Permutation symmetry for the tomographic probability distribution of a system of identical particles

TL;DR

This paper explores how permutation symmetry affects the tomographic probability distributions of identical particles, linking group actions on density matrices to their tomograms, with explicit examples involving a two-dimensional harmonic oscillator.

Contribution

It introduces a method to analyze permutation symmetry directly on tomograms, extending the understanding of symmetry properties from density matrices to probability distributions.

Findings

Permutation symmetry can be represented on tomograms.

Explicit calculations for a two-dimensional harmonic oscillator.

The approach bridges density matrix symmetry and tomographic probability distributions.

Abstract

The symmetry properties under permutation of tomograms representing the states of a system of identical particles are studied. Starting from the action of the permutation group on the density matrix we define its action on the tomographic probability distribution. Explicit calculations are performed in the case of the two-dimensional harmonic oscillator.