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arXiv · 1512.02096

On the structutre of the algebra generated by the non-commutative operator graph demonstrating superactivation for a zero-error capacity

Grigori G. Amosov·I. Yu. Zhdanovskiy
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Abstract

Recently M.E. Shirokov introduced the non-commutative operator graph depending on the complex parameter $θ$ to construct channels with positive quantum zero-error capacity having vanishing n-shot capacity. We study the algebraic structure of this graph. The relations for the algebra generated by the graph are derived. In the limiting case $θ=\pm1$ the graph becomes abelian and degenerates into the direct sum of four one-dimensional irreducible representations of the Klein group.

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Grigori G. Amosov, I. Yu. Zhdanovskiy. 2015-12-07. On the structutre of the algebra generated by the non-commutative operator graph demonstrating superactivation for a zero-error capacity. https://arxiv.org/abs/1512.02096

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