Universality of beamsplitters
Abstract
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 2mode and "almost" any nontrivial real $3$mode beamsplitter is universal on $m\geq3$ modes.
 Publication:

arXiv eprints
 Pub Date:
 July 2015
 DOI:
 10.48550/arXiv.1507.08255
 arXiv:
 arXiv:1507.08255
 Bibcode:
 2015arXiv150708255S
 Keywords:

 Quantum Physics;
 Mathematical Physics
 EPrint:
 19 pages, 1 figure, some minor changes in presentation