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This article is cited in 3 scientific papers (total in 3 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.
DOI:
https://doi.org/10.4213/im8609
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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
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http://mi.mathnet.ru/eng/izv8609https://doi.org/10.4213/im8609 http://mi.mathnet.ru/eng/izv/v81/i5/p165
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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
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D. Ding, D. S. Pavlichin, M. M. Wilde, “Quantum channel capacities per unit cost”, IEEE Trans. Inform. Theory, 65:1 (2019), 418–435
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M. E. Shirokov, “Strong convergence of quantum channels: continuity of the stinespring dilation and discontinuity of the unitary dilation”, J. Math. Phys., 61:8 (2020), 082204
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