arXiv:2601.16845 · v2
Information Contraction under $(\varepsilon,δ)$-Differentially Private Mechanisms
摘要
The distinguishability quantified by information measures after being processed by a private mechanism has been a useful tool in studying various statistical and operational tasks while ensuring privacy. To this end, standard data-processing inequalities and strong data-processing inequalities (SDPI) are employed. Most of the previously known and even tight characterizations of contraction of information measures, including total variation distance, hockey-stick divergences, and $f$-divergences, are applicable for $(\varepsilon,0)$-local differential private (LDP) mechanisms. In this work, we derive both linear and non-linear strong data-processing inequalities for hockey-stick divergence and $f$-divergences that are valid for all $(\varepsilon,δ)$-LDP mechanisms even when $δ\neq 0$. Our results either generalize or improve the previously known bounds on the contraction of these distinguishability measures.
作者备注：6 pages, 3 figures; classical results from the paper arXiv:2512.16778 [quant-ph] that studies related quantum results; v2: Accepted to Information Theory Workshops (ITW-2026)