Engineering multiphoton states for linear optics computation
  Transformations achievable by linear optical components allow to generate the whole unitary group only when restricted to the one-photon subspace of a multimode Fock space. In this paper, we address the more general problem of encoding quantum information by multiphoton states, and elaborating it via ancillary extensions, linear optical passive devices and photodetection. Our scheme stems in a natural way from the mathematical structures underlying the physics of linear optical passive devices. In particular, we analyze an economical procedure for mapping a fiducial 2-photon 2-mode state into an arbitrary 2-photon 2-mode state using ancillary resources and linear optical passive N-ports assisted by post-selection. We found that adding a single ancilla mode is enough to generate any desired target state. The effect of imperfect photodetection in post-selection is considered and a simple trade-off between success probability and fidelity is derived. 
Paolo Aniello, Cosmo Lupo, Mario Napolitano, and Matteo G.A. Paris