Gaussian Maximizers for Quantum Gaussian Observables and Ensembles

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 an arbitrary 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 arbitrary Gaussian ensemble is attained on the multimode generalization of the heterodyne measurement.