We consider quantum discrimination between the Bunch-Davies vacuum and the stationary distribution. To get the theoretical limitation of the statistical discrimination, we assume the knowledge of qq, qp and pp correlations on a two-dimensional sphere (e.g. Last Scattering Surface). For a single direction observation with a short wave length, even if we know the qq, qp and pp correlations, the efficiency of the discrimination becomes bad, similar to the previous work B. Allen, et al (1999). However, if we can carry out the quantum measurement for 2l+1 directions, then the discrimination efficiency can be improved for the observation of a short wave length. (euqacation presented).