Quantum Local Differential Privacy and Quantum Statistical Query Model

TL;DR

This paper explores the relationship between quantum statistical queries and quantum differential privacy, demonstrating their equivalence and applying these concepts to quantum learning, hypothesis testing, and multi-party computation.

Contribution

It establishes an equivalence between quantum statistical queries and quantum differential privacy, extending classical results to the quantum domain and analyzing their implications for quantum learning and computation.

Findings

Parity function is efficiently learnable under quantum local differential privacy.

Quantum relative entropy satisfies strong data processing inequalities.

Quantum multi-party computation benefits from privacy-enhanced robustness.

Abstract

Quantum statistical queries provide a theoretical framework for investigating the computational power of a learner with limited quantum resources. This model is particularly relevant in the current context, where available quantum devices are subject to severe noise and have limited quantum memory. On the other hand, the framework of quantum differential privacy demonstrates that noise can, in some cases, benefit the computation, enhancing robustness and statistical security. In this work, we establish an equivalence between quantum statistical queries and quantum differential privacy in the local model, extending a celebrated classical result to the quantum setting. Furthermore, we derive strong data processing inequalities for the quantum relative entropy under local differential privacy and apply this result to the task of asymmetric hypothesis testing with restricted measurements. Finally, we consider the task of quantum multi-party computation under local differential privacy. As a proof of principle, we demonstrate that the parity function is efficiently learnable in this model, whereas the corresponding classical task requires exponentially many samples.