Related papers: Probability representation of quantum observable a…
We develop an approach where the quantum system states and quantum observables are described as in classical statistical mechanics -- the states are identified with probability distributions and observables, with random variables. An…
We give a review of the tomographic probability representation of quantum mechanics. We present the formalism of quantum states and quantum observables using the formalism of standard probability distributions and classical-like random…
Symplectic and optical joint probability representations of quantum mechanics are considered, in which the functions describing the states are the probability distributions with all random arguments (except the argument of time ). The…
Using the known possibility to associate the completely positive maps with density matrices and recent results on expressing the density matrices with sets of classical probability distributions of dichotomic random variables we construct…
The gauge invariance of the evolution equations of tomographic probability distribution functions of quantum particles in an electromagnetic field is illustrated. Explicit expressions for the transformations of ordinary tomograms of states…
The positive vector optical tomogram fully describing the quantum state of spin 1/2 particle without any redundancy is introduced. Reciprocally the vector symplectic tomogram and vector quasidistributions $\vec W({\mathbf q},{\mathbf p})$,…
The nine-component positive vector optical tomographic probability portrait of quantum state of spin-1 particles containing full spatial and spin information about the state without redundancy is constructed. Also the suggested approach is…
The recently proposed probability representation of quantum mechanics is generalized to quantum field theory. We introduce a probability distribution functional for field configurations and find an evolution equation for such a…
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…
The von Neumann evolution equation for density matrix and the Moyal equation for the Wigner function are mapped onto evolution equation for optical tomogram of quantum state. The connection with known evolution equation for symplectic…
Partial symplectic conditional and joint probability representations of quantum mechanics are considered. The correspondence rules for most interesting physical operators are found and the expressions of the dual symbols of operators are…
Description of system containing classical and quantum subsystems by means of tomographic probability distributions is considered. Evolution equation of the system states is studied.
Introduced recently approach based on tomographic probability distribution of quantum states is shown to be closely related with the known notion of the quantum probability measures discussed in quantum information theory and positive…
The tomographic probability distribution is used to decribe the kinetic equations for open quantum systems. Damped oscillator is studied. Purity parameter evolution for different damping regime is considered.
Probability representation entropy (tomographic entropy) of arbitrary quantum state is introduced. Using the properties of spin tomogram to be standard probability distribution function the tomographic entropy notion is discussed. Relation…
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…
In this paper we propose the idea that there is a corresponding relation between quantum states and points of the complex projective space, given that the number of dimensions of the Hilbert space is finite. We check this idea through…
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…
We consider the problem of the driven harmonic oscillator in the probability representation of quantum mechanics, where the oscillator states are described by fair nonnegative probability distributions of position measured in rotated and…
The probability representation, in which cosmological quantum states are described by a standard positive probability distribution, is constructed for minisuperspace models selected by Noether symmetries. In such a case, the tomographic…