Single-copy-based hyperentanglement purification using high-dimensional positive-operator-valued measures

Hyperentanglement can enlarge the information capacity of quantum information processes, but its quality will be decreased by environment noise. Here, we present a single-copy-based hyperentanglement purification protocol (HEPP) to improve the quality of the polarization-spatial hyperentangled photon state suffering from amplitude-damping noise. By using the local high-dimensional positive-operator-valued measure, a high-quality hyperentangled photon state can be purified from one copy of a noisy hyperentangled state without being destroyed, where only linear optical elements are required. Compared with the previous multicopy-based HEPPs, this single-copy-based HEPP can rapidly increase the fidelity of the noisy hyperentangled state with considerable success probability using fewer entanglement resources and it can extend the scope of application to a wider fidelity range of noisy hyperentangled states. Hence this work will have extensive applications in quantum information technology.