非交换图的Haemers界
The Haemers bound of noncommutative graphs
摘要：
我们继续研究量子信道版本的香农的零错误容量问题。我们推广著名的Haemers绑定到非交换图（从量子信道）。我们证明了这个界的基本性质，如直和下的可加性和张量积下的次乘性。Haemers界上限的香农容量的非交换图，我们表明，它可以优于其他已知的上限，包括非交换类似物的Lovász θ函数（Duan Severini-Winter，IEEE Trans.通知。理论，2013和Boreland-Todorov-Winter，arXiv，2019）。
英文摘要：
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 Lovász theta function (Duan-Severini-Winter, IEEE Trans. Inform. Theory, 2013 and Boreland-Todorov-Winter, arXiv, 2019).
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