Heralded interconversion between hyperentangled W state and hyperentangled KLM state assisted by nitrogen vacancy centers coupled with microresonators.

As the hyperentanglement of photon systems holds lots of remarkable applications for enhancing channel capacity with less quantum resource, the interconversion of various hyperentangled states warrants in-depth investigation and becomes a vital work for quantum information technologies. Here we realize completely mutual conversions between spatial-polarization hyperentangled Knill-Laflamme-Milburn state and hyperentangled W state for three-photon systems, resorting to hyperparallel quantum control gates and the practical nonlinear interaction of nitrogen-vacancy centers coupled with whispering-gallery-mode microresonators. The hyperparallel quantum gates, i.e., hyperparallel controlled-not and controlled-swap gates, are fundamental prerequisites for realizing interconversions of two hyperentangled states in a deterministic way. The fidelities of these conversion processes are robust and their efficiencies are also high due to fewer nonlinear interactions and errors heralded by the response of detectors, which intensify comprehending the properties of hyperentanglement.