Deterministic interconversion of GHZ state and KLM state via Lie-transform-based pulse design in Rydberg atoms

TL;DR

This paper presents a robust, one-step scheme using Lie-transform-based pulse design and Rydberg-mediated interactions to convert between GHZ and KLM entangled states in atomic systems, feasible with current technology.

Contribution

It introduces a novel, simplified method for direct interconversion of GHZ and KLM states in Rydberg atoms using pulse design and Lie transforms.

Findings

The scheme achieves high fidelity in state conversion.

It is robust against decoherence and operational imperfections.

The method is feasible with existing experimental setups.

Abstract

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.