{"title":"关于p=2时最大p -范数的乘法性的注释","authors":"C. King, M. Ruskai","doi":"10.26421/QIC4.6-7-9","DOIUrl":null,"url":null,"abstract":"We consider the maximal p-norm associated with a completely positivemap and the question of its multiplicativity under tensor products. Wegive a condition under which this multiplicativity holds when p = 2, andwe describe some maps which satisfy our condition. This class includesmaps for which multiplicativity is known to fail for large p.Our work raises some questions of independent interest in matrix theory; these are discussed in two appendices.","PeriodicalId":54524,"journal":{"name":"Quantum Information & Computation","volume":"4 1","pages":"500-512"},"PeriodicalIF":0.7000,"publicationDate":"2004-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"38","resultStr":"{\"title\":\"Comments on multiplicativity of maximal p -norms when p=2\",\"authors\":\"C. King, M. Ruskai\",\"doi\":\"10.26421/QIC4.6-7-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider the maximal p-norm associated with a completely positivemap and the question of its multiplicativity under tensor products. Wegive a condition under which this multiplicativity holds when p = 2, andwe describe some maps which satisfy our condition. This class includesmaps for which multiplicativity is known to fail for large p.Our work raises some questions of independent interest in matrix theory; these are discussed in two appendices.\",\"PeriodicalId\":54524,\"journal\":{\"name\":\"Quantum Information & Computation\",\"volume\":\"4 1\",\"pages\":\"500-512\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2004-01-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"38\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Quantum Information & Computation\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.26421/QIC4.6-7-9\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quantum Information & Computation","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.26421/QIC4.6-7-9","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
Comments on multiplicativity of maximal p -norms when p=2
We consider the maximal p-norm associated with a completely positivemap and the question of its multiplicativity under tensor products. Wegive a condition under which this multiplicativity holds when p = 2, andwe describe some maps which satisfy our condition. This class includesmaps for which multiplicativity is known to fail for large p.Our work raises some questions of independent interest in matrix theory; these are discussed in two appendices.
期刊介绍：
Quantum Information & Computation provides a forum for distribution of information in all areas of quantum information processing. Original articles, survey articles, reviews, tutorials, perspectives, and correspondences are all welcome. Computer science, physics and mathematics are covered. Both theory and experiments are included. Illustrative subjects include quantum algorithms, quantum information theory, quantum complexity theory, quantum cryptology, quantum communication and measurements, proposals and experiments on the implementation of quantum computation, communications, and entanglement in all areas of science including ion traps, cavity QED, photons, nuclear magnetic resonance, and solid-state proposals.
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