# Norms of quantum Gaussian multi-mode channels

## TL;DR

This paper calculates the norms of multi-mode Gaussian channels in quantum information theory, confirming key conjectures about their optimality and multiplicativity properties.

## Contribution

It provides a general computation of the Schatten space norms for Gaussian channels, verifying the Gaussian optimizer and multiplicativity conjectures.

## Key findings

- Verified the Gaussian optimizer conjecture for these channels
- Confirmed the multiplicativity conjecture in this setting
- Computed the $
orm{ ext{Gaussian channel}}_{ ext{Schatten}}$ explicitly

## Abstract

We compute the $\mathcal S^p \to \mathcal S^p$ norm of a general Gaussian gauge-covariant multi-mode channel for any $1\leq p<\infty$, where $\mathcal S^p$ is a Schatten space. As a consequence, we verify the Gaussian optimizer conjecture and the multiplicativity conjecture in these cases.