Coherent-state optical qudit cluster state generation and teleportation via homodyne detection

Defining a computational basis of pseudo-number states, we interpret a coherent state of large amplitude, |α|⪢d/2π, as a qudit - a d-level quantum system - that is an even (meaning same size of amplitudes) superposition of d pseudo-number basis states. A pair of such coherent-state qudits can be maximally entangled by generalized Controlled-Z operation that is based on cross-Kerr nonlinearity, which can be weak for large d. Hence, a coherent-state optical qudit cluster state can be prepared by repetitive application of the generalized Controlled-Z operation to a set of coherent states. We thus propose an optical qudit teleportation as a simple demonstration of cluster state quantum computation.