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

Abstract

We investigate the possibilities for a deterministic conversion between two important types of maximally entangled multiqubit states, namely, $W$ and Greenberger-Horne-Zeilinger (GHZ) states, in the Rydberg-blockade regime of a neutral-atom system where each atom is subject to four external laser pulses. Such interconversions between $W$ states and their GHZ counterparts have quite recently been addressed using the method of shortcuts to adiabaticity, more precisely techniques based on Lewis-Riesenfeld invariants [R.-H. Zheng {\em et al.}, Phys. Rev. A {\bf 101}, 012345 (2020)]. Motivated in part by this recent work, we revisit the $W$ to GHZ state-conversion problem using a fundamentally different approach, which is based on the dynamical symmetries of the system and a Lie-algebraic parametrization of its permissible evolutions. In contrast to the previously used invariant-based approach, which leads to a state-conversion protocol characterized by strongly time-dependent Rabi frequencies of external lasers, ours can also yield one with time-independent Rabi frequencies. This feature makes our protocol more easily applicable experimentally, with the added advantage that it allows the desired state conversion to be carried out in a significantly shorter time with the same total laser pulse energy used.

final, published version

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• Dynamical generation of chiral $W$ and Greenberger-Horne-Zeilinger states in laser-controlled Rydberg-atom trimers
• Quantum-brachistochrone approach to the conversion from $W$ to Greenberger-Horne-Zeilinger states for Rydberg-atom qubits
• Interconversion of $W$ and Greenberger-Horne-Zeilinger states for Ising-coupled qubits with transverse global control
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• Single-atom transport in optical conveyor belts: Enhanced shortcuts-to-adiabaticity approach