量子局部差分隐私与量子统计查询模型
Quantum Local Differential Privacy and Quantum Statistical Query Model
AI总结：
本文证明局部模型下量子统计查询与量子差分隐私等价，推导相关强数据处理不等式并应用于假设检验，还验证量子多方计算中奇偶函数可高效学习，优于经典场景的样本需求。
摘要：
量子统计查询为研究量子资源受限的学习器的计算能力提供了理论框架，该模型在当前可用量子设备受严重噪声影响、量子内存有限的背景下尤为适用。另一方面，量子差分隐私框架表明，噪声在某些场景下可对计算产生助益，提升鲁棒性与统计安全性。本研究建立了局部模型下量子统计查询与量子差分隐私的等价性，将一项经典的知名结论拓展至量子场景。此外，我们推导了局部差分隐私下量子相对熵的强数据处理不等式，并将该结果应用于测量受限的非对称假设检验任务。最后，我们研究了局部差分隐私下的量子多方计算任务，作为原理验证，我们证明奇偶函数在该模型下可高效学习，而对应的经典任务需要指数级数量的样本。
英文摘要：
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.
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