Hyperentanglement purification for two-photon six-qubit quantum systems

TL;DR

This paper proposes a practical hyperentanglement purification protocol for two-photon six-qubit states across three degrees of freedom, enhancing quantum communication capacity.

Contribution

It introduces a two-step hyperentanglement purification scheme using parity checks and SWAP gates, applicable to multiple degrees of freedom, with implementation via nitrogen-vacancy centers.

Findings

Efficient correction of bit-flip errors in three DOFs.

Universal applicability of SWAP gates for hyper-EPP.

Feasible implementation with current nitrogen-vacancy center technology.

Abstract

Recently, two-photon six-qubit hyperentangled states were produced in experiment and they can improve the channel capacity of quantum communication largely. Here we present a scheme for the hyperentanglement purification of nonlocal two-photon systems in three degrees of freedom (DOFs), including the polarization, the first-longitudinal-momentum, and the second longitudinal momentum DOFs. Our hyperentanglement purification protocol (hyper-EPP) is constructed with two steps resorting to parity-check quantum nondemolition measurement on the three DOFs and SWAP gates, respectively. With these two steps, the bit-flip errors in the three DOFs can be corrected efficiently. Also, we show that using SWAP gates is a universal method for hyper-EPP in the polarization DOF and multiple longitudinal momentum DOFs. The implementation of our hyper-EPP is assisted by nitrogen-vacancy centers in optical microcavities, which could be achieved with current techniques. It is useful for long-distance high-capacity quantum communication with two-photon six-qubit hyperentanglement.