Generalized entanglement of purification criteria for 2-producible states in multipartite systems.
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| Title: | Generalized entanglement of purification criteria for 2-producible states in multipartite systems. |
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| Authors: | Jin, Tian-Ren1,2 (AUTHOR), Zhang, Yu-Ran3 (AUTHOR) yuranzhang@scut.edu.cn, Fan, Heng1,2,4,5,6,7 (AUTHOR) hfan@iphy.ac.cn |
| Source: | Journal of Physics A: Mathematical & Theoretical. 2026, Vol. 59 Issue 13, p1-28. 28p. |
| Subjects: | Quantum entanglement, Quantum states, Quantum communication, Quantum information theory, Kronecker products |
| Abstract: | Multipartite entanglement has a much more complex structure than bipartite entanglement. A state that lacks generic multipartite entanglement is 2-producible, i.e. it can be written as a tensor product of at most 2-partite entangled states. Recently, it has been proved that a tripartite pure state is 2-producible if and only if the gap between the entanglement of purification and its lower bound vanishes. Here, we show that the entanglement of purification gap is insufficient to detect more than tripartite entanglement in 4-partite stabilizer states. We then generalize entanglement of purification to the multipartite cases, and demonstrate that a multipartite pure state is 2-producible if and only if all the generalized entanglement of purification gaps vanish. The generalized entanglement of purification gap quantifies the quantum communication cost for redistributing one part of the system to the others, and also relates to the local recoverability of a multipartite state and the relative entropy between that state and 2-producible states. Moreover, we calculate the generalized entanglement of purification for states satisfying the general Schmidt decomposition, which implies that 4-partite stabilizer states do not necessarily have a general Schmidt decomposition. Our results provide a quantitative characterization of multipartite entanglement in multipartite system, which will promote further investigations and understanding of multipartite entanglement. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Physics A: Mathematical & Theoretical is the property of IOP Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 192699129 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Generalized entanglement of purification criteria for 2-producible states in multipartite systems. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Jin%2C+Tian-Ren%22">Jin, Tian-Ren</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Zhang%2C+Yu-Ran%22">Zhang, Yu-Ran</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> yuranzhang@scut.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Fan%2C+Heng%22">Fan, Heng</searchLink><relatesTo>1,2,4,5,6,7</relatesTo> (AUTHOR)<i> hfan@iphy.ac.cn</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Physics+A%3A+Mathematical+%26+Theoretical%22">Journal of Physics A: Mathematical & Theoretical</searchLink>. 2026, Vol. 59 Issue 13, p1-28. 28p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Quantum+entanglement%22">Quantum entanglement</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+states%22">Quantum states</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+communication%22">Quantum communication</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+information+theory%22">Quantum information theory</searchLink><br /><searchLink fieldCode="DE" term="%22Kronecker+products%22">Kronecker products</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Multipartite entanglement has a much more complex structure than bipartite entanglement. A state that lacks generic multipartite entanglement is 2-producible, i.e. it can be written as a tensor product of at most 2-partite entangled states. Recently, it has been proved that a tripartite pure state is 2-producible if and only if the gap between the entanglement of purification and its lower bound vanishes. Here, we show that the entanglement of purification gap is insufficient to detect more than tripartite entanglement in 4-partite stabilizer states. We then generalize entanglement of purification to the multipartite cases, and demonstrate that a multipartite pure state is 2-producible if and only if all the generalized entanglement of purification gaps vanish. The generalized entanglement of purification gap quantifies the quantum communication cost for redistributing one part of the system to the others, and also relates to the local recoverability of a multipartite state and the relative entropy between that state and 2-producible states. Moreover, we calculate the generalized entanglement of purification for states satisfying the general Schmidt decomposition, which implies that 4-partite stabilizer states do not necessarily have a general Schmidt decomposition. Our results provide a quantitative characterization of multipartite entanglement in multipartite system, which will promote further investigations and understanding of multipartite entanglement. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Physics A: Mathematical & Theoretical is the property of IOP Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1088/1751-8121/ae5515 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 28 StartPage: 1 Subjects: – SubjectFull: Quantum entanglement Type: general – SubjectFull: Quantum states Type: general – SubjectFull: Quantum communication Type: general – SubjectFull: Quantum information theory Type: general – SubjectFull: Kronecker products Type: general Titles: – TitleFull: Generalized entanglement of purification criteria for 2-producible states in multipartite systems. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Jin, Tian-Ren – PersonEntity: Name: NameFull: Zhang, Yu-Ran – PersonEntity: Name: NameFull: Fan, Heng IsPartOfRelationships: – BibEntity: Dates: – D: 03 M: 04 Text: 2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 17518113 Numbering: – Type: volume Value: 59 – Type: issue Value: 13 Titles: – TitleFull: Journal of Physics A: Mathematical & Theoretical Type: main |
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