Composition is a cornerstone of classical differential privacy, enabling strong end-to-end guarantees for complex algorithms through composition theorems (e.g., basic and advanced). In the quantum setting, however, privacy is defined operationally against arbitrary measurements, and classical composition arguments based on scalar privacy-loss random variables no longer apply. As a result, it has remained unclear when meaningful composition guarantees can be obtained for quantum differential privacy (QDP). In this work, we clarify both the limitations and possibilities of composition in the quantum setting. We first show that classical-style composition fails in full generality for POVM-based approximate QDP: even quantum channels that are individually perfectly private can completely lose privacy when combined through correlated joint implementations. We then identify a setting in which clean composition guarantees can be restored. For tensor-product channels acting on product neighboring inputs, we introduce a quantum moments accountant based on an operator-valued notion of privacy loss and a matrix moment-generating function. Although the resulting Rényi-type divergence does not satisfy a data-processing inequality, we prove that controlling its moments suffices to bound measured Rényi divergence, yielding operational privacy guarantees against arbitrary measurements. This leads to advanced-composition-style bounds with the same leading-order behavior as in the classical theory. Our results demonstrate that meaningful composition theorems for quantum differential privacy require carefully articulated structural assumptions on channels, inputs, and adversarial measurements, and provide a principled framework for understanding which classical ideas do and do not extend to the quantum setting.

翻译：组合性是经典差分隐私的基石，通过组合定理（例如基本和高级组合）为复杂算法提供强有力的端到端保证。然而，在量子场景中，隐私是针对任意测量的操作式定义，基于标量隐私损失随机变量的经典组合论证不再适用。因此，量子差分隐私（QDP）何时能获得有意义的组合保证一直不明确。在本工作中，我们阐明了量子场景中组合性的局限性与可能性。我们首先证明，对于基于POVM的近似QDP，经典风格的组合在完全一般性下失效：即使是单独完全私密的量子信道，在通过相关的联合实现组合时也可能完全丧失隐私性。随后，我们确定了一种可以恢复清晰组合保证的场景。对于作用于乘积相邻输入的张量积信道，我们基于算子值隐私损失和矩阵矩生成函数引入了量子矩会计师。尽管所得的Rényi型散度不满足数据处理不等式，我们证明控制其矩足以约束测量Rényi散度，从而产生针对任意测量的操作式隐私保证。这导出了与经典理论具有相同主阶行为的高级组合风格界。我们的结果表明，量子差分隐私的有意义组合定理需要仔细阐明关于信道、输入和对抗测量的结构性假设，并提供了一个原则性框架以理解哪些经典思想可以或不能推广到量子场景。