  Local mutual-information differential privacy (LMIDP) is a privacy notion
that aims to quantify the reduction of uncertainty about the input data when
the output of a privacy-preserving mechanism is revealed. We study the relation
of LMIDP with local differential privacy (LDP), the de facto standard notion of
privacy in context-independent (CI) scenarios, and with local information
privacy (LIP), the state-of-the-art notion for context-dependent settings. We
establish explicit conversion rules, i.e., bounds on the privacy parameters for
a LMIDP mechanism to also satisfy LDP/LIP, and vice versa. We use our bounds to
formally verify that LMIDP is a weak privacy notion. We also show that
uncorrelated Gaussian noise is the best-case noise in terms of CI-LMIDP if both
the input data and the noise are subject to an average power constraint.
