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Advanced Quantum Technologies

Genuine Multipartite Entanglement Measures Based on Information Complete of Reduced States

Zhi‐Xiang Jin, Massimo Lai, Bing Yu, Wei Chen, Yan‐Ling Wang

Published Jul 9, 2025• 1 citation
Publisher

Abstract

Abstract Quantifying genuine entanglement is a crucial task in quantum information theory. In this work, a new genuine multipartite entanglement measure based on informationally complete entanglement is proposed, termed the informationally complete genuine multipartite entanglement measure(ICGMEM). A set of entanglement inequalities for pure states in ‐partite systems is first established based on constraints on entanglement distribution. These inequalities reveal that the pairwise entanglement between any individual part of the system cannot exceed the collective entanglement of the remaining parts. Building on these inequalities, a series of geometric structures called informationally complete entanglement measure triangles is constructed and the ICGMEM is defined based on the geometric mean area of these triangles. These results demonstrate that the ICGMEM provides a more refined characterization of entanglement compared to existing well‐known measures. Furthermore, it is shown that the ICGMEM significantly enhances computational efficiency for analyzing genuinely entangled pure states, achieving up to a twofold improvement when the number of subsystems is sufficiently large. Through detailed examples, the advantages of the ICGMEM are illustrated, highlighting its effectiveness in distinguishing and quantifying entanglement in multipartite systems. This work can better advance the theoretical understanding of genuine multipartite entanglement.

DOI
10.1002/qute.202500247

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Genuine Multipartite Entanglement Measure Based on ααα-concurrence
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Abstract In this work, the framework of ‐nonseparability is utilized to investigate parameterized multipartite entanglement measures. A ‐nonseparable revised informationally complete entanglement measure(‐RICEM) is proposed for ‐partite quantum systems(), capable of identifying all ‐nonseparable states across arbitrary ‐partite configurations. The ‐RICEM offers enhanced resolution in entanglement characterization compared to conventional measures. It is proven that the proposed ‐nonseparable measure is a valid entanglement measure, satisfying entanglement monotonicity, convexity, and nonzero for ‐nonseparable states. Using properties of ‐concurrence under partial transposition and realignment, analytical lower bounds for mixed states in ‐RICEM are derived. Furthermore, operational connections between ‐RICEM and the global negativity measure are established. A comparative analysis between the genuine multipartite entanglement GME‐RICEM and existing genuine multipartite entanglement measures reveals distinct advantages in state discrimination capability.
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