Differential privacy has been an exceptionally successful concept when it comes to providing provable security guarantees for classical computations. More recently, the concept was generalized to quantum computations. While classical computations are essentially noiseless and differential privacy is often achieved by artificially adding noise, near-term quantum computers are inherently noisy and it was observed that this leads to natural differential privacy as a feature. In this work we discuss quantum differential privacy in an information theoretic framework by casting it as a quantum divergence. A main advantage of this approach is that differential privacy becomes a property solely based on the output states of the computation, without the need to check it for every measurement. This leads to simpler proofs and generalized statements of its properties as well as several new bounds for both, general and specific, noise models. In particular, these include common representations of quantum circuits and quantum machine learning concepts. Here, we focus on the difference in the amount of noise required to achieve certain levels of differential privacy versus the amount that would make any computation useless. Finally, we also generalize the classical concepts of local differential privacy, Renyi differential privacy and the hypothesis testing interpretation to the quantum setting, providing several new properties and insights.

翻译：差分隐私在提供经典计算的可证明安全性保证方面取得了极大成功。近年来，这一概念被推广至量子计算领域。经典计算本质上无噪声，差分隐私通常需通过人工添加噪声实现；而近期量子计算机固有噪声，且已有研究表明这能自然产生差分隐私特性。本文从信息论框架出发，将量子差分隐私视为一种量子散度进行讨论。该方法的主要优势在于，差分隐私成为仅基于计算输出状态的特性，无需对每次测量进行验证。这简化了其性质的证明与泛化表述，并为通用及特定噪声模型提供了若干新界。特别地，这些结果涵盖量子电路与量子机器学习概念的常见表示。本文重点探讨了实现特定差分隐私级别所需噪声量之差，以及该噪声量是否会使任何计算失效。最后，我们还将局部差分隐私、Rényi差分隐私及假设检验解释等经典概念推广至量子场景，揭示了若干新性质与洞见。