License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.TQC.2014.52
URN: urn:nbn:de:0030-drops-48068
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2014/4806/
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Wilde, Mark M. ; Winter, Andreas

Strong Converse for the Quantum Capacity of the Erasure Channel for Almost All Codes

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Abstract

A strong converse theorem for channel capacity establishes that the error probability in any communication scheme for a given channel necessarily tends to one if the rate of communication exceeds the channel's capacity. Establishing such a theorem for the quantum capacity of degradable channels has been an elusive task, with the strongest progress so far being a so-called "pretty strong converse." In this work, Morgan and Winter proved that the quantum error of any quantum communication scheme for a given degradable channel converges to a value larger than 1/sqrt(2) in the limit of many channel uses if the quantum rate of communication exceeds the channel's quantum capacity. The present paper establishes a theorem that is a counterpart to this "pretty strong converse." We prove that the large fraction of codes having a rate exceeding the erasure channel's quantum capacity have a quantum error tending to one in the limit of many channel uses. Thus, our work adds to the body of evidence that a fully strong converse theorem should hold for the quantum capacity of the erasure channel. As a side result, we prove that the classical capacity of the quantum erasure channel obeys the strong converse property.

BibTeX - Entry

@InProceedings{wilde_et_al:LIPIcs:2014:4806,
  author =	{Mark M. Wilde and Andreas Winter},
  title =	{{Strong Converse for the Quantum Capacity of the Erasure Channel for Almost All Codes}},
  booktitle =	{9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014)},
  pages =	{52--66},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-73-6},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{27},
  editor =	{Steven T. Flammia and Aram W. Harrow},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2014/4806},
  URN =		{urn:nbn:de:0030-drops-48068},
  doi =		{10.4230/LIPIcs.TQC.2014.52},
  annote =	{Keywords: strong converse, quantum erasure channel, quantum capacity}
}

Keywords: strong converse, quantum erasure channel, quantum capacity
Collection: 9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014)
Issue Date: 2014
Date of publication: 11.12.2014

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