Related papers: Linking Classical and Quantum Stochastic Processes
The field of classical stochastic processes forms a major branch of mathematics. They are, of course, also very well studied in biology, chemistry, ecology, geology, finance, physics, and many more fields of natural and social sciences.…
Quantum baker`s map is a model of chaotic system. We study quantum dynamics for the quantum baker's map. We use the Schack and Caves symbolic description of the quantum baker`s map. We find an exact expression for the expectation value of…
I develop a theory of classicality from quantum systems. This theory stems from the study of classical and quantum stationary stochastic processes. The stochastic processes are characterized by polyhedral (classical) and semidefinite…
We formulate the notion of quantum channels in the framework of quantum tomography and address there the issue of whether such maps can be regarded as classical stochastic maps. In particular kernels of maps acting on probability…
Stochastic matrices and positive maps in matrix algebras proved to be very important tools for analysing classical and quantum systems. In particular they represent a natural set of transformations for classical and quantum states,…
Full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components and assemble them so that they communicate and cooperate.Moreover, to model concurrent and…
Quantum channels describe subsystem or open system evolution. Using the classical Koopman operator that evolves functions on phase space, 4 classical Koopman channels are identified that are analogs of the 4 possible quantum channels in a…
Quantum computations operate in the quantum world. For their results to be useful in any way, there is an intrinsic necessity of cooperation and communication controlled by the classical world. As a consequence, full formal descriptions of…
Full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components, as well as communications between these components. Moreover, to model concurrent and…
We develop some classical descriptions for processes in the Schwarzschild string atmosphere. These processes suggest relationships between macroscopic and microscopic scales. The classical descriptions developed in this essay highlight the…
We connect quantum graphs with infinite leads, and turn them to scattering systems. We show that they display all the features which characterize quantum scattering systems with an underlying classical chaotic dynamics: typical poles, delay…
The main goal of these notes is to give an introduction to the mathematics of quantum noise and some of its applications in non-equilibrium statistical mechanics. We start with some reminders from the theory of classical stochastic…
In this paper for the first time, we construct quantum analogs starting from classical stochastic processes, by replacing random which path decisions with superpositions of all paths. This procedure typically leads to non-unitary quantum…
In quantum mechanics, wave functions and density matrices represent our knowledge about a quantum system and give probabilities for the outcomes of measurements. If the combined dynamics and measurements on a system lead to a density matrix…
We exploit mappings between quantum and classical systems in order to obtain a class of two-dimensional classical systems with critical properties equivalent to those of the class of one-dimensional quantum systems discussed in a companion…
Recent years have seen a flurry of research activity in the study of minimal and autonomous information ratchets. However, the existing classical and quantum models are somewhat hard to compare, and, hence, quantifying possible quantum…
Recent experimental advances have inspired the development of theoretical tools to describe the non-equilibrium dynamics of quantum systems. Among them an exact representation of quantum spin systems in terms of classical stochastic…
A density matrix formulation of classical bipartite correlations is constructed. This leads to an understanding of the appearance of classical statistical correlations intertwined with the quantum correlations as well as a physical…
Quantum stochastic differential equations have been used to describe the dynamics of an atom interacting with the electromagnetic field via absorption/emission processes. Here, by using the full quantum stochastic Schroedinger equation…
We present a both simple and comprehensive graphical calculus for quantum computing. In particular, we axiomatize the notion of an environment, which together with the earlier introduced axiomatic notion of classical structure enables us to…