Hybrid entanglement purification for quantum repeaters

We present an entanglement purification protocol (EPP) to reconstruct some maximally hybrid entangled states (HESs) from nonmaximally mixed HESs. We use simple linear optical elements such as a polarization beam splitter (PBS) and beam splitter (BS) to achieve this task. Meanwhile, it is shown that the parity-check gates acted by PBS and BS are enough to complete the task, and the controlled-NOT (CNOT) gates or similar logic operations are not needed. Unlike the current EPPs, this protocol can purify not only the conventional bit-flip error and phase-flip error but also the dissipation error coming from the photon loss of the coherent state. It can also be extended to achieve the purification for multiphoton and multicoherent state HES. This protocol may be useful in current hybrid quantum repeaters.