  We present the results of a study of the time-averaged spectral energy
distributions (SEDs) of eight flat spectrum radio quasars (FSRQs) present in
the second catalog of high energy sources detected beyond 50 GeV by the {\it
Fermi}-Large Area Telescope (2FHL). Both leptonic and hadronic scenarios are
adopted to explain the multi-wavelength SEDs and we find them to be marginally
consistent with the 2FHL spectra above 50 GeV. We derive the expected degree of
X-ray and $\gamma$-ray polarizations both for the average and elevated activity
states and note that: (i) a hadronic radiative model consistently predicts a
higher degree of high energy polarization compared to leptonic ones, and (ii)
the X-ray polarization degree is higher than the $\gamma$-ray polarization in
the leptonic scenario, but similar to the $\gamma$-ray polarization if the
observed radiation is powered by hadronic processes. From the leptonic
modeling, the location of the $\gamma$-ray emitting region is found to be at
the outer edge of the broad line region (BLR) and is consistent with the
$\gamma\gamma$ opacity estimates for the $\gamma$-ray absorption by the BLR. We
conclude that a majority of the FSRQs could be detected by the upcoming
Cherenkov Telescope Array, though future high energy polarimeters will be able
to detect them only during elevated activity states, which could provide
supportive evidence for the hadronic origin of the X-ray and $\gamma$-ray
emission.
