  Hyperentanglement --- simultaneous entanglement between multiple degrees of
freedom of two or more systems --- has been used to enhance quantum information
tasks such as quantum communication and photonic quantum computing. Here we
show that hyperentanglement can lead to increased quantum advantage in
metrology, with contributions from the entanglement in each degree of freedom,
allowing for Heisenberg scaling in the precision of parameter estimation. Our
experiment employs photon pairs entangled in polarization and spatial degrees
of freedom to estimate a small tilt angle of a mirror. Precision limits beyond
shot noise are saturated through a simple binary measurement of the
polarization state. The broad validity of the dynamics considered here implies
that similar strategies based on hyperentanglement can offer improvement in a
wide variety of metrological tasks.
