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We investigate the possibilities for a deterministic conversion between twoimportant types of maximally entangled multiqubit states, namely, $W$ andGreenberger-Horne-Zeilinger (GHZ) states, in the Rydberg-blockade regime of aneutral-atom system where each atom is subject to four external laser pulses.Such interconversions between $W$ states and their GHZ counterparts have quiterecently been addressed using the method of shortcuts to adiabaticity, moreprecisely techniques based on Lewis-Riesenfeld invariants [R.-H. Zheng {\em etal.}, Phys. Rev. A {\bf 101}, 012345 (2020)]. Motivated in part by this recentwork, we revisit the $W$ to GHZ state-conversion problem using a fundamentallydifferent approach, which is based on the dynamical symmetries of the systemand a Lie-algebraic parametrization of its permissible evolutions. In contrastto the previously used invariant-based approach, which leads to astate-conversion protocol characterized by strongly time-dependent Rabifrequencies of external lasers, ours can also yield one with time-independentRabi frequencies. This feature makes our protocol more easily applicableexperimentally, with the added advantage that it allows the desired stateconversion to be carried out in a significantly shorter time with the sametotal laser pulse energy used.

Conversion from $W$ to Greenberger-Horne-Zeilinger states in the Rydberg-blockade regime of neutral-atom systems: Dynamical-symmetry-based approach