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Universality of beamsplitters
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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.
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Cited by 1 Pith paper
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Universal programmable waveguide arrays
Cascaded programmable waveguide arrays with strictly positive, nearest-neighbor couplings can approximate any unitary matrix to arbitrary precision, with error decreasing as the number of sections grows.
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