Almost Perfect Privacy for Additive Gaussian Privacy Filters

We study the maximal mutual information about a random variable Y (representing non-private information) displayed through an additive Gaussian channel when guaranteeing that only $$\varepsilon $$ bits of information is leaked about a random variable X (representing private information) that is correlated with Y. Denoting this quantity by $$g_\varepsilon (X,Y)$$, we show that for perfect privacy, i.e., $$\varepsilon =0$$, one has $$g_0(X,Y)=0$$ …