https://doi.org/10.1140/epjp/s13360-025-06570-z
Regular Article
Necessary and sufficient conditions on monogamy of multipartite entanglement
1
School of Computer Science and Technology, Dongguan University of Technology, 523808, Dongguan, People’s Republic of China
2
School of Mathematical Sciences, Capital Normal University, 100048, Beijing, People’s Republic of China
3
Max-Planck-Institute for Mathematics in the Sciences, 04103, Leipzig, Germany
4
Faculty of Science, Kunming University of Science and Technology, 650500, Kunming, People’s Republic of China
Received:
21
December
2024
Accepted:
23
June
2025
Published online:
6
July
2025
We investigate the monogamy of arbitrary quantum entanglement measures E for multipartite quantum systems. Equivalent condition for E to be monogamous in terms of the 
th power of E is explicitly derived. We first define some important equations related to some multipartite quantum states, and then, we show that the monogamy of an entanglement measure E only hangs on the boundedness of the solution set of some certain equations. Moreover, for some special quantum states, the equivalent conditions for monogamy are also valid for some given quantum correlations. Detailed examples are given to demonstrate our results.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
