  We present universal theoretical limits on the operation and performance of
non-magnetic passive ultrathin metasurfaces. In particular, we prove that their
local transmission, reflection, and polarization conversion coefficients are
confined to limited regions of the complex plane. As a result, full control
over the phase of the light transmitted through such metasurfaces cannot be
achieved if the polarization of the light is not to be affected at the same
time. We also establish fundamental limits on the maximum polarization
conversion efficiency of these metasurfaces, and show that they cannot achieve
more than 25% polarization conversion efficiency in transmission.
