Exploring Representation Theory of Unitary Groups via Linear Optical Passive Devices
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- Aniello, P., Lupo, C. & Napolitano, M. Open Syst Inf Dyn (2006) 13: 415. doi:10.1007/s11080-006-9023-1
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In this paper, we investigate some mathematical structures underlying the physics of linear optical passive (LOP) devices. We show, in particular, that with the class of LOP transformations on N optical modes one can associate a unitary representation of U(N) in the N-mode Fock space, representation which can be decomposed into irreducible sub-representations living in the subspaces characterized by a fixed number of photons. These (sub-)representations can be classified using the theory of representations of semi-simple Lie algebras. The remarkable case where N = 3 is studied in detail.