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 -level state superpositions (qudits) for , 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 . In addition, this set of operations realizes the full SU(3) algebra.
- Received 5 June 2007
DOI:https://doi.org/10.1103/PhysRevA.77.012302
©2008 American Physical Society