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arXiv · 0712.1197

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

Gabriel F. Calvo·Antonio Picón
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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 (qu$d$its) 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 to overcome the limit $d=2$. In addition, this set of operations realizes the full SU(3) algebra.

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Gabriel F. Calvo, Antonio Picón. 2007-12-07. Manipulation of single-photon states encoded in transverse spatial modes: possible and impossible tasks. https://doi.org/10.1103/physreva.77.012302

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