  In this paper, we analyze several critical issues in semi-device independent
quantum information processing protocol. In practical experimental realization
randomness generation in that scenario is possible only if the efficiency of
the detectors used is above a certain threshold. Our analysis shows that the
critical detection efficiency is 0.7071 in the symmetric setup, while in the
asymmetric setup if one of the bases has perfect critical detection efficiency
then the other one can be arbitrarily close to 0. We also analyze the
semi-device independent random number generation efficiency based on different
averages of guessing probability. To generate more randomness, the proper
averaging method should be applied. Its choice depends on the value of a
certain dimension witness. More importantly, the general analytical
relationship between the maximal average guessing probability and dimension
witness is given.
