clarity recommendations the reviewers suggest, turning now to the main concerns of each reviewer

We thank the reviewers for their valuable feedback, which will improve the paper. Regarding the reviewer's comments about applications, we chose to limit the number of applications to three because Cauchy, which has unbounded variance), in contrast to our mechanisms. As requested, we will add a discussion about related work on lower bounds for private mechanisms. For the reviewer's main comment on the contributions of this paper with regard to Asi & Duchi 2020, we believe Such general (vector-valued) functions are the main focus of this submission. We thank the reviewer for bringing our attention to the Reimherr & A wan's K-norm mechanism (2019), which certainly We will discuss this work more carefully in the final version.