Purification for Hybrid Logical Qubit Entanglement.

Hybrid logical qubit entangled state (HLES) that consists of both polarization part and coherent state part has drawn much attention and been applied in many quantum information protocols. However, the HLES is inevitable to suffer from environmental noise and may degrade to a mixed state. In this paper, we present a hybrid logical qubit entanglement purification protocol (HLEPP) that can distill one copy of high-quality HLES from two same low-quality copies. This HLEPP can directly purify the bit-flip errors occurring in the polarization part, the coherent state part, and the logical qubit, respectively. In addition, this HLEPP can also work in the photon loss condition. This protocol only requires linear optical elements, so that it is feasible in current experimental technology. Our work may have potential applications in future hybrid entanglement-based quantum information protocols.