Deterministic interconversions between the Greenberger-Horne-Zeilinger states and the W states by invariant-based pulse design

In the paper, we propose a protocol for the one-step interconversions between the Greenberger-Horne-Zeilinger (GHZ) states and the W states with deterministic success probabilities. The Rydberg interactions among three Rydberg atoms are utilized here to structure nonlocal operations for the interconversions. Additionally, we construct a Lewis-Riesenfeld invariant for a four-level system and afterwards use it to reversely design the Rabi frequencies of the effective Hamiltonian. The numerical simulations indicate that the protocol is robust against the spontaneous emission, the dephasing, the thermal noise, the systematic errors on Rabi frequencies, and the frequency mismatching. Therefore, the protocol may contribute to the research of the interconversions between entanglements.