# Photon-number tomography of multimode states and positivity of the density matrix

## TL;DR

This paper calculates photon-number tomograms for Gaussian quantum states in multimode light using multivariable Hermite polynomials, establishing that tomogram positivity is necessary for the density matrix's positivity.

## Contribution

It provides explicit formulas for photon-number tomograms of Gaussian states and links tomogram positivity to density matrix positivity.

## Key findings

- Explicit formulas for multimode Gaussian state tomograms
- Positivity of tomograms is necessary for density matrix positivity
- Use of multivariable Hermite polynomials in quantum state analysis

## Abstract

For one-mode and multimode light, the photon-number tomograms of Gaussian quantum states are explicitly calculated in terms of multivariable Hermite polynomials. Positivity of the tomograms is shown to be necessary condition for positivity of the density matrix.