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

Understand

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 $\vartheta(\overline{G}) \le \vartheta(\overline{H})$ where $\vartheta$ represents the Lov\'asz number.
• We also obtain similar inequalities for the related Schrijver $\vartheta^-$ and Szegedy $\vartheta^+$ numbers.