  Conversion between different types of entangled states is an interesting
problem in quantum mechanics. But research on the conversion between
Greenberger-Horne-Zeilinger (GHZ) state and Knill-Laflamme-Milburn (KLM) state
in atomic system is absent. In this paper, we propose a scheme to realize the
interconversion (one-step) between GHZ state and KLM state with Rydberg atoms.
By utilizing Rydberg-mediated interactions, we simplify the system. By
combining Lie-transform-based pulse design, the evolution path is built up to
realize interconversion of GHZ state and KLM state. The numerical simulation
result shows that the present scheme is robust against decoherence and
operational imperfection, the analysis shows that the scheme is feasible with
current experimental technology.
