Symmetric orthogonalization and probabilistic weights in resource quantification.
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| Title: | Symmetric orthogonalization and probabilistic weights in resource quantification. |
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| Authors: | TORUN, Gökhan1 gokhan.torun@ieu.edu.tr |
| Source: | Turkish Journal of Physics. 2026, Vol. 50 Issue 1, p1-25. 25p. |
| Subjects: | Orthogonalization, Quantum coherence, Quantum superposition |
| Abstract: | Transforming nonorthogonal bases into orthogonal ones often compromises essential properties or physical meaning in quantum systems. Here, we demonstrate that Löwdin symmetric orthogonalization (LSO) outperforms the widely used Gram-Schmidt orthogonalization (GSO) in characterizing and quantifying quantum resources, with particular emphasis on coherence and superposition. We employ LSO both to construct an orthogonal basis from a nonorthogonal one and to obtain a nonorthogonal basis from an orthogonal set, thereby mitigating ambiguity related to the basis choice in defining quantum coherence. Unlike GSO, which depends on the ordering of input states, LSO applies a symmetric transformation that treats all vectors equally and minimizes deviation from the original basis. This procedure yields basis sets with enhanced stability, preserving the closest possible correspondence to the original physical states while satisfying orthogonality. Building on LSO, we also introduce Löwdin weights -- probabilistic weights for nonorthogonal representations that provide a consistent measure of resource content. We explicitly contrast these with Chirgwin-Coulson weights, demonstrating that Löwdin weights ensure nonnegativity, a prerequisite for information-theoretic measures. These weights further enable the quantification of coherence and the characterization of superposition, providing a degree of superposition as a distinct measure, as well as facilitating the assessment of state delocalization through entropy and participation ratios. Our theoretical and numerical analyses confirm LSO's superior preservation of quantum state symmetry and resource characteristics, underscoring the critical role of orthogonalization methods and Löwdin weights in resource theory frameworks involving nonorthogonal bases. [ABSTRACT FROM AUTHOR] |
| Copyright of Turkish Journal of Physics is the property of Scientific and Technical Research Council of Turkey 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 | Links: – Type: pdflink Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 192190147 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Symmetric orthogonalization and probabilistic weights in resource quantification. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22TORUN%2C+Gökhan%22">TORUN, Gökhan</searchLink><relatesTo>1</relatesTo><i> gokhan.torun@ieu.edu.tr</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Turkish+Journal+of+Physics%22">Turkish Journal of Physics</searchLink>. 2026, Vol. 50 Issue 1, p1-25. 25p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Orthogonalization%22">Orthogonalization</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+coherence%22">Quantum coherence</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+superposition%22">Quantum superposition</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Transforming nonorthogonal bases into orthogonal ones often compromises essential properties or physical meaning in quantum systems. Here, we demonstrate that Löwdin symmetric orthogonalization (LSO) outperforms the widely used Gram-Schmidt orthogonalization (GSO) in characterizing and quantifying quantum resources, with particular emphasis on coherence and superposition. We employ LSO both to construct an orthogonal basis from a nonorthogonal one and to obtain a nonorthogonal basis from an orthogonal set, thereby mitigating ambiguity related to the basis choice in defining quantum coherence. Unlike GSO, which depends on the ordering of input states, LSO applies a symmetric transformation that treats all vectors equally and minimizes deviation from the original basis. This procedure yields basis sets with enhanced stability, preserving the closest possible correspondence to the original physical states while satisfying orthogonality. Building on LSO, we also introduce Löwdin weights -- probabilistic weights for nonorthogonal representations that provide a consistent measure of resource content. We explicitly contrast these with Chirgwin-Coulson weights, demonstrating that Löwdin weights ensure nonnegativity, a prerequisite for information-theoretic measures. These weights further enable the quantification of coherence and the characterization of superposition, providing a degree of superposition as a distinct measure, as well as facilitating the assessment of state delocalization through entropy and participation ratios. Our theoretical and numerical analyses confirm LSO's superior preservation of quantum state symmetry and resource characteristics, underscoring the critical role of orthogonalization methods and Löwdin weights in resource theory frameworks involving nonorthogonal bases. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Turkish Journal of Physics is the property of Scientific and Technical Research Council of Turkey 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: 10.55730/1300-0101.2798 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 25 StartPage: 1 Subjects: – SubjectFull: Orthogonalization Type: general – SubjectFull: Quantum coherence Type: general – SubjectFull: Quantum superposition Type: general Titles: – TitleFull: Symmetric orthogonalization and probabilistic weights in resource quantification. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: TORUN, Gökhan IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Text: 2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 13000101 Numbering: – Type: volume Value: 50 – Type: issue Value: 1 Titles: – TitleFull: Turkish Journal of Physics Type: main |
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