Non-Gaussian Entanglement Hierarchy Based on the Schmidt Number

• URL: http://arxiv.org/abs/2605.18605v2
• Date: Tue, 26 May 2026 12:28:09 GMT
• Title: Non-Gaussian Entanglement Hierarchy Based on the Schmidt Number
• Abstract summary: Non-Gaussian entanglement is a promising resource in various quantum tasks.<n>We introduce a quantitative witness $E_rm NG$ in bipartite bosonic systems.<n>We benchmark the framework with some paradigmatic non-Gaussian states, such as NOON states and squeezed Kerr states.
• Score: 2.999888908665658
• License: http://creativecommons.org/licenses/by/4.0/
• 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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