Hyperentangled-state generation in nanophotonic periodically poled lithium niobate waveguides

Hyperentanglement is a promising resource in the realm of quantum communication, owing to its exploitation of multiple degrees of freedom. In this paper, we report the generation of a two-mode hyperentangled state using one nanophotonic periodically poled lithium niobate waveguide. Our approach encompasses the manipulation of polarization, energy-time, and quadrature amplitude-phase degrees of freedom. Theoretical calculations reveal that the magnitude of the Clauser-Horne-Shimony-Holt parameter $|S|$ can reach $2.375$ even considering the multi-photon-pair generation effect, which is indicative of the entanglement in the polarization degree of freedom. Further analysis involved computing the joint spectral amplitude of the two-mode state, followed by Schmidt decomposition and Fourier transformation. The resulting joint uncertainty product $\mathrm{\ensuremath{\Delta}}({\ensuremath{\omega}}_{s}+{\ensuremath{\omega}}_{i})\mathrm{\ensuremath{\Delta}}({t}_{s}\ensuremath{-}{t}_{i})=0.4113$, implying that high-quality energy-time entanglement is achieved. Notably, the von Neumann entropy ${S}_{r}$ of our source reaches 0.192, confirming the presence of quadrature amplitude-phase entanglement within the generated state. Moreover, we theoretically apply our source in a free-space quantum key distribution system to demonstrate its potential to increase secret key rates. Our proposed scheme is an efficient and practical approach for facilitating high-capacity quantum communication systems.