the depolarizing channel and spl psi is a completely arbitrary channel we establish the amosov holevo werner see probl inform transm vol 36 p 305 313 2000 p norm conjecture for this product channel for all p spl ges 1 and deduce from this the additivity of the minimal entropy and of the holevo quantity spl chi sup

on colour superalgebras in parasupersymmetric quantum mechanics the simplest lie parasuperalgebra psqm 2 is identified as an example with a c 2 s colour superalgebra through simple connections between trilinear and bilinear structure relations but by using green cusson ansatze developed in parastatistics some general properties and conclusions are then obtained and illustrated

hypercontractivity for semigroups of unital qubit channels hypercontractivity is proved for products of qubit channels that belong to self adjoint semigroups the hypercontractive bound gives necessary and sufficient conditions for a product of the form e t 1 h 1 otimes cdots otimes e t n h n to be a contraction from l p to l q where l p is the algebra of 2 n dimensional matrices equipped with the normalized schatten norm and each generator h j is a self adjoint positive semidefinite operator on the algebra of 2 dimensional matrices as a particular case the result establishes the hypercontractive bound for a product of qubit depolarizing channels

disturbance localization for left invertible linear periodic discrete time systems the disturbance localization problem for left invertible linear periodic discrete time systems is solved using periodic state feedback controllers the proposed technique is of algebraic nature and has the following two main characteristics i it yields simple algebraic criteria for testing the solvability of the problem as compared to known geometric criteria which may not be so easy to check ii it derives analytically the general expressions of all periodic controllers admissible for disturbance localization as compared to known techniques which lead to nonanalytic parametrizations of the admissible controllers via constructive procedures moreover for the aforementioned class of periodic systems the state feedback simultaneous disturbance localization and stabilization or pole placement problem is treated and conditions for its solvability are established on the basis of a decentralized control approach that makes use of the equivalence between the above problem and the stabilization or pole placement problem of a general proper multichannel system by decentralized static output feedback

a strong converse for classical channel coding using entangled inputs a fully general strong converse for channel coding states that when the rate of sending classical information exceeds the capacity of a quantum channel the probability of correctly decoding goes to zero exponentially in the number of channel uses even when we allow code states which are entangled across several uses of the channel such a statement was previously only known for classical channels and the quantum identity channel by relating the problem to the additivity of minimum output entropies we show that a strong converse holds for a large class of channels including all unital qubit channels the d dimensional depolarizing channel and the werner holevo channel this further justifies the interpretation of the classical capacity as a sharp threshold for information transmission

pole assignment for linear time invariant systems by periodic memoryless output feedback it is well known that the poles of a linear time invariant controllable and observable system can be assigned arbitrarily by state feedback when only the output is available pole assignment is still possible by means of dynamic output feedback in this paper the potential of time varying memoryless output feedback is considered it is shown that up to some technical conditions it is indeed possible to allocate the poles of a linear time invariant discrete time system by memoryless output feedback with periodic gains the period of the gains is n 1 with n the order of the system the power of the design technique is proved to be comparable to what can be achieved by the classical dynamic feedback approach

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

efficient approximation of quantum channel capacities we propose an iterative method for approximating the capacity of classical quantum channels with a discrete input alphabet and a finite dimensional output under additional constraints on the input distribution based on duality of convex programming we derive explicit upper and lower bounds for the capacity to provide an additive varepsilon close estimate to the capacity the presented algorithm requires o n vee m m 3 log n 1 2 varepsilon 1 steps where n denotes the input alphabet size and m denotes the output dimension we then generalize the method to the task of approximating the capacity of classical quantum channels with a bounded continuous input alphabet and a finite dimensional output this using the idea of a universal encoder allows us to approximate the holevo capacity for channels with a finite dimensional quantum mechanical input and output in particular we show that the problem of approximating the holevo capacity can be reduced to a multi dimensional integration problem for certain families of quantum channels we prove that the complexity to derive an additive varepsilon close solution to the holevo capacity is subexponential or even polynomial in the problem size we provide several examples to illustrate the performance of the approximation scheme in practice

the minimum entropy output of a quantum channel is locally additive we show that the minimum von neumann entropy output of a quantum channel is locally additive hastings counterexample for the additivity conjecture makes this result quite surprising in particular it indicates that the nonadditivity of the minimum entropy output is a global effect of quantum channels

pole assignment for linear periodic systems by memoryless output feedback we consider linear periodic discrete time systems we are interested in the problem of placing the poles of the monodromy map by means of periodic output feedback of the same or multiple period it is well known that in general the poles of time invariant systems cannot be assigned by constant output feedback this is in contrast with what can be obtained in the context of time variant systems the main contribution of this paper is that periodic output feedback suffices for pole placement of periodic systems

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

a sharp continuity estimate for the von neumann entropy we derive an inequality relating the entropy difference between two quantum states to their trace norm distance sharpening a well known inequality due to fannes in our inequality equality can be attained for every prescribed value of the trace norm distance

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

quantum rate distortion reverse shannon theorems and source channel separation we derive quantum counterparts of two key theorems of classical information theory namely the rate distortion theorem and the source channel separation theorem the rate distortion theorem gives the ultimate limits on lossy data compression and the source channel separation theorem implies that a two stage protocol consisting of compression and channel coding is optimal for transmitting a memoryless source over a memoryless channel in spite of their importance in the classical domain there has been surprisingly little work in these areas for quantum information theory in this paper we prove that the quantum rate distortion function is given in terms of the regularized entanglement of purification we also determine a single letter expression for the entanglement assisted quantum rate distortion function and we prove that it serves as a lower bound on the unassisted quantum rate distortion function this implies that the unassisted quantum rate distortion function is nonnegative and generally not equal to the coherent information between the source and distorted output in spite of barnum s conjecture that the coherent information would be relevant here moreover we prove several quantum source channel separation theorems the strongest of these are in the entanglement assisted setting in which we establish a necessary and sufficient condition for transmitting a memoryless source over a memoryless quantum channel up to a given distortion

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

simplifying additivity problems using direct sum constructions we study the additivity problems for the classical capacity of quantum channels the minimal output entropy and its convex closure we show for each of them that additivity for arbitrary pairs of channels holds if and only if it holds for arbitrary equal pairs which in turn can be taken to be unital in a similar sense weak additivity is shown to imply strong additivity for any convex entanglement monotone the implications are obtained by considering direct sums of channels or states for which we show how to obtain several information theoretic quantities from their values on the summands this provides a simple and general tool for lifting additivity results

constructive counterexamples to the additivity of the minimum output renyi entropy of quantum channels for all p 2 we present a constructive example of the violation of the additivity of minimum output renyi entropy for each p 2 the example is provided by an antisymmetric subspace of a suitable dimension we discuss the possibility of extension of the result to go beyond p 2 and obtain additivity for p 0 for a class of entanglement breaking channels

on the extreme points of quantum channels abstract let l m n denote the convex set of completely positive trace preserving operators from c m m to c n n i e quantum channels we give a necessary condition for l l m n to be an extreme point we show that generically this condition is also sufficient we characterize completely the extreme points of l 2 2 and l 3 2 i e quantum channels from qubits to qubits and from qutrits to qubits

semidefinite programming strong converse bounds for classical capacity we investigate the classical communication over quantum channels when assisted by no signaling and positive partial transpose preserving ppt codes for which both the optimal success probability of a given transmission rate and the one shot epsilon error capacity are formalized as semidefinite programs sdps based on this we obtain improved sdp finite blocklength converse bounds of general quantum channels for entanglement assisted codes and unassisted codes furthermore we derive two sdp strong converse bounds for the classical capacity of general quantum channels for any code with a rate exceeding either of the two bounds of the channel the success probability vanishes exponentially fast as the number of channel uses increases in particular applying our efficiently computable bounds we derive an improved upper bound on the classical capacity of the amplitude damping channel we also establish the strong converse property for the classical and private capacities of a new class of quantum channels we finally study the zero error setting and provide efficiently computable upper bounds on the one shot zero error capacity of a general quantum channel

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

hall littlewood symmetric functions and the bkp equation the connection between solutions of the bkp equation and hall littlewood symmetric functions is utilised in a unified approach to soliton and polynomial solutions this is analogous to the wronskian formulation of the solution of the kp equation as a by product two novel expressions for certain hall littlewood functions in terms of pfaffians are derived

generating random density matrices we study various methods to generate ensembles of random density matrices of a fixed size n obtained by partial trace of pure states on composite systems structured ensembles of random pure states invariant with respect to local unitary transformations are introduced to analyze statistical properties of quantum entanglement in bi partite systems we analyze the distribution of schmidt coefficients of random pure states such a distribution is derived in the case of a superposition of k random maximally entangled states for another ensemble obtained by performing selective measurements in a maximally entangled basis on a multi partite system we show that this distribution is given by the fuss catalan law and find the average entanglement entropy a more general class of structured ensembles proposed containing also the case of bures forms an extension of the standard ensemble of structureless random pure states described asymptotically as n by the marchenko pastur distribution

a note on pole placement by static output feedback for single input systems abstract in this note we derive necessary and sufficient conditions for the solvability of the problem of pole placement by static output feedback formulated for single input systems

efficient approximation of channel capacities we propose an iterative method for approximately computing the capacity of discrete memoryless channels possibly under additional constraints on the input distribution based on duality of convex programming we derive explicit upper and lower bounds for the capacity the presented method requires o m 2 n sqrt log n varepsilon to provide an estimate of the capacity to within varepsilon where n and m denote the input and output alphabet size a single iteration has a complexity o m n we also show how to approximately compute the capacity of memoryless channels having a bounded continuous input alphabet and a countable output alphabet under some mild assumptions on the decay rate of the channel s tail it is shown that discrete time poisson channels fall into this problem class as an example we compute sharp upper and lower bounds for the capacity of a discrete time poisson channel with a peak power input constraint

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

extending additivity from symmetric to asymmetric channels we prove a lemma which allows one to extend results about the additivity of the minimal output entropy from highly symmetric channels to a much larger class a similar result holds for the maximal output p norm examples are given showing its use in a variety of situations in particular we prove the additivity and the multiplicativity for the shifted depolarizing channel

testing product states quantum merlin arthur games and tensor optimization we give a test that can distinguish efficiently between product states of n quantum systems and states that are far from product if applied to a state whose maximum overlap with a product state is 1 e the test passes with probability 1 e regardless of n or the local dimensions of the individual systems the test uses two copies of we prove correctness of this test as a special case of a more general result regarding stability of maximum output purity of the depolarizing channel a key application of the test is to quantum merlin arthur games with multiple merlins where we obtain several structural results that had been previously conjectured including the fact that efficient soundness amplification is possible and that two merlins can simulate many merlins qma k qma 2 for k 2 building on a previous result of aaronson et al this implies that there is an efficient quantum algorithm to verify 3 sat with constant soundness given two unentangled proofs of o n qubits we also show how qma 2 with log sized proofs is equivalent to a large number of problems some related to quantum information such as testing separability of mixed states as well as problems without any apparent connection to quantum mechanics such as computing injective tensor norms of 3 index tensors as a consequence we obtain many hardness of approximation results as well as potential algorithmic applications of methods for approximating qma 2 acceptance probabilities finally our test can also be used to construct an efficient test for determining whether a unitary operator is a tensor product which is a generalization of classical linearity testing

non commutative nash inequalities a set of functional inequalities called nash inequalities are introduced and analyzed in the context of quantum markov process mixing the basic theory of nash inequalities is extended to the setting of non commutative l p spaces where their relationship to poincare and log sobolev inequalities is fleshed out we prove nash inequalities for a number of unital reversible semigroups

counterexamples to additivity of minimum output p renyi entropy for p close to 0 complementing recent progress on the additivity conjecture of quantum information theory showing that the minimum output p renyi entropies of channels are not generally additive for p 1 we demonstrate here by a careful random selection argument that also at p 0 and consequently for sufficiently small p there exist counterexamples

an application of decomposable maps in proving multiplicativity of low dimensional maps in this paper we present a class of maps for which the multiplicativity of the maximal output p norm holds for p 2 and p 4 the class includes all positive trace preserving maps from b c3 to b c2 in this sense the result is a generalization of the corresponding result in the work of king and koldan new multiplicativity results for qubit maps j math phys 47 042106 2006 where the multiplicativity was proved for all positive trace preserving maps from b c2 to b c2 with p 2 and p 4 interestingly by contrast the multiplicativity of p norm was investigated in the context of quantum information theory and shown not to hold in general for high dimensional quantum channels hayden p and winter a counterexamples to the maximal p norm multiplicativity conjecture for all p 1 commun math phys 284 263 2008 moreover the werner holevo channel which is a map from b c3 to b c3 is a counterexample for p 4 79 werner and holevo j math phys 43 4353 2002

efficient optimization of the quantum relative entropy many quantum information measures can be written as an optimization of the quantum relative entropy between sets of states for example the relative entropy of entanglement of a state is the minimum relative entropy to the set of separable states the various capacities of quantum channels can also be written in this way we propose a unified framework to numerically compute these quantities using off the shelf semidefinite programming solvers exploiting the approximation method proposed in fawzi saunderson and parrilo 2017 arxiv 1705 00812 as a notable application this method allows us to provide numerical counterexamples for a proposed lower bound on the quantum conditional mutual information in terms of the relative entropy of recovery

unital quantum channels convex structure and revivals of birkhoff s theorem the set of doubly stochastic quantum channels and its subset of mixtures of unitaries are investigated we provide a detailed analysis of their structure together with computable criteria for the separation of the two sets when applied to o d covariant channels this leads to a complete characterization and reveals a remarkable feature instances of channels which are not in the convex hull of unitaries can become elements of this set by either taking two copies of them or supplementing with a completely depolarizing channel these scenarios imply that a channel whose noise initially resists any environment assisted attempt of correction can become perfectly correctable

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

on the minimum output entropy of random orthogonal quantum channels we consider the sequences of random quantum channels defined by using the stinespring formula with haar distributed random orthogonal matrices for any fixed sequence of input states we study the asymptotic eigenvalue distribution of the outputs through the tensor powers of random channels we show that the input states achieving minimum output entropy are tensor products of maximally entangled states bell states when the tensor power is even this phenomenon is completely different from the one for random quantum channels constructed from haar distributed random unitary matrices which leads us to formulate some conjectures about the regularized minimum output entropy

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

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

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