The classical capacity of a quantum channel with arbitrary Markovian correlated noise is evaluated. For an irreducible and aperiodic Markov Chain, the channel is forgetful, and one retrieves the known expression [15] for the capacity. For the more general case of a channel with long-term memory, which corresponds to a Markov chain which does not converge to equilibrium, the capacity is expresse...

We propose a variant of temporal{di erence learning that approximates average and di erential costs of an irreducible aperiodic Markov chain. Approximations are comprised of linear combinations of xed basis functions whose weights are incrementally updated during a single endless trajectory of the Markov chain. We present a proof of convergence (with probability 1), and a characterization of th...

We introduce the concept of asymptotic period for an irreducible and aperiodic discrete-time Markov chain on a countable state space. If the chain is transient its asymptotic period may be larger than one. We present some sufficient conditions and, in the more restricted setting of birth-death processes, a necessary and sufficient condition for asymptotic aperiodicity . It is subsequently shown...

In this paper we evaluate the entanglement assisted classical capacity of a class of quantum channels with long-term memory, which are convex combinations of memoryless channels. The memory of such channels can be considered to be given by a Markov chain which is aperiodic but not irreducible. This class of channels was introduced in [7], where its product state capacity was evaluated.

A lumping of a Markov chain is a coordinate-wise projection of the chain. We characterise the entropy rate preservation of a lumping of an aperiodic and irreducible Markov chain on a finite state space by the random growth rate of the cardinality of the realisable preimage of a finite-length trajectory of the lumped chain and by the information needed to reconstruct original trajectories from t...

in this paper, the ambiguity of nite state irreducible markov chain trajectories is reminded and is obtained for two state markov chain. i give an applicable example of this concept in president election

Consider a random source which evolves on a finite set. It follows from existing literature, see for example [1] and [2] (Pages 491-500, in particular, see Definition (9.8.3) and Theorem 9.8.3 for achievability), that the limit of the normalized rate-distortion functions of block-independent approximations of a a stationary, ergodic source is equal to the rate-distortion function of the source....

In this expository paper, we p r o ve the following theorem, which m a y be of some use in studying Markov chain Monte Carlo methods like hit and run, the Metropolis algorithm, or the Gibbs sampler. Suppose a discrete-time Markov c hain is aperiodic, irreducible, and there is a stationary probability distribution. Then from almost all starting points the distribution of the chain at time n conv...

Necessary and sufficient conditions for a Markov chain to be ergodic are that the is irreducible aperiodic. This result manifest in case of random walks on finite groups by statement about support driving probability: walk group if only not concentrated proper subgroup, nor coset normal subgroup. The study extends naturally quantum groups, where state algebra functions plays role probability. e...

We extend the sliding block code in symbolic dynamics to transform two sequences of Markov chains with time delay. Under the assumption that chains are irreducible and aperiodic, we prove the central limit theorem (CLT) for the normalized sums of extended sliding block codes from two sequences of Markov chains. We apply the theorem to evaluations of bit error probabilities in asynchronous sprea...