Self-error-rejecting multipartite entanglement purification for electron systems assisted by quantum-dot spins in optical microcavities

We present a self-error-rejecting multipartite entanglement purification protocol (MEPP) for N-electron-spin entangled states, resorting to the single-side cavity-spin-coupling system. Our MEPP has a high efficiency containing two steps. One is to obtain high-fidelity N-electron-spin entangled systems with error-heralded parity-check devices (PCDs) in the same parity-mode outcome of three electron-spin pairs, as well as M-electron-spin entangled subsystems (2≤M <N) in the different parity-mode outcomes of those. The other is to regain the N-electron-spin entangled systems from M-electron-spin entangled states utilizing entanglement link. Moreover, the quantum circuits of PCDs make our MEPP works faithfully, due to the practical photon-scattering deviations from the finite side leakage of the microcavity, and the limited coupling between a quantum dot and a cavity mode, converted into a failed detection in a heralded way.