A Limit Theorem for Quantum Markov Chains Associated to Beam Splittings

Isometric Cocycles Related to Beam Splittings

We provide in the context of quantum Markov chains due to Accardi coming up from iterated beam splittings a limit theorem concerning with a refinement of the discrete time. The limit object refers to a continuous time and should be called quantum Markov process. Closely related to our construction of such quantum Markov processes are isometric cocycles. We derive, upto technical conditions, a c...

The central limit theorem for stationary Markov chains under invariant splittings

The central limit theorem (CLT) for stationary ergodic Markov chains is investigated. We give a short survey of related results on the CLT for general (not necessarily Harris recurrent) chains and formulate a new sufficient condition for its validity. Furthermore, Markov operators are considered which admit invariant orthogonal splittings of the space of square-integrable functions. We show how...

Central and Local Limit Theories in Markov Dependent Random Variables

Central Limit Theorems for Open Quantum Random Walks∗

Open Quantum Random Walks, as developed in [1], are the exact quantum generalization of Markov chains on finite graphs or on nets. These random walks are typically quantum in their behavior, step by step, but they seem to show up a rather classical asymptotic behavior, as opposed to the quantum random walks usually considered in Quantum Information Theory (such as the well-known Hadamard random...

The Central Limit Theorem for the Normalized Sums of Extended Sliding Block Codes from Sequences of Markov Chains with Time Delay

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...