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Exploring Representation Theory of Unitary Groups via Linear Optical Passive Devices

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Open Systems & Information Dynamics

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.

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Authors and Affiliations

  1. Dipartimento di Scienze Fisiche dell’Università di Napoli Federico II Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Napoli, Complesso Universitario di Monte S. Angelo, via Cintia, 80126, Napoli, Italy

    P. Aniello & C. Lupo

  2. Dipartimento di Scienze Fisiche dell’Università di Napoli Federico II Complesso Universitario di Monte S. Angelo, via Cintia, 80126, Napoli, Italy

    M. Napolitano

Authors
  1. P. Aniello
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  2. C. Lupo
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  3. M. Napolitano
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Correspondence to P. Aniello.

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Aniello, P., Lupo, C. & Napolitano, M. Exploring Representation Theory of Unitary Groups via Linear Optical Passive Devices. Open Syst Inf Dyn 13, 415–426 (2006). https://doi.org/10.1007/s11080-006-9023-1

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  • DOI: https://doi.org/10.1007/s11080-006-9023-1

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