Manipulation of single-photon states encoded in transverse spatial modes: Possible and impossible tasks
Gabriel F. Calvo, Antonio Picón · Physical Review A · 2008
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.