  We consider quantum metrology with arbitrary prior knowledge of the
parameter. We demonstrate that a single sensing two-level system can act as a
virtual multi-level system that offers increased sensitivity in a Bayesian,
single-shot, metrology scenario and that allows one to estimate (arbitrary)
large parameter values by avoiding phase wraps. This is achieved by making use
of additional degrees of freedom or auxiliary systems not participating in the
sensing process. The joint system is manipulated by intermediate control
operations in such a way that an effective Hamiltonian, with an arbitrary
spectrum, is generated that mimics the spectrum of a multi-level system
interacting with the field. We show how to use additional internal degrees of
freedom of a single trapped ion to achieve a high-sensitivity magnetic field
sensor for fields with arbitrary prior.
