Related papers: Partial symplectic quantum tomography schemes. Obs…
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…
The dynamical equation of quantum mechanics are rewritten in form of dynamical equations for the measurable, positive marginal distribution of the shifted, rotated and squeezed quadrature introduced in the so called "symplectic tomography".…
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…
On the base of symplectic quantum tomogram we define a probability distribution on the plane. The dual map transfers all observables which are polynomials of the position and momentum operators to the set of polynomials of two variables. In…
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…
A review of the photon-number tomography and symplectic tomography as examples of star-product quantization is presented. The classical statistical mechanics is considered within the framework of the tomographic representation.
The review of star-product formalism providing the possibility to describe quantum states and quantum observables by means of the functions called symbols of operators which are obtained by means of bijective maps of the operators acting in…
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 probability representation of quantum and classical statistical mechanics is discussed. Symplectic tomography, center-of-mass tomography, and spin tomography are studied. The connection of tomographic probabilities with dynamic…
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…
We introduce the probability distributions describing quantum observables in conventional quantum mechanics and clarify their relations to the tomographic probability distributions describing quantum states. We derive the evolution equation…
By using a generalization of the optical tomography technique we describe the dynamics of a quantum system in terms of equations for a purely classical probability distribution which contains complete information about the system.
A review of the symplectic tomographic approaches within the framework of star-product quantization is presented. The classical statistical mechanics within the framework of the tomographic representation is considered. The kernels of…
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…
This paper combines probabilistic and algebraic techniques for computing quantum expectations of operator exponentials (and their products) of quadratic forms of quantum variables in Gaussian states. Such quadratic-exponential functionals…
It is usually believed that a picture of Quantum Mechanics in terms of true probabilities cannot be given due to the uncertainty relations. Here we discuss a tomographic approach to quantum states that leads to a probability representation…
Explicit expressions for most interesting quantum operators in optical tomography representation are found. General formalism of symbols of operators is presented in optical tomographic representation. The symbols of the operators are found…
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…
Based on a geometric picture, the example of free particle motion for both classical and quantum domains is considered in the tomographic probability representation. Wave functions and density operators as well as optical and symplectic…