Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Universality of beamsplitters   We consider the problem of building an arbitrary $N\times N$ real orthogonal
operator using a finite set, $S$, of elementary quantum optics gates operating
on $m\leq N$ modes - the problem of universality of $S$ on $N$ modes. In
particular, we focus on the universality problem of an $m$-mode beamsplitter.
Using methods of control theory and some properties of rotations in three
dimensions, we prove that any nontrivial real 2-mode and "almost" any
nontrivial real $3$-mode beamsplitter is universal on $m\geq3$ modes.

25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio