Differential Privacy Amplification in Quantum and Quantum-inspired Algorithms
This work addresses privacy concerns in quantum computing for data processing, offering foundational insights with potential broad impact in secure quantum algorithms.
The paper tackles the problem of enhancing differential privacy in quantum and quantum-inspired algorithms by proving that these algorithms amplify privacy through quantum encoding and composition of quantum channels, achieving new privacy amplification bounds.
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.