  We report the first measurements of the transverse ($P_{x}$ and $P_{y}$) and
longitudinal ($P_{z}$) components of the polarization transfer to a bound
proton in the deuteron via the $^{2}\mathrm{H}(\vec{e},e'\vec{p})$ reaction,
over a wide range of missing momentum. A precise determination of the electron
beam polarization reduces the systematic uncertainties on the individual
components, to a level that enables a detailed comparison to a state-of-the-art
calculation of the deuteron that uses free-proton electromagnetic form factors.
We observe very good agreement between the measured and the calculated
$P_{x}/P_{z}$ ratios, but deviations of the individual components. Our results
cannot be explained by medium modified electromagnetic form factors. They point
to an incomplete description of the nuclear reaction mechanism in the
calculation.
