Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficient 2-designs from bases exist   We show that in a complex d-dimensional vector space, one can find O(d) bases
whose elements form a 2-design. Such vector sets generalize the notion of a
maximal collection of mutually unbiased bases (MUBs). MUBs have manifold
applications in quantum information theory (e.g. in state tomography, cloning,
or cryptography) -- however it is suspected that maximal sets exist only in
prime-power dimensions. Our construction offers an efficient alternative for
general dimensions. The findings are based on a framework recently established
in [A. Roy and A. Scott, J. Math. Phys. 48, 072110 (2007)], which reduces the
construction of such bases to the combinatorial problem of finding certain
highly nonlinear functions between abelian groups.

21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ