Characterizing High Schmidt Number Witnesses in Arbitrary Dimensions System
| Title: | Characterizing High Schmidt Number Witnesses in Arbitrary Dimensions System |
|---|---|
| Authors: | Xiong, Liang, Sze, Nung-sing |
| Publication Year: | 2025 |
| Collection: | Computer Science Mathematics Mathematical Physics Quantum Physics |
| Subject Terms: | Quantum Physics, Mathematical Physics, Mathematics - Numerical Analysis, Mathematics - Spectral Theory |
| More Details: | A profound comprehension of quantum entanglement is crucial for the progression of quantum technologies. The degree of entanglement can be assessed by enumerating the entangled degrees of freedom, leading to the determination of a parameter known as the Schmidt number. In this paper, we develop an efficient analytical tool for characterizing high Schmidt number witnesses for bipartite quantum states in arbitrary dimensions. Our methods not only offer viable mathematical methods for constructing high-dimensional Schmidt number witnesses in theory but also simplify the quantification of entanglement and dimensionality. Most notably, we develop high-dimensional Schmidt number witnesses within arbitrary-dimensional systems, with our Schmidt witness coefficients relying solely on the operator Schmidt coefficient. Subsequently, we demonstrate our theoretical advancements and computational superiority by constructing Schmidt number witnesses in arbitrary dimensional bipartite quantum systems with Schmidt numbers four and five. |
| Document Type: | Working Paper |
| Access URL: | http://arxiv.org/abs/2504.11213 |
| Accession Number: | edsarx.2504.11213 |
| Database: | arXiv |
| FullText | Text: Availability: 0 CustomLinks: – Url: http://arxiv.org/abs/2504.11213 Name: EDS - Arxiv Category: fullText Text: View this record from Arxiv MouseOverText: View this record from Arxiv – Url: https://resolver.ebsco.com/c/xy5jbn/result?sid=EBSCO:edsarx&genre=article&issn=&ISBN=&volume=&issue=&date=20250415&spage=&pages=&title=Characterizing High Schmidt Number Witnesses in Arbitrary Dimensions System&atitle=Characterizing%20High%20Schmidt%20Number%20Witnesses%20in%20Arbitrary%20Dimensions%20System&aulast=Xiong%2C%20Liang&id=DOI: Name: Full Text Finder (for New FTF UI) (s8985755) Category: fullText Text: Find It @ SCU Libraries MouseOverText: Find It @ SCU Libraries |
|---|---|
| Header | DbId: edsarx DbLabel: arXiv An: edsarx.2504.11213 RelevancyScore: 1147 AccessLevel: 3 PubType: Report PubTypeId: report PreciseRelevancyScore: 1146.59155273438 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: Characterizing High Schmidt Number Witnesses in Arbitrary Dimensions System – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Xiong%2C+Liang%22">Xiong, Liang</searchLink><br /><searchLink fieldCode="AR" term="%22Sze%2C+Nung-sing%22">Sze, Nung-sing</searchLink> – Name: DatePubCY Label: Publication Year Group: Date Data: 2025 – Name: Subset Label: Collection Group: HoldingsInfo Data: Computer Science<br />Mathematics<br />Mathematical Physics<br />Quantum Physics – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Quantum+Physics%22">Quantum Physics</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+Physics%22">Mathematical Physics</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+-+Numerical+Analysis%22">Mathematics - Numerical Analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+-+Spectral+Theory%22">Mathematics - Spectral Theory</searchLink> – Name: Abstract Label: Description Group: Ab Data: A profound comprehension of quantum entanglement is crucial for the progression of quantum technologies. The degree of entanglement can be assessed by enumerating the entangled degrees of freedom, leading to the determination of a parameter known as the Schmidt number. In this paper, we develop an efficient analytical tool for characterizing high Schmidt number witnesses for bipartite quantum states in arbitrary dimensions. Our methods not only offer viable mathematical methods for constructing high-dimensional Schmidt number witnesses in theory but also simplify the quantification of entanglement and dimensionality. Most notably, we develop high-dimensional Schmidt number witnesses within arbitrary-dimensional systems, with our Schmidt witness coefficients relying solely on the operator Schmidt coefficient. Subsequently, we demonstrate our theoretical advancements and computational superiority by constructing Schmidt number witnesses in arbitrary dimensional bipartite quantum systems with Schmidt numbers four and five. – Name: TypeDocument Label: Document Type Group: TypDoc Data: Working Paper – Name: URL Label: Access URL Group: URL Data: <link linkTarget="URL" linkTerm="http://arxiv.org/abs/2504.11213" linkWindow="_blank">http://arxiv.org/abs/2504.11213</link> – Name: AN Label: Accession Number Group: ID Data: edsarx.2504.11213 |
| PLink | https://login.libproxy.scu.edu/login?url=https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&scope=site&db=edsarx&AN=edsarx.2504.11213 |
| RecordInfo | BibRecord: BibEntity: Subjects: – SubjectFull: Quantum Physics Type: general – SubjectFull: Mathematical Physics Type: general – SubjectFull: Mathematics - Numerical Analysis Type: general – SubjectFull: Mathematics - Spectral Theory Type: general Titles: – TitleFull: Characterizing High Schmidt Number Witnesses in Arbitrary Dimensions System Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Xiong, Liang – PersonEntity: Name: NameFull: Sze, Nung-sing IsPartOfRelationships: – BibEntity: Dates: – D: 15 M: 04 Type: published Y: 2025 |
| ResultId | 1 |