… We formally extend the notion of Markov order to open quantum processes by accounting …
do not exist non-Markovian quantum processes that have finite Markov order with respect to all …

… processes with finite quantum Markov order and the quantum conditional mutual … quantum
conditional mutual information are a special case within the theory of quantum Markov order. …

A new approach to quantum Markov chains is presented. We first define a transition operation
matrix (TOM) as a matrix whose entries are completely positive maps whose column sums …

… quantum version gives rise to a quadratic speed-up. This is the case, in particular, when the
Markov … If we have a single probabilistic function P from X to X (ie a Markov chain), in order to …

… theory of quantum chains. Section 2 studies a particular example of a quantum chain
whose … There are various other approaches to quantum Markov processes that have been …

… The analysis of such phenomena requires the use of tools that go well beyond the Markov
approximation, in order to capture the relevant aspects of the processes. Among these are the …

… dynalmical semigroup) and we give conditions - necessary and sufficient or simply sufficient
in order for the semigroup to be identity preserving (ie Markov). In Chapter 4 first we study …

… a quantum channel as a generative model of directional mid-price movements in a Limit
Order Book (… The emission system is entangled with a second, unobservable quantum system …

… bath becomes Markovian, they derived a quantum Fokker–… the second order is exact for the
CL model in the Markovian bath … -order level can be achieved through our Markovian FQME. …

… In order to reason about the behaviour of a qMC, we need to determine the accumulated
super-operator along certain paths. To this end, we construct a SVM Q s for each s ∈ S as …