  The super-sensitivity attained in quantum phase estimation is known to be
compromised in the presence of decoherence. This is particularly patent at
blind spots -- phase values at which sensitivity is totally lost. One remedy is
to use a precisely known reference phase to shift the operation point of the
sensor to a less vulnerable phase value. We present here an alternative
approach based on combining the probe with an ancillary degree of freedom
containing adjustable parameters to create an entangled quantum state of higher
dimension. We validate this concept by simulating a configuration of a
Mach-Zehnder interferometer with a two-photon probe and a polarization ancilla
of adjustable parameters, entangled at a polarizing beam splitter. At the
interferometer output, the photons are measured after an adjustable unitary
transformation in the polarization subspace. Through calculation of the Fisher
information and simulation of an adaptive estimation procedure, we show that
optimizing the adjustable polarization parameters using an adaptive measurement
process provides globally super-sensitive unbiased phase estimates for a range
of decoherence levels, without prior information or a reference phase.
