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

TL;DR

This paper presents a new dynamical-symmetry-based method for converting W states to GHZ states in neutral-atom systems, offering protocols with simpler, potentially time-independent laser controls and faster operation times.

Contribution

It introduces a Lie-algebraic, symmetry-based approach for W to GHZ state conversion, differing from previous invariant-based methods, and enables protocols with constant Rabi frequencies and shorter durations.

Findings

Protocol with time-independent Rabi frequencies achieved

Conversion can be completed in shorter time

Method simplifies experimental implementation

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.