Related papers: Partial symplectic quantum tomography schemes. Obs…
Within the framework of the probability representation of quantum mechanics, we study a superposition of generic Gaussian states associated to symmetries of a regular polygon of n sides; in other words, the cyclic groups (containing the…
It is proposed the scheme of quantum mechanics, in which a Hilbert space and the linear operators are not primary elements of the theory. Instead of it certain variant of the algebraic approach is considered. The elements of noncommutative…
Some inequalities for probability vector are discussed. The probability representation of quantum mechanics where the states are mapped onto probability vectors (either finite or infinite dimensional) called the state tomograms is used.…
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…
Invertible maps from operators of quantum obvservables onto functions of c-number arguments and their associative products are first assessed. Different types of maps like Weyl-Wigner-Stratonovich map and s-ordered quasidistribution are…
We discuss the classical statistics of isolated subsystems. Only a small part of the information contained in the classical probability distribution for the subsystem and its environment is available for the description of the isolated…
Special stochastic representation of the wave function in Quantum Mechanics (QM), based on soliton realization of extended particles, is suggested with the aim to model quantum states via classical computer. Entangled solitons construction…
This paper is concerned with quadratic-exponential moments (QEMs) for dynamic variables of quantum stochastic systems with position-momentum type canonical commutation relations. The QEMs play an important role for statistical…
Stochastic representation for interaction of quantum systems is formulated which allows to replace some of them by equivalent but purely commutative random sources. The formalism is applied to two-level systems interacting with Gaussian…
Probabilistic cellular automata with deterministic updating are quantum systems. We employ the quantum formalism for an investigation of random probabilistic cellular automata, which start with a probability distribution over initial…
In this work, we consider a probability representation of quantum dynamics for finite-dimensional quantum systems with the use of pseudostochastic maps acting on true probability distributions. These probability distributions are obtained…
The question of the representation of quantum stationary partially polarized waves as random superpositions of different polarization ellipses is addressed. To this end, the Bohmian formulation of quantum mechanics is considered and…
The "marginal" distributions for measurable coordinate and spin projection is introduced. Then, the analog of the Pauli equation for spin-1/2 particle is obtained for such probability distributions instead of the usual wave functions. That…
The symlectic quantum tomography for the general linear quantization is introduced. Using the approach based upon the Wigner function techniques the evolution equation of quantum tomograms is derived for a parametric driven oscillator.
A general prescription for the treatment of constrained quantum motion is outlined. We consider in particular constraints defined by algebraic submanifolds of the quantum state space. The resulting formalism is applied to obtain solutions…
The contextuality and noncontextuality notions are considered in framework of probability representation of quantum states. Example of qutrit states and violation of the noncontextuality inequalities are presented by using the spin tomogram…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, Born rule,…
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…
The probability representation for quantum states of the universe in which the states are described by a fair probability distribution instead of wave function (or density matrix) is developed to consider cosmological dynamics. The…
In a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented. Here the application of this formalism to the system of a particle moving on a…