2022/03/07 by Armando Angrisani, Elham Kashefi, Angrisani, Armando +1 · 3 citations
Computer Science · Physics and Astronomy · #Cryptography and Security (cs.CR) #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #FOS: Physical sciences #Machine Learning (cs.LG) #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2203.03591
openalex publication_date 2022/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.