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A central limit theorem for partial transposes of multipartite Wishart matrices

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Titel: A central limit theorem for partial transposes of multipartite Wishart matrices
Autoren: Park, Gyunam, Youn, Sang-Gyun
Quelle: Proceedings of the Royal Society of Edinburgh: Section A Mathematics. :1-38
Publication Status: Preprint
Verlagsinformationen: Cambridge University Press (CUP), 2025.
Publikationsjahr: 2025
Schlagwörter: 46L54, 15B52, Mathematics - Operator Algebras, FOS: Mathematics, Operator Algebras (math.OA)
Beschreibung: The partial transposition from quantum information theory provides a new source to distill the so-called asymptotic freeness without the assumption of classical independence between random matrices. Indeed, a recent paper [10] established asymptotic freeness between partial transposes in the bipartite situation. In this paper, we prove almost sure asymptotic freeness in the general multipartite situation and establish a central limit theorem for the partial transposes.
Publikationsart: Article
Sprache: English
ISSN: 1473-7124
0308-2105
DOI: 10.1017/prm.2025.10054
DOI: 10.48550/arxiv.2405.02822
Zugangs-URL: http://arxiv.org/abs/2405.02822
Rights: Cambridge Core User Agreement
arXiv Non-Exclusive Distribution
Dokumentencode: edsair.doi.dedup.....08da4baa6bed7d76c641baf6919e68b2
Datenbank: OpenAIRE
Beschreibung
Abstract:The partial transposition from quantum information theory provides a new source to distill the so-called asymptotic freeness without the assumption of classical independence between random matrices. Indeed, a recent paper [10] established asymptotic freeness between partial transposes in the bipartite situation. In this paper, we prove almost sure asymptotic freeness in the general multipartite situation and establish a central limit theorem for the partial transposes.
ISSN:14737124
03082105
DOI:10.1017/prm.2025.10054