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The Haemers bound of noncommutative graphs

Research paper by Sander Gribling, Yinan Li

Indexed on: 10 Feb '20Published on: 07 Feb '20Published in: arXiv - Quantum Physics



Abstract

We continue the study of the quantum channel version of Shannon's zero-error capacity problem. We generalize the celebrated Haemers bound to noncommutative graphs (obtained from quantum channels). We prove basic properties of this bound, such as additivity under the direct sum and submultiplicativity under the tensor product. The Haemers bound upper bounds the Shannon capacity of noncommutative graphs, and we show that it can outperform other known upper bounds, including noncommutative analogues of the Lov\'asz theta function (Duan-Severini-Winter, IEEE Trans. Inform. Theory, 2013 and Boreland-Todorov-Winter, arXiv, 2019).