Center-of-Mass Tomography and Wigner Function for Multimode Photon States

Abstract

Tomographic probability representation of multimode electromagnetic field states in the scheme of center-of-mass tomography is reviewed. Both connection of the field state Wigner function and observable Weyl symbols with the center-of-mass tomograms as well as connection of Grönewold kernel with the center-of-mass tomographic kernel determining the noncommutative product of the tomograms are obtained. The dual center-of-mass tomogram of the photon states are constructed and the dual tomographic kernel is obtained. The models of other generalised center-of-mass tomographies are discussed. Example of two-mode Schrödinger cat states is presented in details.

Dynamics of System States in the Probability Representation of Quantum Mechanics

“…There is another type of tomography, named center-of-mass tomography. It was introduced in [56] and developed in [57,58]. In center-of-mass tomography, the state is determined by the center-of-mass tomogram.…”

Dynamics of System States in the Probability Representation of Quantum Mechanics

“…Since the system state tomogram is given by the symbol of the density operator ρ(t), i.e. (50), where the density operator evolution for the von Neumann equation is described by the evolution operator û(t), i.e. ρ(t) = û(t) ρ(0) û † (t) the symbol of the density operator can be rewritten in the form Tr ρ(0)δ(X − µ û † (t) q û(t) − ν û † (t) p û(t) .…”

“…There is another type of tomography, named the center-of-mass tomography. It was introduced in [49] and developed in [50,51]. In the center-of-mass tomography the state is determined by the center-of-mass tomogram.…”

Characterization of the nonlinear qubit map using the probability parametrization

“…(a) E-mail: dudinets@phystech.edu Along with the conventional description of states in quantum mechanics using vectors in a Hilbert space or density matrices, there are many alternative descriptions such as, for example, probability distributions or quantum tomograms. The corresponding representation of quantum mechanics is called the tomographic probability representation [3,4] (see also recent publications [5,6]). In this representation the states of a quantum system are described by probability distributions.…”