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This article is cited in 26 scientific papers (total in 26 papers)
Measures of correlations in infinite-dimensional quantum systems
M. E. Shirokov Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Abstract:
Several important measures of correlations of the state of a finite-dimensional composite quantum system are defined as linear combinations of marginal entropies of this state. This paper is devoted to infinite-dimensional generalizations of such quantities and to an analysis of their properties.
We introduce the notion of faithful extension of a linear combination of marginal entropies and consider several concrete examples, the simplest of which are quantum mutual information and quantum conditional entropy. Then we show that quantum conditional mutual information can be defined uniquely as a lower semicontinuous function on the set of all states of a tripartite infinite-dimensional system possessing all the basic properties valid in finite dimensions. Infinite-dimensional generalizations of some other measures of correlations in multipartite quantum systems are also considered. Applications of the results to the theory of infinite-dimensional quantum channels and their capacities are considered. The existence of a Fawzi-Renner recovery channel reproducing marginal states for all tripartite states (including states with infinite marginal entropies) is shown.
Bibliography: 47 titles.
Keywords:
von Neumann entropy, marginal entropy, quantum mutual information, quantum channel, entanglement-assisted capacity.
Received: 22.06.2015 and 25.10.2015
Citation:
M. E. Shirokov, “Measures of correlations in infinite-dimensional quantum systems”, Sb. Math., 207:5 (2016), 724–768
Linking options:
https://www.mathnet.ru/eng/sm8561https://doi.org/10.1070/SM8561 https://www.mathnet.ru/eng/sm/v207/i5/p93
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Abstract page: | 517 | Russian version PDF: | 89 | English version PDF: | 18 | References: | 55 | First page: | 24 |
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