  Geometrical phases have been applied in virtually every major branch of
physics and they play an important role in topology and knot theory in
mathematics and quantum computation. However, most of the early works focus on
pure quantum states which are very unrealistic and almost never occur in
practice. The two existed definitions -Uhlmann's and Sj\"{o}qvist's- would
result in different values for the geometric phase in general. The definition
of geometric phase in mixed state scenario is still an open question. Here we
present a unified framework for both approaches within one and the same
formalism based on simple interferometry. We then present experimental results
which confirm both approaches to mixed state geometric phase and clearly
demonstrate that their unification is possible. Our experiments are furthermore
the first such to measure Uhlmann's mixed state geometric phase and show in
addition that it is different to the Sj\"{o}qvist's phase.
