On the rank of extremal marginal states.
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| Title: | On the rank of extremal marginal states. |
|---|---|
| Authors: | Devendra, Repana1 (AUTHOR) ma16d020@smail.iitm.ac.in, Dey, Pankaj1 (AUTHOR) pankaj@math.iitb.ac.in, Dey, Santanu1 (AUTHOR) dey@math.iitb.ac.in |
| Source: | Linear Algebra & its Applications. May2026, Vol. 737, p146-172. 27p. |
| Subjects: | Quantum states, Density matrices, Matrices (Mathematics) |
| Abstract: | Given two invertible states ρ 1 on C d 1 and ρ 2 on C d 2 , the marginal state space C (ρ 1 , ρ 2) is defined as the set of all states ρ on C d 1 ⊗ C d 2 with partial traces ρ 1 and ρ 2. A fundamental result by K. R. Parthasarathy establishes that if ρ is an extreme point of the set C (ρ 1 , ρ 2) , then the rank of ρ does not exceed d 1 2 + d 2 2 − 1. A naturally raised question, also posed by Rudolph, is that are there any extreme points of C (ρ 1 , ρ 2) whose rank is equal to ⌊ d 1 2 + d 2 2 − 1 ⌋ , where ⌊ a ⌋ indicates the largest integer that does not exceed a. In 2010, Ohno gave an affirmative answer for low-dimensional matrix algebras M 3 and M 4. In this article, we provide a positive answer to the Rudolph question in various matrix algebras by explicitly constructing the extreme points of C (ρ 1 , ρ 2) whose rank is equal to ⌊ d 1 2 + d 2 2 − 1 ⌋. [ABSTRACT FROM AUTHOR] |
| Copyright of Linear Algebra & its Applications is the property of Elsevier B.V. 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: 192196631 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: On the rank of extremal marginal states. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Devendra%2C+Repana%22">Devendra, Repana</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> ma16d020@smail.iitm.ac.in</i><br /><searchLink fieldCode="AR" term="%22Dey%2C+Pankaj%22">Dey, Pankaj</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> pankaj@math.iitb.ac.in</i><br /><searchLink fieldCode="AR" term="%22Dey%2C+Santanu%22">Dey, Santanu</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> dey@math.iitb.ac.in</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Linear+Algebra+%26+its+Applications%22">Linear Algebra & its Applications</searchLink>. May2026, Vol. 737, p146-172. 27p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Quantum+states%22">Quantum states</searchLink><br /><searchLink fieldCode="DE" term="%22Density+matrices%22">Density matrices</searchLink><br /><searchLink fieldCode="DE" term="%22Matrices+%28Mathematics%29%22">Matrices (Mathematics)</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Given two invertible states ρ 1 on C d 1 and ρ 2 on C d 2 , the marginal state space C (ρ 1 , ρ 2) is defined as the set of all states ρ on C d 1 ⊗ C d 2 with partial traces ρ 1 and ρ 2. A fundamental result by K. R. Parthasarathy establishes that if ρ is an extreme point of the set C (ρ 1 , ρ 2) , then the rank of ρ does not exceed d 1 2 + d 2 2 − 1. A naturally raised question, also posed by Rudolph, is that are there any extreme points of C (ρ 1 , ρ 2) whose rank is equal to ⌊ d 1 2 + d 2 2 − 1 ⌋ , where ⌊ a ⌋ indicates the largest integer that does not exceed a. In 2010, Ohno gave an affirmative answer for low-dimensional matrix algebras M 3 and M 4. In this article, we provide a positive answer to the Rudolph question in various matrix algebras by explicitly constructing the extreme points of C (ρ 1 , ρ 2) whose rank is equal to ⌊ d 1 2 + d 2 2 − 1 ⌋. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Linear Algebra & its Applications is the property of Elsevier B.V. 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: 10.1016/j.laa.2026.02.011 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 27 StartPage: 146 Subjects: – SubjectFull: Quantum states Type: general – SubjectFull: Density matrices Type: general – SubjectFull: Matrices (Mathematics) Type: general Titles: – TitleFull: On the rank of extremal marginal states. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Devendra, Repana – PersonEntity: Name: NameFull: Dey, Pankaj – PersonEntity: Name: NameFull: Dey, Santanu IsPartOfRelationships: – BibEntity: Dates: – D: 15 M: 05 Text: May2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 00243795 Numbering: – Type: volume Value: 737 Titles: – TitleFull: Linear Algebra & its Applications Type: main |
| ResultId | 1 |
