$k$-Entanglement Measure for Multipartite Systems without Convex-Roof Extensions and its Evaluation
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915673356107776 |
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| author | Guo, Jie Yang, Shuyuan Hou, Jinchuan Qi, Xiaofei He, Kan |
| author_facet | Guo, Jie Yang, Shuyuan Hou, Jinchuan Qi, Xiaofei He, Kan |
| contents | Multipartite entanglement underpins quantum technologies but its study is limited by the lack of universal measures, unified frameworks, and the intractability of convex-roof extensions. We establish an axiomatic framework and introduce the first \emph{true} $k$-entanglement measure, $E_w^{(k,n)}$, which satisfies all axioms, establishes $k$-entanglement as a multipartite quantum resource, avoids convex-roof constructions, and is efficiently computable. A universal algorithm evaluates arbitrary finite-dimensional states, with open-source software covering all partitions of four-qubit systems. Numerical tests certify $k$-entanglement within 200 seconds, consistent with necessary-and-sufficient criteria, tightening bounds and revealing new thresholds. This framework offers a scalable, practical tool for rigorous multipartite entanglement quantification. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12588 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $k$-Entanglement Measure for Multipartite Systems without Convex-Roof Extensions and its Evaluation Guo, Jie Yang, Shuyuan Hou, Jinchuan Qi, Xiaofei He, Kan Quantum Physics Multipartite entanglement underpins quantum technologies but its study is limited by the lack of universal measures, unified frameworks, and the intractability of convex-roof extensions. We establish an axiomatic framework and introduce the first \emph{true} $k$-entanglement measure, $E_w^{(k,n)}$, which satisfies all axioms, establishes $k$-entanglement as a multipartite quantum resource, avoids convex-roof constructions, and is efficiently computable. A universal algorithm evaluates arbitrary finite-dimensional states, with open-source software covering all partitions of four-qubit systems. Numerical tests certify $k$-entanglement within 200 seconds, consistent with necessary-and-sufficient criteria, tightening bounds and revealing new thresholds. This framework offers a scalable, practical tool for rigorous multipartite entanglement quantification. |
| title | $k$-Entanglement Measure for Multipartite Systems without Convex-Roof Extensions and its Evaluation |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2512.12588 |