Decoherence-free-subspace-based deterministic conversions for entangled states with heralded robust-fidelity quantum gates.

The decoherence-free subspace (DFS) serves as a protective shield against certain types of environmental noise, allowing the system to remain coherent for extended periods of time. In this paper, we propose two protocols, i.e., one converts two-logic-qubit Knill-Laflamme-Milburn (KLM) state to two-logic-qubit Bell states, and the other converts three-logic-qubit KLM state to three-logic-qubit Greenberger-Horne-Zeilinger states, through cavity-assisted interaction in DFS. Especially, our innovative protocols achieve their objectives in a heralded way, thus enhancing experimental accessibility. Moreover, single photon detectors are incorporated into the setup, which can predict potential failures and ensure seamless interaction between the nitrogen-vacancy center and photons. Rigorous analyses and evaluations of two schemes demonstrate their abilities to achieve near-unit fidelities in principle and exceptional efficiencies. Further, our protocols offer progressive solutions to the challenges posed by decoherence, providing a pathway towards practical quantum technologies.