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In recent years there has been a significant development of the dynamical map formalism for initially correlated states of a system and its environment. Based on some of these results, we study quantum process tomography for initially…

Dynamical maps describe general transformations of the state of a physical system, and their iteration can be interpreted as generating a discrete time evolution. Prime examples include classical nonlinear systems undergoing transitions to…

We use the fact that some linear Hamiltonian systems can be considered as ``finite level'' quantum systems, and the description of quantum mechanics in terms of probabilities, to associate probability distributions with this particular…

This research applies concepts from algorithmic probability to Boolean and quantum combinatorial logic circuits. A tutorial-style introduction to states and various notions of the complexity of states are presented. Thereafter, the…

Quantum probabilities are defined for several important physical cases characterizing measurements with multimode quantum systems. These are the probabilities for operationally testable measurements, for operationally uncertain…

The central physical concepts and mathematical techniques used in the theory of open quantum systems are reviewed. Particular emphasis is laid on the interrelations of apparently different approaches. Starting from the appropriate…

The quasidistributions corresponding to the diagonal representation of quantum states are discussed within the framework of operator-symbol construction. The tomographic-probability distribution describing the quantum state in the…

Tomograms introduced for the description of quantum states in terms of probability distributions are shown to be related to a standard star-product quantization with appropriate kernels. Examples of symplectic tomograms and spin tomograms…

The quantum density matrix generalises the classical concept of probability distribution to quantum theory. It gives the complete description of a quantum state as well as the observable quantities that can be extracted from it. Its…

Both the set of quantum states and the set of classical states described by symplectic tomographic probability distributions (tomograms) are studied. It is shown that the sets have common part but there exist tomograms of classical states…

We consider the problem of decoherence and relaxation of open bosonic quantum systems from a perspective alternative to the standard master equation or quantum trajectories approaches. Our method is based on the dynamics of expectation…

We review the formalism of center-of-mass tomograms that allows us to describe quantum states in terms of probability distribution functions. We introduce the concept of separable and entangled probability distributions for the…

In this article we propose a dynamic quantum tomography model for open quantum systems with evolution given by phase-damping channels. Mathematically, these channels correspond to completely positive trace-preserving maps defined by the…

In this work, the operator-sum representation of a quantum process is extended to the probability representation of quantum mechanics. It is shown that each process admitting the operator-sum representation is assigned a kernel, convolving…

Tomographic probability representation is introduced for fermion fields. The states of the fermions are mapped onto probability distribution of discrete random variables (spin projections). The operators acting on the fermion states are…

Quantum circuits generating probability distributions has applications in several areas. Areas like finance require quantum circuits that can generate distributions that mimic some given data pattern. Hamiltonian simulations require…

We revise fundamental concepts in the dynamics of open quantum systems in the light of modern developments in the field. Our aim is to present a unified approach to the quantum evolution of open systems that incorporates the concepts and…

In quantum physics, the theoretical study of unbound many-body systems is typically quite complex -- owing to the combination of their large spatial extension and the so-called {\it curse of dimensionality}. Often, such systems are studied…

The notion of standard positive probability distribution function (tomogram) which describes the quantum state of universe alternatively to wave function or to density matrix is introduced. Connection of the tomographic probability…

A possibility of describing two-level atom states in terms of positive probability distributions (analog to the symplectic tomography scheme) is considered. As a result the basis of the irreducible representation of a rotation group can be…