Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Euclidean distance matrices and separations in communication complexity
  theory   A Euclidean distance matrix $D(\alpha)$ is defined by
$D_{ij}=(\alpha_i-\alpha_j)^2$, where $\alpha=(\alpha_1,\ldots,\alpha_n)$ is a
real vector. We prove that $D(\alpha)$ cannot be written as a sum of
$\left[2\sqrt{n}-2\right]$ nonnegative rank-one matrices, provided that the
coordinates of $\alpha$ are algebraically independent. This result allows one
to solve several open problems in computation theory. In particular, we provide
an asymptotically optimal separation between the complexities of quantum and
classical communication protocols computing a matrix in expectation.

25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga