Gaussian superpositions for bosonic encodings

TL;DR

This paper introduces an exact finite-manifold encoding for non-Gaussian bosonic states, enabling efficient analysis of their quantum properties and bridging continuous-variable resources with discrete-variable measures.

Contribution

The authors develop a novel finite-manifold encoding for Gaussian superpositions, allowing standard quantum-information tools to analyze non-Gaussian bosonic states efficiently.

Findings

Closed-form evaluations of entropies and non-Gaussianity.

Analytic expression for bipartite entanglement negativity.

Practical framework for benchmarking non-Gaussian resources.

Abstract

Non-Gaussian bosonic states are ubiquitous in interacting light--matter systems, many-body platforms, and relativistic quantum field settings, but their quantitative characterization is hindered by the infinite-dimensional Hilbert space and by the poor scalability of Fock-space truncation methods. We introduce an exact finite-manifold encoding for states supported on a finite span of Gaussian branches, enabling the use of standard finite-dimensional quantum-information tools directly on an effective density matrix whose entries are determined by Gaussian overlaps. As demonstrations, we obtain closed-form and numerically stable evaluations of entropies and relative-entropy non-Gaussianity, and derive an analytic expression for the bipartite entanglement negativity of arbitrary multimode two-branch Gaussian superpositions, including a minimal which-branch dephasing model. Our framework provides a practical bridge between experimentally accessible continuous-variable resources (e.g., cat-like and measurement-conditioned states) and discrete-variable information measures, with immediate applications to benchmarking non-Gaussian resources in several quantum technology platforms.