Manipulation of single-photon states encoded in transverse spatial modes: Possible and impossible tasks

Gabriel F. Calvo and Antonio Picón
Phys. Rev. A 77, 012302 – Published 3 January 2008

Abstract

Controlled generation and manipulation of photon states encoded in their spatial degrees of freedom is a crucial ingredient in many quantum-information tasks exploiting higher-than-two dimensional encoding. Here, we prove the impossibility to arbitrarily modify d-level state superpositions (qudits) for d>2, encoded in the transverse modes of light, with optical components associated to the group of symplectic transforms (Gaussian operations). Surprisingly, we also provide an explicit construction of how non-Gaussian operations acting on mode subspaces do enable one to overcome the limit d=2. In addition, this set of operations realizes the full SU(3) algebra.

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  • Received 5 June 2007

DOI:https://doi.org/10.1103/PhysRevA.77.012302

©2008 American Physical Society

Authors & Affiliations

Gabriel F. Calvo and Antonio Picón

  • Grup de Física Teòrica, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain

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Vol. 77, Iss. 1 — January 2008

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