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Markovianity of the quantum open system processes is a topic of the considerable current interest. Typically, invertibility is assumed to be non-essential for Markovianity of the open-quantum-system dynamical maps. Nevertheless, in this…
The study of time-inhomogeneous Markov jump processes is a traditional topic within probability theory that has recently attracted substantial attention in various applications. However, their flexibility also incurs a substantial…
Is quantum mechanics about 'states'? Or is it basically another kind of probability theory? It is argued that the elementary formalism of quantum mechanics operates as a well-justified alternative to 'classical' instantiations of a…
A major question in our understanding of the fabric of the world is where the randomness of some quantum phenomena comes from and how to represent it in a rational theory. The statistical interpretation of quantum mechanics made its way…
I propose to treat quantum evolution as a stochastic process consisting from a sequence of doubly stochastic matrices, which naturally arise in the generalized quantum evolution. Then it is proved that the law of non-decreasing entropy is…
Quantum stochastic master equations of jump type are formulated in a general way and connections with quantum/classical hybrid systems and quantum filtering theory are discussed. By introducing the notion of ``typical trajectory", we show…
The paper deals with a certain class of random evolutions. We develop a construction that yields an invariant measure for a continuous-time Markov process with random transitions. The approach is based on a particular way of constructing…
We celebrate this year hundred years of quantum mechanics but there is still no consensus regarding its interpretation and limitations. In this article we advocate the statistical contextual interpretation which is free of paradoxes. State…
This paper presents a comprehensive review of stochastic processes, with a particular focus on Markov chains and jump processes. The main results related to queuing systems are analyzed. Additionally, conditions that ensure the stability,…
The descriptions of the quantum realm and the macroscopic classical world differ significantly not only in their mathematical formulations but also in their foundational concepts and philosophical consequences. When and how physical systems…
Quantum trajectories of a Markovian open quantum system arise from the back-action of measurements performed in the environment with which the system interacts. In this work, we consider counting measurements of quantum jumps, corresponding…
A systematic exposition of scale functions is given for positive self-similar Markov processes (pssMp) with one-sided jumps. The scale functions express as convolution series of the usual scale functions associated with spectrally one-sided…
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.
We present a comprehensive and up to date review on the concept of quantum non-Markovianity, a central theme in the theory of open quantum systems. We introduce the concept of quantum Markovian process as a generalization of the classical…
The question about the existence of so-called ``hidden'' variables in quantum mechanics and the perception of the completeness of quantum mechanics are two sides of the same coin. Quantum analytical mechanics constitutes a completion of…
A jumping process, defined in terms of jump size distribution and waiting time distribution, is presented. The jumping rate depends on the process value. The process, which is Markovian and stationary, relaxes to an equilibrium and is…
Quantum walks are a promising framework that can be used to both understand and implement quantum information processing tasks. The quantum stochastic walk is a recently developed framework that combines the concept of a quantum walk with…
While ultimately they are described by quantum mechanics, macroscopic mechanical systems are nevertheless observed to follow the trajectories predicted by classical mechanics. Hence, in the regime defining macroscopic physics, the…
We investigate a new symmetry of the large deviation function of certain time-integrated currents in non-equilibrium systems. The symmetry is similar to the well-known Gallavotti-Cohen-Evans-Morriss-symmetry for the entropy production, but…
We present a detailed study of a simple quantum stochastic process, the quantum phase space Brownian motion, which we obtain as the Markovian limit of a simple model of open quantum system. We show that this physical description of the…