High-efficient two-step entanglement purification using hyperentanglement

TL;DR

This paper introduces a highly efficient two-step entanglement purification protocol utilizing hyperentanglement across multiple degrees of freedom, significantly reducing resource consumption and improving practical implementation in quantum communication.

Contribution

The proposed protocol uniquely combines hyperentanglement in polarization, spatial-mode, and time-bin DOFs for a two-step purification, enhancing efficiency and residual entanglement reuse.

Findings

Higher purification efficiency than previous methods.

Effective reduction of entanglement consumption and experimental complexity.

Residual entanglement can be reused to improve yield.

Abstract

Entanglement purification is a powerful method to distill the high-quality entanglement from low-quality entanglement. In the paper, we propose an efficient two-step entanglement purification protocol (EPP) for the polarization entanglement by using only one copy of two-photon hyperentangled state in polarization, spatial-mode, and time-bin DOFs. We suppose that the entanglement in all DOFs suffer from channel noise. In two purification steps, the parties can reduce the bit-flip error and phase-flip error in polarization DOF by consuming the imperfect entanglement in the spatial-mode and time-bin DOFs, respectively. This EPP effectively reduces the consumption of entanglement pairs and the experimental difficulty. Moreover, if consider the practical photon transmission and detector efficiencies, our EPP has much higher purification efficiency than previous recurrence EPPs. Meanwhile, when one or two purification steps fail, the distilled mixed state may have residual entanglement. Taking use of the residual entanglement, the parties may still distill higher-quality polarization entanglement. Even if not, they can still reuse the residual entanglement in the next purification round. The existence of residual entanglement benefits for increasing the yield of the EPP. All the above advantages make our EPP have potential application in future quantum information processing.