Strong converse for the quantum capacity of the erasure channel for almost all codes
Wilde, Mark M. (Louisiana State University. Department of Physics and Astronomy)
Winter, Andreas (Universitat Autònoma de Barcelona. Departament de Física)

Imprint:	Dagstuhl : Leibniz-Zentrum fuer Informatik, 2014
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/√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.
Grants:	Ministerio de Economía y Competitividad FIS2008-01236
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Language:	Anglès
Series:	Leibniz International Proceedings in Informatics (LIPIcs) ; 27
Document:	Capítol de llibre ; recerca ; Versió publicada
Subject:	Strong converse ; Quantum erasure channel ; Quantum capacity
Published in:	9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014), 2014, p. 52-66, ISBN 978-3-939897-73-6

DOI: 10.4230/LIPIcs.TQC.2014.52

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