📝 SummarXiv

Abstract

Hyperentanglement, which refers to entanglement across more than one degree of freedom (DoF), is a valuable resource in photonic quantum technology. Although hyperentangled states inherently facilitate access to high-dimensional Hilbert spaces, their distinguishing feature lies in the cross-DoF structures beyond independent entanglement in each DoF, which can be leveraged to enable novel and robust information processing schemes. In particular, for a spatial-polarization hyperentangled state generated from spontaneous parametric downconversion, the resulting polarization entanglement is structured by the spatial distribution of all interacting optical fields. Characterizing such cross-DoF structures is a crucial step towards employing hyperentangled states for practical quantum applications. Here, by performing polarization state tomography on all spatially correlated photon pairs, we have, for the first time, resolved the full-field spatial-polarization structure in a 251-dimensional hyperentangled biphoton state. We observe an entire class of near-maximally polarization-entangled states with an average concurrence of $0.8303 \pm 0.0004$, characterized by biphoton polarization phases that exhibit radial and linear gradients induced by the transverse momenta of the down-converted photons and the pump beam, respectively. Our study lays important groundwork for further exploiting the high dimensionality and cross-DoF correlations in hyperentangled states for future quantum technologies.