{"title":"可降解的强纠缠断裂图","authors":"","doi":"10.1016/j.laa.2024.09.006","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we provide a structure theorem and various characterizations of degradable strong entanglement breaking maps on separable Hilbert spaces. In the finite-dimensional case, we prove that unital degradable entanglement breaking maps are precisely the <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-extreme points of the convex set of unital entanglement breaking maps on matrix algebras. Consequently, we get a structure for unital degradable positive partial transpose (PPT) maps.</p></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Degradable strong entanglement breaking maps\",\"authors\":\"\",\"doi\":\"10.1016/j.laa.2024.09.006\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we provide a structure theorem and various characterizations of degradable strong entanglement breaking maps on separable Hilbert spaces. In the finite-dimensional case, we prove that unital degradable entanglement breaking maps are precisely the <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-extreme points of the convex set of unital entanglement breaking maps on matrix algebras. Consequently, we get a structure for unital degradable positive partial transpose (PPT) maps.</p></div>\",\"PeriodicalId\":18043,\"journal\":{\"name\":\"Linear Algebra and its Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-09-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Linear Algebra and its Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0024379524003689\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Linear Algebra and its Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0024379524003689","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
In this paper, we provide a structure theorem and various characterizations of degradable strong entanglement breaking maps on separable Hilbert spaces. In the finite-dimensional case, we prove that unital degradable entanglement breaking maps are precisely the -extreme points of the convex set of unital entanglement breaking maps on matrix algebras. Consequently, we get a structure for unital degradable positive partial transpose (PPT) maps.
期刊介绍：
Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.
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