  Two photons can simultaneously share entanglement between several degrees of
freedom such as polarization, energy-time, spatial mode and orbital angular
momentum. This resource is known as hyperentanglement, and it has been shown to
be an important tool for optical quantum information processing. Here we
demonstrate the quantum storage and retrieval of photonic hyperentanglement in
a solid-state quantum memory. A pair of photons entangled in polarization and
energy-time is generated such that one photon is stored in the quantum memory,
while the other photon has a telecommunication wavelength suitable for
transmission in optical fibre. We measured violations of a
Clauser-Horne-Shimony-Holt (CHSH) Bell inequality for each degree of freedom,
independently of the other one, which proves the successful storage and
retrieval of the two bits of entanglement shared by the photons. Our scheme is
compatible with long-distance quantum communication in optical fibre, and is in
particular suitable for linear-optical entanglement purification for quantum
repeaters.
