Article

Open Systems & Information Dynamics

, Volume 13, Issue 4, pp 415-426

Exploring Representation Theory of Unitary Groups via Linear Optical Passive Devices

  • P. AnielloAffiliated withDipartimento di Scienze Fisiche dell’Università di Napoli Federico II Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Napoli, Complesso Universitario di Monte S. Angelo Email author 
  • , C. LupoAffiliated withDipartimento di Scienze Fisiche dell’Università di Napoli Federico II Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Napoli, Complesso Universitario di Monte S. Angelo
  • , M. NapolitanoAffiliated withDipartimento di Scienze Fisiche dell’Università di Napoli Federico II Complesso Universitario di Monte S. Angelo

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Abstract

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.