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Cubitt, Toby [Author]; Mancinska, Laura [Author]; Roberson, David [Author]; Severini, Simone [Author]; Stahlke, Dan [Author]; Winter, Andreas [Author] ; Toby Cubitt and Laura Mancinska and David Roberson and Simone Severini and Dan Stahlke and Andreas Winter [Contributor]

Bounds on Entanglement Assisted Source-channel Coding Via the Lovász Theta Number and Its Variants

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  • Media type: E-Article; Electronic Conference Proceeding; Text
  • Title: Bounds on Entanglement Assisted Source-channel Coding Via the Lovász Theta Number and Its Variants
  • Contributor: Cubitt, Toby [Author]; Mancinska, Laura [Author]; Roberson, David [Author]; Severini, Simone [Author]; Stahlke, Dan [Author]; Winter, Andreas [Author]
  • imprint: Schloss Dagstuhl – Leibniz-Zentrum für Informatik, 2014
  • Language: English
  • DOI: https://doi.org/10.4230/LIPIcs.TQC.2014.48
  • Keywords: source-channel coding ; zero-error capacity ; Lovász theta
  • Origination:
  • Footnote: Diese Datenquelle enthält auch Bestandsnachweise, die nicht zu einem Volltext führen.
  • Description: 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.
  • Access State: Open Access