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We experimentally investigate the properties of hyperentangled statesdisplaying simultaneous entanglement in multiple degrees of freedom, and findthat Bell tests beyond the standard Clauser, Horne, Shimony, Holt inequalitycan reveal a higher-dimensional nature in a device-independent way.Specifically, we show that hyperentangled states possess more than justsimultaneous entanglement in separate degrees of freedom but also entanglementin a higher dimensional Hilbert space. We also verify the steerability ofhyperentangled quantum states by steering different photonic degrees offreedom.

Entanglement Verification of Hyperentangled Photon Pairs