Generation of a three-qudit GHZ state with diamond defect spins

Diamond defect spins have emerged as potential qudits (d-dimensional quantum bit) in quantum information and quantum computing. A new scheme is proposed for realizing entangled states of GHZ (Greenberger-Horne-Zeilinger) class in a 3-qudit solid-state register. The qudits are the electron spin-1 carried by the negatively charged nitrogen-vacancy color center (NV⁻¹) in diamond and the nuclear spin-$\frac{1}{2}$ of two carbon-13 impurities in the first neighbour shell. Multipartite entanglements between qudits are obtained by bringing the spin system in the vicinity of a level anticrossing. The degree of entanglement between all three qudits is quantified rigorously. GHZ and GHZ-like entangled states have applications in quantum communication and computation protocols. (letter)