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This article is cited in 11 scientific papers (total in 11 papers)
Coding Theory
On classical capacities of infinite-dimensional quantum channels
A. S. Holevo, M. E. Shirokov
Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow
Abstract:
A coding theorem for entanglement-assisted communication via an infinite-dimensional quantum channel with linear constraints is extended to a natural degree of generality. Relations between the entanglement-assisted classical capacity and $\chi$-capacity of constrained channels are obtained, and conditions for their coincidence are given. Sufficient conditions for continuity of the entanglement-assisted classical capacity as a function of a channel are obtained. Some applications of the obtained results to analysis of Gaussian channels are considered. A general (continuous) version of the fundamental relation between coherent information and the measure of privacy of classical information transmission via an infinite-dimensional quantum channel is proved.
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English version:
Problems of Information Transmission, 2013, 49:1, 15–31
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UDC:
621.391.1+519.72
Received: 22.10.2012
Citation:
A. S. Holevo, M. E. Shirokov, “On classical capacities of infinite-dimensional quantum channels”, Probl. Peredachi Inf., 49:1 (2013), 19–36; Problems Inform. Transmission, 49:1 (2013), 15–31
Citation in format AMSBIB
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http://mi.mathnet.ru/eng/ppi2099 http://mi.mathnet.ru/eng/ppi/v49/i1/p19
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This publication is cited in the following articles:
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A. S. Holevo, “Gaussian classical-quantum channels: gain from entanglement-assistance”, Problems Inform. Transmission, 50:1 (2014), 1–14
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M. E. Shirokov, “Criteria for equality in two entropic inequalities”, Sb. Math., 205:7 (2014), 1045–1068
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A. S. Holevo, M. E. Shirokov, “On the Gain of Entanglement Assistance in the Classical Capacity of Quantum Gaussian Channels”, Math. Notes, 97:6 (2015), 974–977
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M. E. Shirokov, “Measures of correlations in infinite-dimensional quantum systems”, Sb. Math., 207:5 (2016), 724–768
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M. E. Shirokov, A. S. Holevo, “On lower semicontinuity of the entropic disturbance and its applications in quantum information theory”, Izv. Math., 81:5 (2017), 1044–1060
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M. E. Shirokov, “On the energy-constrained diamond norm and its application in quantum information theory”, Problems Inform. Transmission, 54:1 (2018), 20–33
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M. M. Wilde, H. Qi, “Energy-constrained private and quantum capacities of quantum channels”, IEEE Trans. Inf. Theory, 64:12 (2018), 7802–7827
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M. E. Shirokov, “Uniform finite-dimensional approximation of basic capacities of energy-constrained channels”, Quantum Inf. Process., 17:12 (2018), 322
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N. Davis, M. E. Shirokov, M. M. Wilde, “Energy-constrained two-way assisted private and quantum capacities of quantum channels”, Phys. Rev. A, 97:6 (2018), 062310
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Oskouei S.Kh., Mancini S., Wilde M.M., “Union Bound For Quantum Information Processing”, Proc. R. Soc. A-Math. Phys. Eng. Sci., 475:2221 (2019), 20180612
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Becker S., Datta N., “Convergence Rates For Quantum Evolution and Entropic Continuity Bounds in Infinite Dimensions”, Commun. Math. Phys., 374:2 (2020), 823–871
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