Center of mass tomography and Wigner function for multimode photon states

TL;DR

This paper reviews the center-of-mass tomography approach for multimode photon states, linking Wigner functions and observable symbols with tomograms, and explores dual tomograms and generalized models with examples.

Contribution

It introduces a comprehensive framework connecting Wigner functions, Weyl symbols, and tomograms in center-of-mass tomography for multimode photon states, including dual tomograms and generalized models.

Findings

Derived connection between Wigner functions and tomograms.

Constructed dual center-of-mass tomograms for photon states.

Analyzed two-mode Schrödinger cat states in detail.

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 Gr\"onewold 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 Schr\"odinger cat states is presented in details