Lossless multiple release, where any set of private releases is only as revealing as the least private one, is achievable for a broad class of additive noise mechanisms including Gaussian, Laplace, and Poisson.
We will need the following lemma that determines the sampling step of private lossless multiple release for the Poisson mechanism: Lemma E.4
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Private Lossless Multiple Release
Lossless multiple release, where any set of private releases is only as revealing as the least private one, is achievable for a broad class of additive noise mechanisms including Gaussian, Laplace, and Poisson.