Universality of beamsplitters (pp0291-0312)
          Adam Sawicki
          doi: https://doi.org/10.26421/QIC16.3-4-6
Abstracts: We consider the problem of building an arbitrary N × N real orthogonal operator using a finite set, S, of elementary quantum optics gates operating on m ≤ 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 ≥ 3 modes.
Key words: linear optics, beamsplitters, universality, orthogonal group, control theory, Lie algebras