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Generation of universal linear optics by any beam splitter

Author(s)
Aaronson, Scott; Bouland, Adam Michael
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Abstract
In 1994, Reck et al. showed how to realize any unitary transformation on a single photon using a product of beam splitters and phase shifters. Here we show that any single beam splitter that nontrivially mixes two modes also densely generates the set of unitary transformations (or orthogonal transformations, in the real case) on the single-photon subspace with m ≥ 3 modes. (We prove the same result for any two-mode real optical gate, and for any two-mode optical gate combined with a generic phase shifter.) Experimentally, this means that one does not need tunable beam splitters or phase shifters for universality: any nontrivial beam splitter is universal for linear optics. Theoretically, it means that one cannot produce “intermediate” models of linear optical computation (analogous to the Clifford group for qubits) by restricting the allowed beam splitters and phase shifters: there is a dichotomy; one either gets a trivial set or else a universal set. No similar classification theorem for gates acting on qubits is currently known. We leave open the problem of classifying optical gates that act on three or more modes.
Date issued
2014-06
URI
http://hdl.handle.net/1721.1/88647
Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Journal
Physical Review A
Publisher
American Physical Society
Citation
Bouland, Adam, and Scott Aaronson. “Generation of Universal Linear Optics by Any Beam Splitter.” Phys. Rev. A 89, no. 6 (June 2014). © 2014 American Physical Society
Version: Final published version
ISSN
1050-2947
1094-1622

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