论文标题
在量子设置中的渐近维度和粗嵌入
Asymptotic dimension and coarse embeddings in the quantum setting
论文作者
论文摘要
我们将渐近维度和粗嵌入的概念从公制空间到量子公制空间的概念在Kuperberg和Weaver的意义上。我们表明，量子渐近维度相对于度量标和直接总和很好，并且在量子粗嵌入下保留。此外，我们证明了一个等值的量子度量空间，其中包含一系列反身量子扩张器必须具有无限的渐近维度。这是通过证明由于Temme，Kastoryano，Ruskai，Wolf和Verstraete而导致的先前已知的Edge-Isoperimetric，这可以证明扩展器的顶点 - 异常不平等的量子版本。
We generalize the notions of asymptotic dimension and coarse embeddings from metric spaces to quantum metric spaces in the sense of Kuperberg and Weaver. We show that quantum asymptotic dimension behaves well with respect to metric quotients and direct sums, and is preserved under quantum coarse embeddings. Moreover, we prove that a quantum metric space that equi-coarsely contains a sequence of reflexive quantum expanders must have infinite asymptotic dimension. This is done by proving a quantum version of a vertex-isoperimetric inequality for expanders, based upon a previously known edge-isoperimetric one due to Temme, Kastoryano, Ruskai, Wolf, and Verstraete.
