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 Melectron-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.