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Probl. Peredachi Inf., 2014, Volume 50, Issue 2, Pages 3–19 (Mi ppi2136)  

This article is cited in 8 scientific papers (total in 8 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.

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English version:
Problems of Information Transmission, 2014, 50:2, 117–132

Bibliographic databases:

UDC: 621.391.1+519.72
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

Citation in format AMSBIB
\by M.~M.~Wilde, A.~Winter
\paper Strong converse for the classical capacity of the pure-loss bosonic channel
\jour Probl. Peredachi Inf.
\yr 2014
\vol 50
\issue 2
\pages 3--19
\jour Problems Inform. Transmission
\yr 2014
\vol 50
\issue 2
\pages 117--132

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    This publication is cited in the following articles:
    1. X. Wang, W. Xie, R. Duan, “Semidefinite Programming Converse Bounds For Classical Communication Over Quantum Channels”, 2017 IEEE International Symposium on Information Theory, ISIT 2017, IEEE, 1728–1732  isi
    2. A. Anshu, “An Upper Bound on Quantum Capacity of Unital Quantum Channels”, 2017 IEEE Information Theory Workshop, ITW 2017, IEEE, 214–218  isi
    3. Sabapathy K.K., “Quantum-Optical Channels That Output Only Classical States”, Phys. Rev. A, 92:5 (2015), 052301  crossref  isi  elib  scopus
    4. Bardhan B.R., Garcia-Patron R., Wilde M.M., Winter A., “Strong Converse For the Classical Capacity of Optical Quantum Communication Channels”, IEEE Trans. Inf. Theory, 61:4 (2015), 1842–1850  crossref  mathscinet  isi  elib  scopus
    5. M. M. Wilde, J. M. Renes, S. Guha, “Second-Order Coding Rates For Pure-Loss Bosonic Channels”, Quantum Inf. Process., 15:3, SI (2016), 1289–1308  crossref  mathscinet  isi  elib  scopus
    6. M. Tomamichel, M. M. Wilde, A. Winter, “Strong Converse Rates For Quantum Communication”, IEEE Trans. Inf. Theory, 63:1 (2017), 715–727  crossref  mathscinet  zmath  isi  scopus
    7. F. Furrer, T. Gehring, Ch. Schaffner, Ch. Pacher, R. Schnabel, S. Wehner, “Continuous-variable protocol for oblivious transfer in the noisy-storage model”, Nat. Commun., 9 (2018), 1450  crossref  isi  scopus
    8. X. Wang, W. Xie, R. Duan, “Semidefinite programming strong converse bounds for classical capacity”, IEEE Trans. Inf. Theory, 64:1 (2018), 640–653  crossref  mathscinet  zmath  isi  scopus
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