论文标题
图形渐近光谱中参数的非共同扩展
Noncommutative extensions of parameters in the asymptotic spectrum of graphs
论文作者
论文摘要
经典信道的零误差容量是其混淆性图的参数，等于在不连接结合下加性的图形参数的最小值，在强产物下乘法，在补语之间单态下单调，并归一化。我们表明，任何此类函数要么具有无数的扩展到具有相似属性的非交换图，要么根本没有此类扩展。更确切地说，我们发现每个扩展名都有一个指数，该指数在身份量子通道的混淆性图上表征其值，并且可允许的指数的集合是$ [1，\ infty）$的无界子互和$。特别是，Lovász数字，投影等级和绑定在复数上的分数呼出者的一组可接受的指数是最大的，而分数集团封面号则没有任何扩展。
The zero-error capacity of a classical channel is a parameter of its confusability graph, and is equal to the minimum of the values of graph parameters that are additive under the disjoint union, multiplicative under the strong product, monotone under homomorphisms between the complements, and normalized. We show that any such function either has uncountably many extensions to noncommutative graphs with similar properties, or no such extensions at all. More precisely, we find that every extension has an exponent that characterizes its values on the confusability graphs of identity quantum channels, and the set of admissible exponents is either an unbounded subinterval of $[1,\infty)$ or empty. In particular, the set of admissible exponents for the Lovász number, the projective rank, and the fractional Haemers bound over the complex numbers are maximal, while the fractional clique cover number does not have any extensions.
