Quantum Local Differential Privacy and Quantum Statistical Query Model
This work addresses the challenge of learning with limited quantum resources under noise, providing theoretical insights for quantum machine learning and privacy, though it is incremental as it extends classical results to quantum domains.
The paper established an equivalence between quantum statistical queries and quantum local differential privacy, extending a classical result to quantum settings, and demonstrated that the parity function is efficiently learnable in this model, requiring exponentially fewer samples than the classical counterpart.
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.