Deterministic Conversion of Hyperentangled States with Error-Heralded Quantum Units

In the paper, the possibility of two complete conversions is investigated, one is from the two-photon hyperentangled Knill-Laflamme-Milburn (KLM) state to hyperentangled Bell states, the other is from three-photon KLM state to the hyperentangled Greenberger-Horne-Zeilinger states, for photonic systems hyper-encoded in polarization and spatial degrees of freedom assisted by error-heralded quantum units (EHQUs). The system inhomogeneity and/or the imperfect photon scattering often restrict the performance of effective conversions of two types of hyperentangled states, and result in the reductions of the fidelity and the efficiency in tangible quantum information technologies. The polarization EHQU and spatial EHQU are two critical tools for actualizing two hyperentangled conversions in a heralded way, as the errors stemming from the system inhomogeneity and practically imperfect scattering are converted into efficacious responses of the detectors in our protocols. Thus, the fidelities of these conversion cases keep unchanged and have close to unity fidelities, which deepen the understanding of the properties of hyperentanglement. The two complete conversion possibilities from the two-photon hyperentangled Knill-Laflamme-Milburn (KLM) state to Bell states and three-photon hyperentangled KLM state to Greenberger-Horne-Zeilinger states hyper-encoded in polarization and spatial degrees of freedom assisted by error-heralded quantum units, respectively, are investigated. As the errors stemming from practically imperfect scattering are converted into efficacious responses of the detectors, the fidelities keep close to unity.image