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Title: Bounds on entanglement-assisted source-channel coding via the Lovász ϑ number and its variants
Authors: Cubitt, Toby
Mancinska, Laura
Roberson, David E.
Severini, Simone
Stahlke, Dan
Winter, Andreas
Keywords: DRNTU::Engineering::Computer science and engineering::Information systems
Issue Date: 2014
Source: Cubitt, T., Mancinska, L., Roberson, D. E., Severini, S., Stahlke, D., & Winter, A. (2014). Bounds on entanglement-assisted source-channel coding via the Lovász ϑ number and its variants. IEEE transactions on information theory, 60(11), 7330-7344.
Series/Report no.: IEEE transactions on information theory
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 ϑ(G̅) ≤ ϑ(H̅), where ϑ represents the Lovász number. We also obtain similar inequalities for the related Schrijver ϑ- and Szegedy ϑ+ 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) ≤ ϑ-(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) = ⌊ϑ(G)⌋. We answer this in the affirmative and show that a related quantity is equal to ⌊ϑ(G)⌋. We show that a quantity χvect(G) recently introduced in the context of Tsirelson's problem is equal to ⌊ϑ+(G)⌋. In an appendix, we investigate multiplicativity properties of Schrijver's and Szegedy's numbers, as well as projective rank.
DOI: 10.1109/TIT.2014.2349502
Rights: © 2014 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. The published version is available at: [].
Fulltext Permission: open
Fulltext Availability: With Fulltext
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