Related papers: Quantum Markov Processes (Correspondences and Dila…
This brief article gives an overview of quantum mechanics as a {\em quantum probability theory}. It begins with a review of the basic operator-algebraic elements that connect probability theory with quantum probability theory. Then quantum…
We show that if a product system comes from a quantum Markov semigroup, then it carries a natural Borel structure with respect to which the semigroup may be realized in terms of a measurable representation. We show, too, that the dual…
This paper shows a novel way of simulating a Markov process by a quantum computer. The main purpose of the paper is to show a particular application of quantum computing in the field of stochastic processes analysis. Using a Quantum…
The possibility of simulating a stochastic process by the intrinsic randomness of quantum system is investigated. Two simulations of Markov Chains by the measurements of quantum systems are proposed.
Markov processes are popular mathematical models, studied by theoreticians for their intriguing properties, and applied by practitioners for their flexible structure. With this book we teach how to model and analyze Markov processes. We…
Non-Markovian quantum processes exhibit different memory effects when measured in different ways; an unambiguous characterization of memory length requires accounting for the sequence of instruments applied to probe the system dynamics.…
We construct a large class of non-Markovian master equations that describe the dynamics of open quantum systems featuring strong memory effects, which relies on a quantum generalization of the concept of classical semi-Markov processes.…
We consider Markov processes, which describe e.g. queueing network processes, in a random environment which influences the network by determining random breakdown of nodes, and the necessity of repair thereafter. Starting from an explicit…
The non-Markovianity of the stochastic process called the quantum semi-Markov (QSM) process is studied using a recently proposed quantification of memory based on the deviation from semigroup evolution, that provides a unified description…
A number of ideas and questions related to the construction of quantum processes are discussed. Quantum state extension, entanglement and asymptotic behaviour of the entropy are some of the issues explored. These topics are studied in more…
A process model of quantum mechanics utilizes a combinatorial game to generate a discrete and finite causal space upon which can be defined a self-consistent quantum mechanics. An emergent space-time M and continuous wave function arise…
We provide a systematic study of the notion of duality of Markov processes with respect to a function. We discuss the relation of this notion with duality with respect to a measure as studied in Markov process theory and potential theory…
The act of describing how a physical process changes a system is the basis for understanding observed phenomena. For quantum-mechanical processes in particular, the affect of processes on quantum states profoundly advances our knowledge of…
We derive a necessary and sufficient condition for a quantum process to be Markovian which coincides with the classical one in the relevant limit. Our condition unifies all previously known definitions for quantum Markov processes by…
The program relative to the investigation of quantum Markov states for spin chains based on Canonical Anticommutation Relations algebra is carried on. This analysis provides a further step for a satisfactory theory of quantum Markov…
In this paper we propose a (sub)distribution-based bisimulation for labelled Markov processes and compare it with earlier definitions of state and event bisimulation, which both only compare states. In contrast to those state-based…
We introduce and study a family of Markov processes on partitions. The processes preserve the so-called z-measures on partitions previously studied in connection with harmonic analysis on the infinite symmetric group. We show that the…
In this paper, we introduce the notion of Bi-entangled hidden Markov processes. These are hidden quantum processes where the hidden processes themselves exhibit entangled Markov process, and the observable processes also exhibit…
We investigate the stability of quantum Markov processes with respect to perturbations of their transition maps. In the first part, we introduce a condition number that measures the sensitivity of fixed points of a quantum channel to…
The representation of numbers by product states in quantum mechanics can be extended to the representation of words and word sequences in languages by product states. This can be used to study quantum systems that generate text that has…