  Careful tailoring the quantum state of probes offers the capability of
investigating matter at unprecedented precisions. Rarely, however, the
interaction with the sample is fully encompassed by a single parameter, and the
information contained in the probe needs to be partitioned on multiple
parameters. There exist then practical bounds on the ultimate joint-estimation
precision set by the unavailability of a single optimal measurement for all
parameters. Here we discuss how these considerations are modified for two-level
quantum probes - qubits - by the use of two copies and entangling measurements.
We find that the joint estimation of phase and phase diffusion benefits from
such collective measurement, while for multiple phases, no enhancement can be
observed. We demonstrate this in a proof-of-principle photonics setup.
