Purification for Hybrid Entanglement between Discrete- and Continuous-Variable States

Hybrid entangled states (HES) have attracted significant attention and been utilized in various quantum information processing applications. However, like many other entangled states, maximally entangled HES may degrade to mixed states due to environmental noise and operational imperfections. In this paper, a hybrid entanglement purification protocol (HEPP) for the HES, which consists of photon-number state and coherent state is proposed. This HEPP is designed to effectively purify a bit-flip error occurring in any qubit of the HES. Furthermore, HEPP is extended to a general condition, say, the multi-party scenario, and integrates the generation of HES into the HEPP. Moreover, if different initial mixed states are chosen, then the residual entanglement can be utilized to distill high-quality entanglement. The HEPP has important applications in the future quantum information processing field. The hybrid entanglement purification protocol integrated with the generation of the hybrid entangled state (HES). The "Source" generates two pairs of desired HESs shared by Alice and Bob. Md and Mc are designed to make the parity checks for the discrete- and continuous-variable parts of the HESs, respectively.image