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Izvestiya: Mathematics, 2006, Volume 70, Issue 6, Pages 1265–1292
DOI: https://doi.org/10.1070/IM2006v070n06ABEH002346 (Mi im730) 		 
This article is cited in 28 scientific papers (total in 28 papers)

Entropy characteristics of subsets of states. I

M. E. Shirokov

Steklov Mathematical Institute, Russian Academy of Sciences
English version PDF (408 kB) Citations (28)
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DOI: https://doi.org/10.1070/IM2006v070n06ABEH002346
Abstract: We study the properties of quantum entropy and $\chi$-capacity (regarded as a function of sets of quantum states) in the infinite-dimensional case. We obtain conditions for the boundedness and continuity of the restriction of the entropy to a subset of quantum states, as well as conditions for the existence of the state with maximal entropy in certain subsets. The notion of $\chi$-capacity is considered for an arbitrary subset of states. The existence of an optimal average is proved for an arbitrary subset with finite $\chi$-capacity. We obtain a sufficient condition for the existence of an optimal measure and prove a generalized maximal distance property.
Received: 23.12.2005
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2006, Volume 70, Issue 6, Pages 193–222
DOI: https://doi.org/10.4213/im730
Bibliographic databases:
Document Type: Article
UDC: 519.722
MSC: 62B10, 81P68, 94A40
Language: English
Original paper language: Russian
Citation: M. E. Shirokov, “Entropy characteristics of subsets of states. I”, Izv. RAN. Ser. Mat., 70:6 (2006), 193–222; Izv. Math., 70:6 (2006), 1265–1292
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/im/v70/i6/p193
    Cycle of papers
    This publication is cited in the following 28 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:708
    Russian version PDF:208
    English version PDF:32
    References:86
    First page:4
     
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