  We investigate the tradeoff between privacy and utility in a situation where
both privacy and utility are measured in terms of mutual information. For the
binary case, we fully characterize this tradeoff in case of perfect privacy and
also give an upper-bound for the case where some privacy leakage is allowed. We
then introduce a new quantity which quantifies the amount of private
information contained in the observable data and then connect it to the optimal
tradeoff between privacy and utility.
