  We present a nondestructive parity-check detector (PCD) scheme for two
single-electron quantum dots embedded in double-sided optical microcavities.
Using a polarization-entangled photon pair, the PCD works in a parallel style
and is robust to the phase fluctuation of the optical path length. In addition,
we present an economic entanglement purification protocol for electron pairs
with our nondestructive PCD. The parties in quantum communication can increase
the purification efficiency and simultaneously decrease the quantum source
consumed for some particular fidelity thresholds. Therefore, our protocol has
good applications in the future quantum communication and distributed quantum
networks.
