Heralded robust-fidelity mutual conversions of Λ-type three-atom entangled states

Quantum entanglement is a cornerstone in the development of quantum information technology. In this paper, we propose two deterministic approaches for interconversion between the Λ-type three-atom Knill–Laflamme–Milburn (KLM) entangled state and the three-atom W state. Interconversion requires error-manifested parity-check gates (EMPCGs), leveraging interactions between the Λ-type atom–cavity system and an auxiliary photon. Additionally, the quantum circuit of the EMPCG ensures predictable function by transforming practical imperfections from photon scattering into failure-heralded detection events. Our analysis demonstrates that two reversible conversions not only achieve robust fidelity but also maintain high efficiency, thereby providing deeper insights into the fundamental nature of entanglement.