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Problemy Peredachi Informatsii, 2014, Volume 50, Issue 2, Pages 3–19
(Mi ppi2136)
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This article is cited in 15 scientific papers (total in 15 papers)
Information Theory
Strong converse for the classical capacity of the pure-loss bosonic channel
M. M. Wildea, A. Winterbc a Department of Physics and Astronomy, Center for Computation and Technology, Louisiana State University, Baton Rouge, LA, USA
b School of Mathematics, University of Bristol, Bristol, UK
c ICREA & Física Teòrica: Informació i Fenomens Quàntics, Universitat Autònoma de Barcelona, Barcelona, Spain
Abstract:
This paper strengthens the interpretation and understanding of the classical capacity of the pure-loss bosonic channel, first established in [1]. In particular, we first prove that there exists a trade-off between communication rate and error probability if one imposes only a mean photon number constraint on the channel inputs. That is, if we demand that the mean number of photons at the channel input cannot be any larger than some positive number $N_S$, then it is possible to respect this constraint with a code that operates at a rate $g(\eta N_S/(1-p))$, where $p$ is the code error probability, $\eta$ is the channel transmissivity, and $g(x)$ is the entropy of a bosonic thermal state with mean photon number $x$. Then we prove that a strong converse theorem holds for the classical capacity of this channel (that such a rate-error trade-off cannot occur) if one instead demands for a maximum photon number constraint, in such a way that mostly all of the “shadow” of the average density operator for a given code is required to be on a subspace with photon number no larger than $nN_S$, so that the shadow outside this subspace vanishes as the number $n$ of channel uses becomes large. Finally, we prove that a small modification of the well-known coherent-state coding scheme meets this more demanding constraint.
Received: 13.09.2013 Revised: 16.12.2013
Citation:
M. M. Wilde, A. Winter, “Strong converse for the classical capacity of the pure-loss bosonic channel”, Probl. Peredachi Inf., 50:2 (2014), 3–19; Problems Inform. Transmission, 50:2 (2014), 117–132
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https://www.mathnet.ru/eng/ppi2136 https://www.mathnet.ru/eng/ppi/v50/i2/p3
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Abstract page: | 289 | Full-text PDF : | 53 | References: | 43 | First page: | 21 |
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