Survey parameters for detecting 21cm - Ly$\alpha$ emitter cross
  correlations with the Square Kilometre Array
  Detections of the cross correlation signal between the 21cm signal during
reionization and high-redshift Lyman Alpha emitters (LAEs) are subject to
observational uncertainties which mainly include systematics associated with
radio interferometers and LAE selection. These uncertainties can be reduced by
increasing the survey volume and/or the survey luminosity limit, i.e. the
faintest detectable Lyman Alpha (Ly$\alpha$) luminosity. We use our model of
high-redshift LAEs and the underlying reionization state to compute the
uncertainties of the 21cm-LAE cross correlation function at $z\simeq6.6$ for
observations with SKA1-Low and LAE surveys with $\Delta z=0.1$ for three
different values of the average IGM ionization state
($\langle\chi_\mathrm{HI}\rangle$=0.1, 0.25, 0.5). At $z\simeq6.6$, we find
SILVERRUSH type surveys, with a field of view of 21 deg$^2$ and survey
luminosity limits of $L_\alpha\geq7.9\times10^{42}$erg~s$^{-1}$, to be optimal
to distinguish between an inter-galactic medium (IGM) that is 50%, 25% and 10%
neutral, while surveys with smaller fields of view and lower survey luminosity
limits, such as the 5 and 10 deg$^2$ surveys with WFIRST, can only discriminate
between a 50% and 10% neutral IGM.
