Gaussian maximizers for quantum Gaussian observables and ensembles

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.

18 pages; Presentation improved. Gauge invariance discussed in detail

References in corpus (1)

• Information capacity of continuous variable measurement channel

Cited by in corpus (6)

• On the classical capacity of quantum Gaussian measurement
• Deep thermalization in Gaussian continuous-variable quantum systems
• Accessible information of a general quantum Gaussian ensemble
• Proof of the Gaussian maximizers conjecture for the communication capacity of noisy heterodyne measurements
• The structure of general quantum Gaussian observable
• Pretty good measurement for bosonic Gaussian ensembles