  Quantum metrology uses quantum states with no classical counterpart to
measure a physical quantity with extraordinary sensitivity or precision. Most
metrology schemes measure a single parameter of a dynamical process by probing
it with a specially designed quantum state. The success of such a scheme
usually relies on the process belonging to a particular one-parameter family.
If this assumption is violated, or if the goal is to measure more than one
parameter, a different quantum state may perform better. In the most extreme
case, we know nothing about the process and wish to learn everything. This
requires quantum process tomography, which demands an informationally-complete
set of probe states. It is very convenient if this set is group-covariant --
i.e., each element is generated by applying an element of the quantum system's
natural symmetry group to a single fixed fiducial state. In this paper, we
consider metrology with 2-photon ("biphoton") states, and report experimental
studies of different states' sensitivity to small, unknown collective SU(2)
rotations ("SU(2) jitter"). Maximally entangled N00N states are the most
sensitive detectors of such a rotation, yet they are also among the worst at
fully characterizing an a-priori unknown process. We identify (and confirm
experimentally) the best SU(2)-covariant set for process tomography; these
states are all less entangled than the N00N state, and are characterized by the
fact that they form a 2-design.
