Giovanni Scala, Anindita Bera, Gniewomir Sarbicki, Dariusz Chruściński
{"title":"Optimality of generalized Choi maps in $M_3$","authors":"Giovanni Scala, Anindita Bera, Gniewomir Sarbicki, Dariusz Chruściński","doi":"arxiv-2312.02814","DOIUrl":null,"url":null,"abstract":"A family of linear positive maps in the algebra of $3 \\times 3$ complex\nmatrices proposed recently in Bera et al. arXiv:2212.03807 is further analyzed.\nIt provides a generalization of a seminal Choi nondecomposable extremal map in\n$M_3$. We investigate when generalized Choi maps are optimal, i.e. cannot be\nrepresented as a sum of positive and completely positive maps. This property is\nweaker than extremality, however, it turns out that it plays a key role in\ndetecting quantum entanglement.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Mathematical Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2312.02814","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
A family of linear positive maps in the algebra of $3 \times 3$ complex
matrices proposed recently in Bera et al. arXiv:2212.03807 is further analyzed.
It provides a generalization of a seminal Choi nondecomposable extremal map in
$M_3$. We investigate when generalized Choi maps are optimal, i.e. cannot be
represented as a sum of positive and completely positive maps. This property is
weaker than extremality, however, it turns out that it plays a key role in
detecting quantum entanglement.