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 2-mode and "almost" any nontrivial real $3$-mode beamsplitter is universal on $m\geq3$ modes.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2015
- DOI:
- 10.48550/arXiv.1507.08255
- arXiv:
- arXiv:1507.08255
- Bibcode:
- 2015arXiv150708255S
- Keywords:
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- Quantum Physics;
- Mathematical Physics
- E-Print:
- 19 pages, 1 figure, some minor changes in presentation