Bounds on entanglement assisted source-channel coding via the lovász number and its variants

Toby Cubitt, Laura Mancinska, David Roberson, Simone Severini, Dan Stahlke, Andreas Winter

Publikation: Beitrag in Buch/Bericht/KonferenzbandKonferenzbeitragBegutachtung

Abstract

We study zero-error entanglement assisted source-channel coding (communication in the presence of side information). Adapting a technique of Beigi, we show that such coding requires existence of a set of vectors satisfying orthogonality conditions related to suitably defined graphs G and H. Such vectors exist if and only if (G) ≤ (H) where represents the Lovász number. We also obtain similar inequalities for the related Schrijver - and Szegedy + numbers. These inequalities reproduce several known bounds and also lead to new results. We provide a lower bound on the entanglement assisted cost rate. We show that the entanglement assisted independence number is bounded by the Schrijver number: α∗(G) ≤ -(G). Therefore, we are able to disprove the conjecture that the one-shot entanglement-assisted zero-error capacity is equal to the integer part of the Lovász number. Beigi introduced a quantity β as an upper bound on α∗ and posed the question of whether β(G) = ⌊(G)⌋. We answer this in the affirmative and show that a related quantity is equal to ⌈(G)⌉. We show that a quantity χvect(G) recently introduced in the context of Tsirelson's conjecture is equal to ⌈+(G)⌉.

OriginalspracheEnglisch
Titel9th Conference on the Theory of Quantum Computation, Communication and Cryptography, TQC 2014
Redakteure/-innenSteven T. Flammia, Aram W. Harrow
Herausgeber (Verlag)Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Seiten48-51
Seitenumfang4
ISBN (elektronisch)9783939897736
DOIs
PublikationsstatusVeröffentlicht - 1 Nov. 2014
Extern publiziertJa
Veranstaltung9th Conference on the Theory of Quantum Computation, Communication and Cryptography, TQC 2014 - Singapore, Singapur
Dauer: 21 Mai 201423 Mai 2014

Publikationsreihe

NameLeibniz International Proceedings in Informatics, LIPIcs
Band27
ISSN (Print)1868-8969

Konferenz

Konferenz9th Conference on the Theory of Quantum Computation, Communication and Cryptography, TQC 2014
Land/GebietSingapur
OrtSingapore
Zeitraum21/05/1423/05/14

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