Non-Gaussian Entanglement Hierarchy Based on the Schmidt Number

2026/05/18 by Jiajie Guo, Shuheng Liu, Matteo Fadel +1 · 1 voice
Physics and Astronomy · #quant-ph

paper · pdf

arxiv published 2026/05/18 · arxiv updated 2026/05/26

Abstract

Non-Gaussian entanglement is a promising resource in various quantum tasks. A recently defined class identifies entanglement that cannot be generated by applying Gaussian operations to separable inputs. To further explore the entanglement in this context, we introduce a quantitative witness E_{\rm NG} in bipartite bosonic systems, which satisfies E_{\rm NG}=1 for all Gaussian-entanglable states, while E_{\rm NG}>1 certifies non-Gaussian entanglement. Its ceiling d=\lceil E_{\rm NG}\rceil provides a lower bound on the Schmidt number irreducible by Gaussian transformations, thereby defining a natural hierarchy of non-Gaussian entanglement. For pure states, the condition is sharp and the hierarchy reflects the complexity of state learning. We benchmark the framework with some paradigmatic non-Gaussian states, such as NOON states and squeezed Kerr states, and analyze its robustness against loss. Moreover, we construct an experimentally economical NOON-type witness requiring only four density-matrix element measurements. These results establish an operationally meaningful and experimentally accessible framework for identifying non-Gaussian entanglement resources in continuous-variable quantum platforms.

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Discussions

• Next, a new preprint from Shuheng looking at how to distinguish between different kinds of non-Gaussian entanglement using our old friend the Schmidt number! arxiv.org/abs/2605.18605 [bsky, 1 points, 0 comments]