$k$-Entanglement Measure for Multipartite Systems without Convex-Roof Extensions and its Evaluation

• URL: http://arxiv.org/abs/2512.12588v1
• Date: Sun, 14 Dec 2025 07:51:23 GMT
• Title: $k$-Entanglement Measure for Multipartite Systems without Convex-Roof Extensions and its Evaluation
• Authors: Jie Guo, Shuyuan Yang, Jinchuan Hou, Xiaofei Qi, Kan He,
• Abstract summary: Multipartite entanglement underpins quantum technologies but its study is limited by the lack of universal measures.<n>We introduce the first emphtrue $k$-entanglement measure, $E_w(k,n)$, which satisfies all axioms.<n>A universal algorithm evaluates arbitrary finite-dimensional states, with open-source software covering all partitions of four-qubit systems.
• Score: 12.462680093105286
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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