# Gaussian maximizers for quantum Gaussian observables and ensembles

## TL;DR

This paper proves that for multimode bosonic systems with gauge symmetry, the classical capacity of Gaussian observables and the accessible information of Gaussian ensembles are achieved by Gaussian states and measurements, extending known single-mode results.

## Contribution

It establishes that Gaussian ensembles optimize classical capacity and accessible information in multimode bosonic systems, generalizing single-mode findings.

## Key findings

- Classical capacity of Gaussian observables is attained on Gaussian ensembles.
- Accessible information of Gaussian ensembles is achieved by multimode heterodyne measurement.
- Results extend single-mode Gaussian optimization to multimode systems.

## Abstract

In this paper we prove two results related to the Gaussian optimizers conjecture for multimode bosonic system with gauge symmetry. First, we argue that the classical capacity of a Gaussian observable is attained on a Gaussian ensemble of coherent states. This generalizes results previously known for heterodyne measurement in one mode. By using this fact and continuous variable version of ensemble-observable duality, we prove an old conjecture that accessible information of a Gaussian ensemble is attained on the multimode generalization of the heterodyne measurement.