The Haemers bound of noncommutative graphs

• URL: http://arxiv.org/abs/2002.02743v1
• Date: Fri, 7 Feb 2020 12:46:39 GMT
• Title: The Haemers bound of noncommutative graphs
• Authors: Sander Gribling and Yinan Li
• Abstract summary: We show that the Haemers bound upper bounds the Shannon capacity of noncommutative graphs. We also show that it can outperform other known upper bounds, including noncommutative analogues of the Lov'asz theta function.
• Score: 10.293135569592833
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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).

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