Differential privacy provides a theoretical framework for processing a dataset about $n$ users, in a way that the output reveals a minimal information about any single user. Such notion of privacy is usually ensured by noise-adding mechanisms and amplified by several processes, including subsampling, shuffling, iteration, mixing and diffusion. In this work, we provide privacy amplification bounds for quantum and quantum-inspired algorithms. In particular, we show for the first time, that algorithms running on quantum encoding of a classical dataset or the outcomes of quantum-inspired classical sampling, amplify differential privacy. Moreover, we prove that a quantum version of differential privacy is amplified by the composition of quantum channels, provided that they satisfy some mixing conditions.

翻译：差分隐私为处理包含n个用户数据集的算法提供了理论框架，确保输出结果泄露任何单个用户的信息量极小。这种隐私通常通过噪声添加机制实现，并通过子采样、混洗、迭代、混合及扩散等过程进行放大。在本研究中，我们提出了量子与量子启发算法的隐私放大界。特别地，我们首次证明：运行于经典数据集的量子编码或量子启发经典采样结果上的算法，能够放大差分隐私。此外，我们证明了量子版本的差分隐私可通过满足特定混合条件的量子信道组合实现放大。