exponential error bounds for random codes in the arbitrarily varying channel random codes for the arbitrarily varying channel are investigated the code ensemble is restricted to increase only exponentially with codeword length a quantity called key rate is used as a measure of the rate of increase the reliability function for such codes is related to the reliability function for codes with unlimited key rate explicit results are obtained in some examples of practical interest

large deviations hypotheses testing and source coding for finite markov chains let x n n geq 1 be a finite markov chain with transition probability matrix of strictly positive entries a large deviation theorem is proved for the empirical transition count matrix and is used to get asymptotically optimal critical regions for testing simple hypotheses about the transition matrix as a corollary the error exponent in the source coding theorem for x n is obtained these results generalize the corresponding results for the independent and identically distributed case

two proofs of pinsker s conjecture concerning arbitrarily varying channels m s pinsker 1990 conjectured the following theorem for an arbitrary varying channel avc every rate below the random code capacity is achievable with deterministic list codes of constant list size if the average error criterion is used two proofs of this theorem are given

common randomness in information theory and cryptography i secret sharing as the first part of a study of problems involving common randomness at distance locations information theoretic models of secret sharing generating a common random key at two terminals without letting an eavesdropper obtain information about this key are considered the concept of key capacity is defined single letter formulas of key capacity are obtained for several models and bounds to key capacity are derived for other models

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

sparse quantum codes from quantum circuits we describe a general method for turning quantum circuits into sparse quantum subsystem codes the idea is to turn each circuit element into a set of low weight gauge generators that enforce the input output relations of that circuit element using this prescription we can map an arbitrary stabilizer code into a new subsystem code with the same distance and number of encoded qubits but where all the generators have constant weight at the cost of adding some ancilla qubits with an additional overhead of ancilla qubits the new code can also be made spatially local applying our construction to certain concatenated stabilizer codes yields families of subsystem codes with constant weight generators and with minimum distance d n 1 epsilon where epsilon o 1 sqrt log n for spatially local codes in d dimensions we nearly saturate a bound due to bravyi and terhal and achieve d n 1 epsilon 1 d previously the best code distance achievable with constant weight generators in any dimension due to freedman meyer and luo was o sqrt n log n for a stabilizer code

a varshamov gilbert bound for a class of formally self dual codes and related quantum codes it is proved that a class of q ary 2n n formally self dual codes obtained from symmetric matrices over gf q contains codes that meet the varshamov gilbert bound the codes are self dual with respect to the symplectic inner product and yield quantum codes encoding one state with n q ary qubits and having minimum distance proportional to n

krawtchouk polynomials and universal bounds for codes and designs in hamming spaces universal bounds for the cardinality of codes in the hamming space f sub r sup n with a given minimum distance d and or dual distance d are stated a self contained proof of optimality of these bounds in the framework of the linear programming method is given the necessary and sufficient conditions for attainability of the bounds are found the parameters of codes satisfying these conditions are presented in a table a new upper bound for the minimum distance of self dual codes and a new lower bound for the crosscorrelation of half linear codes are obtained

horvitz thompson estimators for double platform line transect surveys summary horvitz thompson estimators based on estimated inclusion probabilities are developed for line transect surveys in which some of the central assumptions of conventional line transect theory fail the estimators are designed to accommodate uncertain detection of animals in the observers path simultaneously with dependence of detection probabilities on explanatory variables other than perpendicular distance they require that data be collected by two observer teams simultaneously searching the survey region recording for each detection both positional data and details of any other variables that may affect detectability one of the estimators is designed to correct for responsive animal movement this method requires that the primary observer team searches independently of the secondary team whereas the second estimator requires both observer teams to search independently of each other the methods can be viewed as specific forms of mark recapture experiments in which individual capture probabilities are modelled as functions of observable explanatory variables and in which animals detected by both observer teams correspond to recaptures they differ from existing mark recapture horvitz thompson estimators primarily in that they use an assumption about the distribution of perpendicular distances that is implicit in conventional

nonbinary quantum codes we present several results on quantum codes over general alphabets that is in which the fundamental units may have more than two states in particular we consider codes derived from finite symplectic geometry assumed to have additional global symmetries from this standpoint the analogs of calderbank shor steane codes and of gf 4 linear codes turn out to be special cases of the same construction this allows us to construct families of quantum codes from certain codes over number fields in particular we get analogs of quadratic residue codes including a single error correcting code encoding one letter in five for any alphabet size we also consider the problem of fault tolerant computation through such codes generalizing ideas of gottesman see phys rev a vol 57 no 1 p127 37 1998

the asymptotic probability distribution of the relative distance of additive quantum codes abstract for given information rate r it is proved as n tends to infinite that almost all additive n n r quantum codes pure and impure are the codes with their relative distance tending to h 1 1 r where h x x log 2 x 3 1 x log 2 1 x is an entropy function

arbitrarily varying channels with general alphabets and states previous results of csiszar and narayan 1988 1989 1991 on the capacity of discrete arbitrarily varying channels with input and state constraints are extended to the case of arbitrary alphabets and state sets for channels with scalar or vector inputs and additive interference consisting of a deterministic part and noise both arbitrarily varying subject to power constraints the capacity for deterministic codes is shown to be equal to the random coding capacity if the input power exceeds the power of the deterministic interference and zero otherwise explicit capacity formulas are also given

new upper bounds on error exponents we derive new upper bounds on the error exponents for the maximum likelihood decoding and error detecting in the binary symmetric channels this is an improvement on the best earlier known bounds by shannon gallager berlekamp 1967 and mceliece omura 1977 for the probability of undetected error the new bounds are better than the bounds by levenshtein 1978 1989 and the bound by abdel ghaffar see ibid vol 43 p 1489 502 1997 moreover we further extend the range of rates where the undetected error exponent is known to be exact the new bounds are based on an analysis of possible distance distributions of the codes along with some inequalities relating the distance distributions to the error probabilities

asymptotically optimal classification for multiple tests with empirically observed statistics the decision problem of testing m hypotheses when the source is kth order markov and there are m or fewer training sequences of length n and a single test sequence of length n is considered k m n n are all given it is shown what the requirements are on m n n to achieve vanishing exponential error probabilities and how to determine or bound the exponent a likelihood ratio test that is allowed to produce a no match decision is shown to provide asymptotically optimal error probabilities and minimum no match decisions as an important serial case the binary hypotheses problem without rejection is discussed it is shown that for this configuration only one training sequence is needed to achieve an asymptotically optimal test

the method of types information theory the method of types is one of the key technical tools in shannon theory and this tool is valuable also in other fields in this paper some key applications are presented in sufficient detail enabling an interested nonspecialist to gain a working knowledge of the method and a wide selection of further applications are surveyed these range from hypothesis testing and large deviations theory through error exponents for discrete memoryless channels and capacity of arbitrarily varying channels to multiuser problems while the method of types is suitable primarily for discrete memoryless models its extensions to certain models with memory are also discussed

a model based approach for making ecological inference from distance sampling data summary we consider a fully model based approach for the analysis of distance sampling data distance sampling has been widely used to estimate abundance or density of animals or plants in a spatially explicit study area there is however no readily available method of making statistical inference on the relationships between abundance and environmental covariates spatial poisson process likelihoods can be used to simultaneously estimate detection and intensity parameters by modeling distance sampling data as a thinned spatial point process a model based spatial approach to distance sampling data has three main benefits it allows complex and opportunistic transect designs to be employed it allows estimation of abundance in small subregions and it provides a framework to assess the effects of habitat or experimental manipulation on density we demonstrate the model based methodology with a small simulation study and analysis of the dubbo weed data set in addition a simple ad hoc method for handling overdispersion is also proposed the simulation study showed that the model based approach compared favorably to conventional distance sampling methods for abundance estimation in addition the overdispersion correction performed adequately when the number of transects was high analysis of the dubbo data set indicated a transect effect on abundance via akaike s information criterion model selection further goodness of fit analysis however indicated some potential confounding of intensity with the detection function

nonbinary stabilizer codes over finite fields one formidable difficulty in quantum communication and computation is to protect information carrying quantum states against undesired interactions with the environment to address this difficulty many good quantum error correcting codes have been derived as binary stabilizer codes fault tolerant quantum computation prompted the study of nonbinary quantum codes but the theory of such codes is not as advanced as that of binary quantum codes this paper describes the basic theory of stabilizer codes over finite fields the relation between stabilizer codes and general quantum codes is clarified by introducing a galois theory for these objects a characterization of nonbinary stabilizer codes over fq in terms of classical codes over fq 2 is provided that generalizes the well known notion of additive codes over f4 of the binary case this paper also derives lower and upper bounds on the minimum distance of stabilizer codes gives several code constructions and derives numerous families of stabilizer codes including quantum hamming codes quadratic residue codes quantum melas codes quantum bose chaudhuri hocquenghem bch codes and quantum character codes the puncturing theory by rains is generalized to additive codes that are not necessarily pure bounds on the maximal length of maximum distance separable stabilizer codes are given a discussion of open problems concludes this paper

capacity of the gaussian arbitrarily varying channel the gaussian arbitrarily varying channel with input constraint gamma and state constraint lambda admits input sequences x x sub 1 x sub n of real numbers with sigma x sub i sup 2

the maximal error capacity of arbitrarily varying channels for constant list sizes the capacity of an arbitrarily varying channel avc for list codes of arbitrarily small list rate under the maximal error criterion has previously been determined the authors prove that for an avc a any rate r below the list code capacity c sub 1 a is achievable with a particular list size dependent on a r and y where y is the output alphabet

small intersections of principal blocks abstract in this note it is shown that a finite group g is solvable if for each odd prime divisor p of g irr b 0 g 2 irr b 0 g p 2 where irr b 0 g p is the set of complex irreducible characters of the principal p block b 0 g p of g also the structure of such groups is investigated examples show that the bound 2 is best possible

constant compositions in the sphere packing bound for classical quantum channels the sphere packing bound in the form given by shannon gallager and berlekamp was recently extended to classical quantum channels and it was shown that this creates a natural setting for combining probabilistic approaches with some combinatorial ones such as the lovasz theta function in this paper we extend the study to the case of constant composition codes we first extend the sphere packing bound for classical quantum channels to this case and we then show that the obtained result is related to a variation of the lovasz theta function studied by marton we then propose a further extension to the case of varying channels and codewords with a constant conditional composition given a particular sequence this extension is finally applied to auxiliary channels to deduce a bound which is useful in the low rate region and which can be interpreted as an extension of the elias bound

random coding bound and codes produced by permutations for the multiple access channel a random coding bound for the multiple access channel mac is given and it is shown to be obtainable universally for all mac s with common input and output alphabets for channels for which the random coding bound may be achieved by codes consisting of codewords of a single type for each sender this bound is also achievable by codes produced by permutations

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

on the statistical analysis of capture experiments summary a procedure is given for estimating the size of a closed population in the presence of heterogeneous capture probabilities using capture recapture data when it is possible to model the capture probabilities of individuals in the population using covariates the results include the estimation of the parameters associated with the model of the capture probabilities and the use of these estimated capture probabilities to estimate the population size confidence intervals for the population size using both the asymptotic normality of the estimator and a bootstrap procedure for small samples are given

nonbinary quantum stabilizer codes we define and show how to construct nonbinary quantum stabilizer codes our approach is based on nonbinary error bases it generalizes the relationship between self orthogonal codes over f sub 4 and binary quantum codes to one between self orthogonal codes over f q sup 2 and q ary quantum codes for any prime power q

strong converse exponents for a quantum channel discrimination problem and quantum feedback assisted communication this paper studies the difficulty of discriminating between an arbitrary quantum channel and a replacer channel that discards its input and replaces it with a fixed state the results obtained here generalize those known in the theory of quantum hypothesis testing for binary state discrimination we show that in this particular setting the most general adaptive discrimination strategies provide no asymptotic advantage over non adaptive tensor power strategies this conclusion follows by proving a quantum stein s lemma for this channel discrimination setting showing that a constant bound on the type i error leads to the type ii error decreasing to zero exponentially quickly at a rate determined by the maximum relative entropy registered between the channels the strong converse part of the lemma states that any attempt to make the type ii error decay to zero at a rate faster than the channel relative entropy implies that the type i error necessarily converges to one we then refine this latter result by identifying the optimal strong converse exponent for this task as a consequence of these results we can establish a strong converse theorem for the quantum feedback assisted capacity of a channel sharpening a result due to bowen furthermore our channel discrimination result demonstrates the asymptotic optimality of a non adaptive tensor power strategy in the setting of quantum illumination as was used in prior work on the topic the sandwiched renyi relative entropy is a key tool in our analysis finally by combining our results with recent results of hayashi and tomamichel we find a novel operational interpretation of the mutual information of a quantum channel mathcal n as the optimal type ii error exponent when discriminating between a large number of independent instances of mathcal n and an arbitrary worst case replacer channel chosen from the set of all replacer channels

a comment on a rate of convergence result for a universal d semifaithful code in the above paper see ibid vol 39 no 3 p 813 20 1993 yu and speed propose a universal pointwise d semifaithful code whose expected compression ratio for discrete memoryless sources approaches the rate distortion function at a rate o n sup 1 log n they also conjecture that this is the fastest achievable convergence rate for pointwise d semifaithful codes in this correspondence we use a simple extension of kraft s inequality and prove that this conjecture is true at least for the hamming distortion measure

capacity and decoding rules for classes of arbitrarily varying channels the capacity of an arbitrarily varying channel avc is considered for deterministic codes with the average probability of error criterion and typically subject to at state constraint first sufficient conditions are provided that enable relatively simple decoding rules such as typicality maximum mutual information and minimum distance to attain capacity then the possibly noisy or channels and group adder channels are studied in detail for the former the capacity is explicitly determined and shown to be attainable by minimum distance decoding next for a large class of addictive avcs in addition to providing an intuitively suggestive simplification of the general avc capacity formula it is proven that capacity can be attained by a universal decoding rule finally the effect of random state selections on capacity is studied the merits and limitations of a previous mutual information game approach are also discussed

nonidentifiability of population size from capture recapture data with heterogeneous detection probabilities heterogeneity in detection probabilities has long been recognized as problematic in mark recapture studies and numerous models developed to accommodate its effects individual heterogeneity is especially problematic in that reasonable alternative models may predict essentially identical observations from populations of substantially different sizes thus even with very large samples the analyst will not be able to distinguish among reasonable models of heterogeneity even though these yield quite distinct inferences about population size the problem is illustrated with models for closed and open populations

logistic regression in capture recapture models the effect of population heterogeneity in capture recapture or dual registration models is discussed an estimator of the unknown population size based on a logistic regression model is introduced the model allows different capture probabilities across individuals and across capture times the probabilities are estimated from the observed data using conditional maximum likelihood the resulting population estimator is shown to be consistent and asymptotically normal a variance estimator under population heterogeneity is derived the finite sample properties of the estimators are studied via simulation an application to finnish occupational disease registration data is presented

lower bounds on the probability of error for classical and classical quantum channels in this paper lower bounds on error probability in coding for discrete classical and classical quantum channels are studied the contribution of the paper goes in two main directions 1 extending classical bounds of shannon to classical quantum channels and 2 proposing a new framework for lower bounding the probability of error of channels with a zero error capacity in the low rate region the relation between these two problems is revealed by showing that lovasz bound on zero error capacity emerges as a natural consequence of the sphere packing bound once we move to the more general context of classical quantum channels a variation of lovasz bound is then derived to lower bound the probability of error in the low rate region by means of auxiliary channels as a result of this study connections between the lovasz theta function the expurgated bound of gallager the cutoff rate of a classical channel and the sphere packing bound for classical quantum channels are established

reliability of calderbank shor steane codes and security of quantum key distribution after mayers 1996 advances in cryptography proc crypto 96 pp 343 57 2001 j assoc comput mach 48 351 406 gave a proof of the security of the bennett brassard 1984 proc ieee int conf on computers systems and signal processing bangalore india pp 175 9 bb84 quantum key distribution protocol shor and preskill 2000 phys rev lett 85 441 4 made a remarkable observation that a calderbank shor steane css code had been implicitly used in the bb84 protocol and suggested its security could be proved by bounding the fidelity say fn of the incorporated css code of length n in the form for some positive number e this work presents such a number e e r as a function of the rate of codes r and a threshold r0 such that e r 0 whenever r r0 which is larger than the achievable rate based on the gilbert varshamov bound that is essentially given by shor and preskill the codes in the present work are robust against fluctuations of channel parameters which fact is needed to establish the security rigorously and was not proved for rates above the gilbert varshamov rate before in the literature as a byproduct the security of a modified bb84 protocol against any joint coherent attacks is proved quantitatively

extremal properties of rate distortion functions an attempt is made to determine whether it is true that for a fixed distortion level delta the rate distortion function r p delta has in the distribution p no local maxima with values different from the global maximum it is shown that in general the answer is negative however the answer is positive for hamming distortion measures moreover their r is schur concave

concavity of the auxiliary function for classical quantum channels the auxiliary function of a classical channel appears in two fundamental quantities the random coding exponent and the sphere packing exponent which yield upper and lower bounds on the error probability of decoding respectively a crucial property of the auxiliary function is its concavity and this property consequently leads to several important results in finite blocklength analysis in this paper we prove that the auxiliary function of a classical quantum channel also enjoys the same concavity property extending an earlier partial result to its full generality we also prove that the auxiliary function satisfies the data processing inequality among various other important properties furthermore we show that the concavity property of the auxiliary function enables a geometric interpretation of the random coding exponent and the sphere packing exponent of a classical quantum channel the key component in our proof is an important result from the theory of matrix geometric means

fixed rate universal lossy source coding and rates of convergence for memoryless sources a fixed rate universal lossy coding scheme is introduced for independent and identically distributed i i d sources it is shown for finite alphabet sources and arbitrary single letter distortion measures that as the sample size n grows the expected distortion obtained using this universal scheme converges to shannon s distortion rate function d r at a rate o log n n the scheme can be extended to universal quantization of real i i d sources subject to a squared error criterion it is shown in this case that the per letter distortion converges to d r at a rate o spl radic log n n both in expectation and almost surely for any real valued bounded i i d source

moderate deviation analysis for classical quantum channels and quantum hypothesis testing in this paper we study the tradeoffs between the error probabilities of classical quantum channels and the blocklength n when the transmission rates approach the channel capacity at a rate lower than 1 sqrt n a research topic known as moderate deviation analysis we show that the optimal error probability vanishes under this rate convergence our main technical contributions are a tight quantum sphere packing bound obtained via chaganty and sethuraman s concentration inequality in strong large deviation theory and asymptotic expansions of error exponent functions moderate deviation analysis for quantum hypothesis testing is also established the converse directly follows from our channel coding result while the achievability relies on a martingale inequality

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 capacity of the arbitrarily varying channel revisited positivity constraints a well known result of r ahlswede 1970 asserts that the deterministic code capacity of an arbitrarily varying channel avc under the average error probability criterion either equals its random code capacity or else is zero a necessary and sufficient condition is identified for deciding between these alternative namely the capacity is zero if and only if the avc is symmetrizable the capacity of the avc is determined with constraints on the transmitted codewords as well as on the channel state sequences and it is demonstrated that it may be positive but less than the corresponding random code capacity a special case of the results resolves a weakened version of a fundamental problem of coding theory

incorporating covariates into standard line transect analyses summary an implicit assumption of standard line transect methodology is that detection probabilities depend solely on the perpendicular distance of detected objects to the transect line heterogeneity in detection probabilities is commonly minimized using stratification but this may be precluded by small sample sizes we develop a general methodology which allows the effects of multiple covariates to be directly incorporated into the estimation procedure using a conditional likelihood approach small sample size properties of estimators are examined via simulations as an example the method is applied to eastern tropical pacific dolphin sightings data

universal coding for the slepian wolf data compression system and the strong converse theorem universal coding for the slepian wolf 1973 data compression system is considered we shall demonstrate based on a simple observation that the error exponent given by csiszar and korner 1980 for the universal coding system can strictly be sharpened in general for a region of relatively higher rates this kind of observation can be carried over also to the case of lower rates outside the slepian wolf region which establishes the strong converse along with the optimal exponent

quantum error detection i statement of the problem this paper is devoted to the problem of error detection with quantum codes we show that it is possible to give a consistent definition of the undetected error event to prove this we examine possible problem settings for quantum error detection our goal is to derive a functional that describes the probability of undetected error under natural physical assumptions concerning transmission with error detection with quantum codes we discuss possible transmission protocols with stabilizer and unrestricted quantum codes the set of results proved in the paper shows that in all the cases considered the average probability of undetected error for a given code is essentially given by one and the same function of its weight enumerators we examine polynomial invariants of quantum codes and show that coefficients of rains s see ibid vol44 p 1388 94 1998 unitary weight enumerators are known for classical codes under the name of binomial moments of the distance distribution as in the classical situation these enumerators provide an alternative expression for the probability of undetected error

reliability function of general classical quantum channel in information theory the reliability function and its bounds describing the exponential behavior of the error probability are important quantitative characteristics of the channel performance from a more general point of view these bounds provide certain measures of distinguishability of a given set of classical states in a previous paper quantum analogs of the random coding and expurgation lower bounds for the case of pure signal states were introduced here we discuss the case of general quantum states in particular we prove the expurgation bound conjectured previously and find the quantum cutoff rate for arbitrary mixed signal states

on trace inequalities and their applications to noncommutative communication theory abstract certain trace inequalities related to matrix logarithm are shown these results enable us to give a partial answer of the open problem conjectured by a s holevo that is concavity of the auxiliary function which appears in the random coding exponent as the lower bound of the quantum reliability function for general quantum states is proven in the case of 0 s 1

quantum error detection ii bounds for pt i see ibid vol 46 no 3 p 778 88 2000 in part i of this paper we formulated the problem of error detection with quantum codes on the depolarizing channel and gave an expression for the probability of undetected error via the weight enumerators of the code in this part we show that there exist quantum codes whose probability of undetected error falls exponentially with the length of the code and derive bounds on this exponent the lower existence bound is proved for stabilizer codes by a counting argument for classical self orthogonal quaternary codes upper bounds are proved by linear programming first we formulate two linear programming problems that are convenient for the analysis of specific short codes next we give a relaxed formulation of the problem in terms of optimization on the cone of polynomials in the krawtchouk basis we present two general solutions of the problem together they give an upper bound on the exponent of undetected error the upper and lower asymptotic bounds coincide for a certain interval of code rates close to 1

universal coding for correlated sources with linked encoders on the coding for correlated sources we extend the slepian wolf 1973 data compression system called the sw system to define a new system called the swl system where two separate encoders of the sw system are mutually linked determining the optimal error exponent for all rates inside the admissible rate region remains an open problem for the sw system we completely solve this problem for the swl system and show that the optimal exponents can be achieved by universal codes furthermore it is shown that the linkage of two encoders does not extend the admissible rate region and does not even improve the exponent of correct decoding outside this region the zero error data transmission problem for the swl system is also considered we determine the zero error rate region the admissible rate region under the condition that the decoding error probability is strictly zero and show that this region can be attained by universal codes furthermore we make it clear that the linkage of encoders enlarges the zero error rate region it is interesting to note that the above results for the swl system correspond in some sense to the previous results for the discrete memoryless channel with feedback

noisy non transitive quantum games we study the effect of quantum noise in 3 3 entangled quantum games by taking into account different noisy quantum channels we analyze how a twoplayer three strategy rock scissor paper game is influenced by the quantum noise we consider the winning non transitive strategies r s and p such that r beats s s beats p and p beats r the game behaves as a noiseless game for the maximum value of the quantum noise it is seen that alice s payoff is heavily influenced by the depolarizing noise as compared to the amplitude damping noise a depolarizing channel causes a monotonic decrease in players payoffs as we increase the amount of quantum noise in the case of the amplitude damping channel alice s payoff function reaches its minimum for 0 5 and is symmetrical this means that larger values of quantum noise influence the game weakly on the other hand the phase damping channel does not influence the game furthermore the nash equilibrium and non transitive character of the game are not affected under the influence of quantum noise

concatenated quantum codes can attain the quantum gilbert varshamov bound a family of quantum codes of increasing block length with positive rate is asymptotically good if the ratio of its distance to its block length approaches a positive constant the asymptotic quantum gilbert varshamov gv bound states that there exist q ary quantum codes of sufficiently long block length n having fixed rate r with distance at least n h 1 q 2 1 r 2 where h q 2 is the q 2 ary entropy function for q only random quantum codes are known to asymptotically attain the quantum gv bound however random codes have little structure in this paper we generalize the classical result of thommesen to the quantum case thereby demonstrating the existence of concatenated quantum codes that can asymptotically attain the quantum gv bound the outer codes are quantum generalized reed solomon codes and the inner codes are random independently chosen stabilizer codes where the rates of the inner and outer codes lie in a specified feasible region

graph decomposition a new key to coding theorems a new and simple method is proposed for finding good encoders both for channels and for sources with side information this method relies on the continuous version of a graph decomposition result of lovasz the presently known best exponential error bounds for both problems follow in a unified manner with an improvement on the source coding bound the previous bounds for universal codes of the authors and marton are also improved

classical and quantum evaluation codes at the trace roots we introduce a new class of evaluation linear codes by evaluating polynomials at the roots of a suitable trace function we give conditions for self orthogonality of these codes and their subfield subcodes with respect to the hermitian inner product they allow us to construct stabilizer quantum codes over several finite fields which substantially improve the codes in the literature for the binary case we obtain records at http codetables de moreover we obtain several classical linear codes over the field mathbb f 4 which are records at http codetables de

accommodating unmodeled heterogeneity in double observer distance sampling surveys mark recapture models applied to double observer distance sampling data neglect the information on relative detectability of objects contained in the distribution of observed distances a difference between the observed distribution and that predicted by the mark recapture model is symptomatic of a failure of the assumption of zero correlation between detection probabilities implicit in the mark recapture model we develop a mark recapture based model that uses the observed distribution to relax this assumption to zero correlation at only one distance we demonstrate its usefulness in coping with unmodeled heterogeneity using data from an aerial survey of crabeater seals in the antarctic

conditional limit theorems under markov conditioning let x 1 x 2 cdots be independent identically distributed random variables taking values in a finite set x and consider the conditional joint distribution of the first m elements of the sample x 1 cdots x n on the condition that x 1 x 1 and the sliding block sample average of a function h cdot cdot defined on x 2 exceeds a threshold alpha eh x 1 x 2 for m fixed and n rightarrow infty this conditional joint distribution is shown to converge m the m step joint distribution of a markov chain started in x 1 which is closest to x l x 2 cdots in kullback leibler information divergence among all markov chains whose two dimensional stationary distribution p cdot cdot satisfies sum p x y h x y geq alpha provided some distribution p on x 2 having equal marginals does satisfy this constraint with strict inequality similar conditional limit theorems are obtained when x 1 x 2 cdots is an arbitrary finite order markov chain and more general conditioning is allowed

fidelity lower bounds for stabilizer and css quantum codes in this paper we estimate the fidelity of stabilizer and css codes first we derive a lower bound on the fidelity of a stabilizer code via its quantum enumerator next we find the average quantum enumerators of the ensembles of finite length stabilizer and css codes we use the average quantum enumerators for obtaining lower bounds on the average fidelity of these ensembles we further improve the fidelity bounds by estimating the quantum enumerators of expurgated ensembles of stabilizer and css codes finally we derive fidelity bounds in the asymptotic regime when the code length tends to infinity these results tell us which code rate we can afford for achieving a target fidelity with codes of a given length the results also show that in symmetric depolarizing channel a typical stabilizer code has better performance in terms of fidelity and code rate compared with a typical css codes and that balanced css codes significantly outperform other css codes asymptotic results demonstrate that css codes have a fundamental performance loss compared with stabilizer codes

double observer line transect methods levels of independence double observer line transect methods are becoming increasingly widespread especially for the estimation of marine mammal abundance from aerial and shipboard surveys when detection of animals on the line is uncertain the resulting data supplement conventional distance sampling data with two sample mark recapture data like conventional mark recapture data these have inherent problems for estimating abundance in the presence of heterogeneity unlike conventional mark recapture methods line transect methods use knowledge of the distribution of a covariate which affects detection probability namely distance from the transect line in inference this knowledge can be used to diagnose unmodeled heterogeneity in the mark recapture component of the data by modeling the covariance in detection probabilities with distance we show how the estimation problem can be formulated in terms of different levels of independence at one extreme full independence is assumed as in the petersen estimator which does not use distance data at the other extreme independence only occurs in the limit as detection probability tends to one between the two extremes there is a range of models including those currently in common use which have intermediate levels of independence we show how this framework can be used to provide more reliable analysis of double observer line transect data we test the methods by simulation and by analysis of a dataset for which true abundance is known we illustrate the approach through analysis of minke whale sightings data from the north sea and adjacent waters

quantum sphere packing bounds with polynomial prefactors we study lower bounds on the optimal error probability in classical coding over classical quantum channels at rates below the capacity commonly termed quantum sphere packing bounds winter and dalai have derived such bounds for classical quantum channels however the exponents in their bounds only coincide when the channel is classical in this paper we show that these two exponents admit a variational representation and are related by the golden thompson inequality reaffirming that dalai s expression is stronger in general classical quantum channels second we establish a finite blocklength sphere packing bound for classical quantum channels which significantly improves dalai s prefactor from the order of subexponential to polynomial furthermore the gap between the obtained error exponent for constant composition codes and the best known classical random coding exponent vanishes in the order of o log n n indicating our sphere packing bound is almost exact in the high rate regime finally for a special class of symmetric classical quantum channels we can completely characterize its optimal error probability without the constant composition code assumption the main technical contributions are two converse hoeffding bounds for quantum hypothesis testing and the saddle point properties of error exponent functions

a nonparametric approach to the analysis of two stage mark recapture experiments we present a new approach to the analysis of two stage mark recapture experiments where individual covariates are available which describe the detectability of individuals in the population central to the theory is a single quantity which we call the heterogeneity index and which measures the variability in the detectability of individuals this theory also has implications for the analysis of independent observer line transect surveys an estimator of is provided by combining kernel density estimates of the underlying densities of the covariate conditional on capture histories we derive expressions for the asymptotic bias and variance and show that our new estimator is as efficient as the petersen estimator when individuals all have the sames detectability we also report the results of a simulation study of the new estimator for a range of mark recapture conditions

the error exponent for the noiseless encoding of finite ergodic markov sources a new approach to the classical fixed length noiseless source coding problem is proposed for the case of finite ergodic markov sources this approach is based on simple counting arguments the central notion of markov type a set containing all the source sequences having the same transition counts from letter to letter is introduced and the cardinality of such a set is evaluated via graph theoretical tools the error exponent is shown to be a weighted average of informational divergences and the universal character of the result is stressed as a corollary the classical source coding theorem determining the achievable rates is rederived

a low rate bound on the reliability of a quantum discrete memoryless channel we extend a low rate improvement of the random coding bound on the reliability of a classical discrete memoryless channel dmc to its quantum counterpart the key observation that we make is that the problem of bounding below the error exponent for a quantum channel relying on the class of stabilizer codes is equivalent to the problem of deriving error exponents for a certain symmetric classical channel

a rate of convergence result for a universal d semifaithful code the problem of optimal rate universal coding is considered in the context of rate distortion theory a d semifaithful universal coding scheme for discrete memoryless sources is given the main result is a refined covering lemma based on the random coding argument and the method of types the average codelength of the code is shown to approach its lower bound the rate distortion function at a rate o n sup 1 log n and this is conjectured to be optimal based on a result of a j pilc 1968 issues of constructiveness and universality are addressed

feedback does not affect the reliability function of a dmc at rates above capacity corresp asymptotically coincident upper and lower bounds on the exponent of the largest possible probability of correct decoding for block codes of any given rate above capacity have been given by dueck and korner their method is extended to show that the same bounds also hold in the presence of noiseless feedback

linear codes for sources and source networks error exponents universal coding for slepian wolf source networks the error exponents obtained by korner marton and the author are shown to be universally attainable by linear codes also improved exponents are derived for linear codes with large rates specializing the results to simple discrete memoryless sources reveals their relationship to the random coding and expurgated bounds for channels with additive noise one corollary is that there are universal linear codes for this class of channels which attain the random coding error exponent for each channel in the class the combinatorial approach of csiszar korner marton is used in particular all results are derived from a lemma specifying good encoders in terms of purely combinatorial properties

cryptographic distinguishability measures for quantum mechanical states this paper mostly expository in nature surveys four measures of distinguishability for quantum mechanical states this is done from the point of view of the cryptographer with a particular eye on applications in quantum cryptography each of the measures considered is rooted in an analogous classical measure of distinguishability for probability distributions namely the probability of an identification error the kolmogorov distance the bhattacharyya coefficient and the shannon 1948 distinguishability as defined through mutual information these measures have a long history of use in statistical pattern recognition and classical cryptography we obtain several inequalities that relate the quantum distinguishability measures to each other one of which may be crucial for proving the security of quantum cryptographic key distribution in another vein these measures and their connecting inequalities are used to define a single notion of cryptographic exponential indistinguishability for two families of quantum states this is a tool that may prove useful in the analysis of various quantum cryptographic protocols

a trace inequality arising from quantum information theory abstract we introduce a skew information of lieb s type s f g a x tr f a xg a x tr f a g a x 2 for selfadjoint matrices a x we give conditions for f and g so that sf g is positive or negative as another important application we settle the problem posed by yanagi furuichi and kuriyama from quantum information theory

on the error exponent of source channel transmission with a distortion threshold the author s previous results on the exponent of probability of error for joint source channel codes are improved and extended to distortion threshold fidelity criteria the maximum error version of the problem is also considered

computing matrix group decompositions with respect to a normal subgroup abstract we describe an algorithm which can be used to investigate whether a matrix group defined over a finite field decomposes with respect to a normal subgroup defined as the normal closure of a given set of matrices the possible decompositions correspond to classes in aschbacher s classification of subgroups of the general linear group

constructive sylow theorems for the classical groups abstract let r be a prime we provide efficient algorithms to construct and solve the conjugacy problem for the sylow r subgroups of the classical groups over finite fields in their natural representations we also provide algorithms to construct the normaliser of a sylow r subgroup of gl n f q sp 2 m f q go 2 m 1 f q go 2 m f q go 2 m f q or gu n f q 2 the algorithms described here are implemented in the magma computer algebra system

on the distance distribution of codes the distinct distribution of a binary code c is the sequence b sub i sub i 0 sup n defined as follows let b sub i w be the number of codewords at distance i from the codeword w and let b sub i be the average of b sub i w over all w in c in this correspondence we study the distance distribution for codes of length n and minimal distance spl delta n with spl delta 0 fixed and n spl rarr spl infin our main aim is to relate the size of the code with the distribution of distances near the minimal distance

bounds on information combining with quantum side information bounds on information combining are entropic inequalities that determine how the information entropy of a set of random variables can change when these are combined in certain prescribed ways such bounds play an important role in classical information theory particularly in coding and shannon theory entropy power inequalities are special instances of them the arguably most elementary kind of information combining is the addition of two binary random variables a cnot gate and the resulting quantities play an important role in belief propagation and polar coding we investigate this problem in the setting where quantum side information is available which has been recognized as a hard setting for entropy power inequalities our main technical result is a non trivial and close to optimal lower bound on the combined entropy which can be seen as an almost optimal quantum mrs gerber s lemma our proof uses three main ingredients 1 a new bound on the concavity of von neumann entropy which is tight in the regime of low pairwise state fidelities 2 the quantitative improvement of strong subadditivity due to fawzi renner in which we manage to handle the minimization over recovery maps and 3 recent duality results on classical quantum channels due to renes et al we furthermore present conjectures on the optimal lower and upper bounds under quantum side information supported by interesting analytical observations and strong numerical evidence we finally apply our bounds to polar coding for binary input classical quantum channels and show the following three results 1 even non stationary channels polarize under the polar transform 2 the blocklength required to approach the symmetric capacity scales at most sub exponentially in the gap to capacity and 3 under the aforementioned lower bound conjecture a blocklength polynomial in the gap suffices

the redundancy of source coding with a fidelity criterion 1 known statistics the problem of redundancy of source coding with respect to a fidelity criterion is considered for any fixed rate r 0 and any memoryless source with finite source and reproduction alphabets and a common distribution p the nth order distortion redundancy d sub n r of fixed rate coding is defined as the minimum of the difference between the expected distortion per symbol of any block code with length n and rate r and the distortion rate function d p r of the source p it is demonstrated that for sufficiently large n d sub n r is equal to spl part spl part r d p r ln n 2n o ln n n where spl part spl part r d p r is the partial derivative of d p r evaluated at r and assumed to exist for any fixed distortion level d 0 and any memoryless source p the nth order rate redundancy r sub n d of coding at fixed distortion level d or by using d semifaithful codes is defined as the minimum of the difference between the expected rate per symbol of any d semifaithful code of length n and the rate distortion function r p d of p evaluated at d it is proved that for sufficiently large n r sub n d is upper bounded by ln n n o ln n n and lower bounded by in n 2n o in n n as a by product the lower bound of r sub n d derived in this paper gives a positive answer to a conjecture proposed by yu and speed 1993

concavity of the auxiliary function appearing in quantum reliability function reliability functions characterize the asymptotic behavior of the error probability for transmission of data on a channel holevo introduced the quantum channel and gave an expression for a random coding lower bound involving an auxiliary function holevo ogawa and nagaoka conjectured that this auxiliary function is concave here we give a proof of this conjecture

hardness of decoding quantum stabilizer codes in this paper we address the computational hardness of optimally decoding a quantum stabilizer code much like classical linear codes errors are detected by measuring certain check operators which yield an error syndrome and the decoding problem consists of determining the most likely recovery given the syndrome the corresponding classical problem is known to be np complete and are appropriate a similar decoding problem for quantum codes is also known to be np complete however this decoding strategy is not optimal in the quantum setting as it does not consider error degeneracy which causes distinct errors to have the same effect on the code here we show that optimal decoding of stabilizer codes previously known to be np hard is in fact computationally much harder than optimal decoding of classical linear codes it is p complete

polar codes for arbitrary classical quantum channels and arbitrary cq macs we prove polarization theorems for arbitrary classical quantum cq channels the input alphabet is endowed with an arbitrary abelian group operation and an arikan style transformation is applied using this operation it is shown that as the number of polarization steps becomes large the synthetic cq channels polarize to deterministic homomorphism channels that project their input to a quotient group of the input alphabet this result is used to construct polar codes for arbitrary cq channels and arbitrary cq multiple access channels the encoder can be implemented in o n log n operations where n is the blocklength of the code a quantum successive cancellation decoder for the constructed codes is proposed it is shown that the probability of error of this decoder decays faster than 2 n beta for any beta

moderate deviation analysis for classical communication over quantum channels we analyse families of codes for classical data transmission over quantum channels that have both a vanishing probability of error and a code rate approaching capacity as the code length increases to characterise the fundamental tradeoff between decoding error code rate and code length for such codes we introduce a quantum generalisation of the moderate deviation analysis proposed by alt g and wagner as well as polyanskiy and verdu we derive such a tradeoff for classical quantum as well as image additive channels in terms of the channel capacity and the channel dispersion giving further evidence that the latter quantity characterises the necessary backoff from capacity when transmitting finite blocks of classical data to derive these results we also study asymmetric binary quantum hypothesis testing in the moderate deviations regime due to the central importance of the latter task we expect that our techniques will find further applications in the analysis of other quantum information processing tasks

testing matrix groups for primitivity abstract we describe an algorithm which seeks to decide whether or not a matrix group defined over a finite field acts to preserve blocks of imprimitivity and if so to find a block system implementations of the algorithm are publicly available

linear programming bounds for entanglement assisted quantum error correcting codes by split weight enumerators linear programming approaches have been applied to derive upper bounds on the size of classical and quantum codes in this paper we derive similar results for general quantum codes with entanglement assistance by considering a type of split weight enumerator after deriving the macwilliams identities for these enumerators we are able to prove algebraic linear programming bounds such as the singleton bound the hamming bound and the first linear programming bound our singleton bound and hamming bound are more general than the previous bounds for entanglement assisted quantum stabilizer codes in addition we show that the first linear programming bound improves the hamming bound when the relative distance is sufficiently large on the other hand we obtain additional constraints on the size of pauli subgroups for quantum codes which allow us to improve the linear programming bounds on the minimum distance of quantum codes of small length in particular we show that there is no 27 15 5 or 28 14 6 stabilizer code we also discuss the existence of some entanglement assisted quantum stabilizer codes with maximal entanglement as a result the upper and lower bounds on the minimum distance of maximal entanglement quantum stabilizer codes with length up to 20 are significantly improved