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Izv. RAN. Ser. Mat., 2017, Volume 81, Issue 5, Pages 165–182 (Mi izv8609)  

This article is cited in 2 scientific papers (total in 2 papers)

On lower semicontinuity of the entropic disturbance and its applications in quantum information theory

M. E. Shirokov, A. S. Holevo

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: We consider an important characteristic of a quantum channel called the entropic disturbance. It is defined as the difference between the $\chi$-quantity of a generalized ensemble and that of the image of the ensemble under the channel. We prove the lower semicontinuity of the entropic disturbance for any infinite-dimensional quantum channel on its natural domain. A number of useful corollaries of this property are established, in particular, the existence of a $\chi$-optimal ensemble for any quantum channel and the continuity of the output $\chi$-quantity under the energy-type input constraint.

Keywords: von Neumann entropy, $\chi$-quantity, ensemble of quantum states, quantum channel, classical capacity.

Funding Agency Grant Number
Russian Science Foundation 14-21-00162


DOI: https://doi.org/10.4213/im8609

Full text: PDF file (622 kB)
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English version:
Izvestiya: Mathematics, 2017, 81:5, 1044–1060

Bibliographic databases:

UDC: 519.248.3
MSC: 81P45, 46L53
Received: 13.01.2017

Citation: M. E. Shirokov, A. S. Holevo, “On lower semicontinuity of the entropic disturbance and its applications in quantum information theory”, Izv. RAN. Ser. Mat., 81:5 (2017), 165–182; Izv. Math., 81:5 (2017), 1044–1060

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. P. Naaijkens, “Subfactors and quantum information theory”, Mathematical Problems in Quantum Physics, Contemporary Mathematics, 717, eds. F. Bonetto, D. Borthwick, E. Harrell, M. Loss, Amer. Math. Soc., 2018, 257–279  crossref  mathscinet  isi  scopus
    2. Ding D., Pavlichin D.S., Wilde M.M., “Quantum Channel Capacities Per Unit Cost”, IEEE Trans. Inf. Theory, 65:1 (2019), 418–435  crossref  mathscinet  zmath  isi
  • Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya Izvestiya: Mathematics
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