高量子局部差分隐私破坏纠缠
High quantum local differential privacy breaks entanglement
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中文总结 AI 辅助
本研究证明高隐私级别的量子局部差分隐私信道必然破坏纠缠，并应用于私有量子学习，得出样本复杂度下界。
中文摘要 AI 辅助
差分隐私为保障敏感数据的隐私提供了一个数学框架。在量子信息处理中，隐私约束与纠缠等量子资源的相互作用仍是一个值得关注的问题。鉴于许多协议的效用，以及通常量子优势的存在，依赖于纠缠等量子资源，因此理解量子信道的隐私要求与该信道保持纠缠的能力何时兼容至关重要。我们针对量子局部差分隐私（QLDP）研究了这一问题。我们的主要结果表明，当 ε≤log(d/(d−1)) 时，每个具有 d 维输入的 ε-QLDP 信道都是纠缠破坏的。我们还证明了 (ε,δ)-QLDP 的近似版本，其中同一高隐私机制下的信道在钻石范数上接近于纠缠破坏信道。我们进一步证明了在高隐私机制下，具有纠缠输入和全局测量的私有量子信道集合的组合结果。最后，我们将我们的结果应用于私有量子学习理论。我们证明，任何使用任意量子存储器对纠缠破坏信道输出的副本进行学习的学习协议，都可以通过一个协议来模拟，该协议一次一个地测量相应的未处理输入副本，同时仅存储经典信息。将此结果与我们的高隐私纠缠破坏定理相结合，我们表明在足够私密的局部噪声下，用于纯度测试和二分乘积测试的具有量子存储器的学习协议，其样本复杂度下界与对无噪声任务进行单副本测量的协议相同。当单个高度私密的信道作用于整个多部分输入时，我们还获得了更强的样本复杂度下界。
英文摘要
Differential privacy provides a mathematical framework for guaranteeing privacy for sensitive data. In quantum information processing, the interaction of privacy constraints with quantum resources such as entanglement remains a question of interest. Given that the utility of many protocols, and often the presence of a quantum advantage, relies on quantum resources such as entanglement, it is crucial to understand when a privacy requirement for a quantum channel is compatible with the channel's ability to preserve entanglement. We study this question for quantum local differential privacy (QLDP). Our main result shows that every $\varepsilon$-QLDP channel with a $d$-dimensional input is entanglement-breaking whenever $\varepsilon\leq\log\frac{d}{d-1}$. We also prove an approximate version for $(\varepsilon,δ)$-QLDP, where channels in the same high-privacy regime are close in diamond norm to an entanglement-breaking channel. We further prove a composition result for a collection of private quantum channels having entangled inputs and global measurements in the high-privacy regime. Finally, we apply our results to private quantum learning theory. We prove that any learning protocol using arbitrary quantum memory on copies of the output of an entanglement-breaking channel can be simulated by a protocol that measures the corresponding unprocessed input copies one at a time while storing only classical information. Combining this result with our high-privacy entanglement-breaking theorem, we show that under sufficiently private local noise, a learning protocol with quantum memory for purity testing and bipartite product testing is subject to the sample complexity lower bounds for protocols with single-copy measurements on the noiseless tasks. We also obtain stronger sample complexity lower bounds when a single highly private channel acts on the entire multipartite input.
发表机构
- University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
- Illinois Quantum Information Science and Technology (IQUIST) Center, University of Illinois Urbana-Champaign（伊利诺伊量子信息科学与技术中心）
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