标题： 量子Ramsey数$QR(2,k)$ 显示英文标题

标题： The quantum Ramsey numbers $QR(2,k)$

摘要： 矩阵的算子系统可以看作是有限图的量子模拟。 这种类比在线性代数中提出了许多自然的组合问题。 我们确定了量子Ramsey数$QR(2,k)$和下界量子Turán数$T^\downarrow(n, m)$，其中包含$m \geq n/4$。 特别是，我们得出结论$QR(2,2) = 4$并确认Weaver的猜想，即$T^\downarrow(4, 1) = 4$。 我们还得到了关于低维量子图中反团存在的新结果。 显示英文摘要

摘要： Operator systems of matrices can be viewed as quantum analogues of finite graphs. This analogy suggests many natural combinatorial questions in linear algebra. We determine the quantum Ramsey numbers $QR(2,k)$ and the lower quantum Tur\'an numbers $T^\downarrow(n, m)$ with $m \geq n/4$. In particular, we conclude that $QR(2,2) = 4$ and confirm Weaver's conjecture that $T^\downarrow(4, 1) = 4$. We also obtain a new result for the existence of anticliques in quantum graphs of low dimension.