In addition to displaying strong nonclassical correlations in polarization, energy, momentum and spatial mode, photons from spontaneous downconversion may be entangled in multiple degrees of freedom simultaneously (“hyperentangled”). Such hyperentangled states reside in a much larger Hilbert space, and enable new capabilities in quantum communication and metrology. For example, hyperentanglement enables one to deterministically identify all four maximally entangled Bell states, leading to improved quantum dense coding. I will discuss this results and it’s extensions, in addition to another application, the remote preparation of entangled polarization/spatial-mode states. Specifically, by making a particular measurement on one photon of a hyperentangled pair (effectively a CNOT gate between polarization and spatial mode), Alice may remotely prepare Bob’s photon in entangled state of these two degrees of freedom. One example is a ‘radial-polarization’ state, in which the polarization of a light beam is everywhere radially directed. Such states have been shown to enable the largest possible longitudinal electric field component in the focal point of a lens, as well as the most efficient mode converter for light-atom coupling in free space. More generally, using these techniques, a wide range of other complex entangled polarization-spatial modes may be remotely prepared.The remotely prepared photons were analyzed in two ways, by quantum state tomography of the entire beam in the spin-orbit basis, and by direct tomography of the polarization state over the transverse spatial mode, using a small scanning pinhole.
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