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Bounds on Entanglement Assisted Source-channel Coding Via the Lovász Theta Number and Its Variants Cubitt, Toby Mancinska, Laura Roberson, David Severini, Simone Stahlke, Dan Winter, Andreas source-channel coding zero-error capacity Lovász theta 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 theta(G) <= theta(H) where theta represents the Lovász number. We also obtain similar inequalities for the related Schrijver theta^- and Szegedy theta^+ 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: alpha^*(G) <= theta^-(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 beta as an upper bound on alpha^* and posed the question of whether beta(G) = \lfloor theta(G) \rfloor. We answer this in the affirmative and show that a related quantity is equal to \lceil theta(G) \rceil. We show that a quantity chi_{vect}(G) recently introduced in the context of Tsirelson's conjecture is equal to \lceil theta^+(G) \rceil. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Toby Cubitt and Laura Mancinska and David Roberson and Simone Severini and Dan Stahlke and Andreas Winter 2014 Is Part Of LIPIcs, Volume 27, 9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.TQC.2014.48 urn:nbn:de:0030-drops-48054 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2014.48 eng https://creativecommons.org/licenses/by/3.0/legalcode