Hierarchies of quantum non-Gaussian coherences for bosonic systems: A theoretical study

TL;DR

This paper develops a hierarchical framework for analyzing quantum non-Gaussian coherence in bosonic systems, focusing on context-dependent certification to better understand and classify quantum resources under realistic noise conditions.

Contribution

It introduces a novel hierarchical classification of quantum coherence in bosonic systems based on context-dependent certification, enhancing analysis of non-Gaussian quantum resources.

Findings

Hierarchies effectively classify quantum coherence in bosonic systems.

Framework remains robust under loss and thermal noise.

Versatile approach applicable to multi-state and multi-mode systems.

Abstract

Quantum coherence in bosonic systems is a fundamental resource for quantum technology applications. In this work, we introduce a framework for analyzing coherence in the Fock-state basis, utilizing context-dependent certification to reveal the quantum non-Gaussian nature of the tested coherence. Rather than relying on global coherence measures, our approach targets specific aspects of coherence, enabling a tailored hierarchical classification. We derive and compare two distinct hierarchies, each representing a different context for coherence in bosonic systems. Motivated by current advancements in optical quantum state engineering, we assess the feasibility and depth of these hierarchies under conditions of loss and thermal noise. The methodology introduced here is versatile and can be extended to multi-state and multi-mode coherences, making it adaptable to a wide range of experimental scenarios and platforms.