We continue the study of the quantum channel version of Shannon's zero-error capacity problem. We generalize the celebrated Haemers bound to noncommutative graph

Gribling, S.J. (Sander)

Li, Y. (Yinan)

English

arXiv

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\xc3\xa1sz theta function (Duan-Severini-Winter, IEEE Trans. Inform. Theory, 2013 and Boreland-Todorov-Winter, arXiv, 2019)

The Haemers bound of noncommutative graphs

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