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

TitleManipulation of single-photon states encoded in transverse spatial modes: Possible and impossible tasks
Publication TypeJournal Article
Year of Publication2008
AuthorsCalvo, GF, Picon, A
JournalPhysical Review A (Atomic, Molecular, and Optical Physics)
Volume77
Issue1
Pagination012302–7
Date Published01/2008
KeywordsSU(3) theory
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.

URLhttp://link.aps.org/doi/10.1103/PhysRevA.77.012302
DOI10.1103/PhysRevA.77.012302
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