Error-Heralded and Deterministic Interconversion Between W State and Greenberger-Horne-Zeilinger State with Faithful Quantum Gates in Decoherence-Free-Subspace

The interconversion of a variety of entangled states can facilitate the information transmission and decline the risk of error rates. Here two faithful protocols to achieve deterministic interconversion between three-logic-qubit W state and three-logic-qubit Greenberger-Horne-Zeilinger state in decoherence-free subspace (DFS), resorting to the state-selective property of the quantum dot (QD)-cavity systems and robust-fidelity quantum control gates are presented. Moreover, the single-photon detectors introduced can effectively herald and mitigate potential failures from imperfect interaction between the QD-cavity system and photons, significantly enhancing experimental feasibility. Through comprehensive analysis and evaluation, the protocols demonstrate exceptional conversion efficiencies and deliver near-perfect fidelities. Additionally, the DFS makes system coherence over extended periods to overcome the decoherence effect caused by specific environmental noise, paving the way for quantum information processing.