A novel definition for quantum privacy based on hypothesis testing is presented. This privacy notion possesses an operational interpretation based on the false positive and negative rates of adversaries attempting to distinguish among private categories to which quantum states belong using arbitrary measurements. Important properties of post processing and composition are established. The relationship between privacy against hypothesis-testing adversaries and quantum differential privacy are then examined. This enables analysis of hypothesis testing under differential privacy and in noisy quantum systems. It also provides an operational interpretation for quantum differential privacy.
A novel definition for quantum privacy based on hypothesis testing is presented. This privacy notion possesses an operational interpretation based on the false positive and negative rates of adversaries attempting to distinguish among private categories to which quantum states belong using arbitrary measurements. Important properties of post processing and composition are established. The relationship between privacy against hypothesis-testing adversaries and quantum differential privacy are then examined. This enables analysis of hypothesis testing under differential privacy and in noisy quantum systems. It also provides an operational interpretation for quantum differential privacy.
A novel definition for data privacy in quantum computing based on quantum hypothesis testing is presented in this paper. The parameters in this privacy notion possess an operational interpretation based on the success/failure of an omnipotent adversary being able to distinguish the private categories to which the data belongs using arbitrary measurements on quantum states. Important properties of post processing and composition are then proved for the new notion of privacy. The relationship between privacy against hypothesis-testing adversaries, defined in this paper, and quantum differential privacy are then examined. It is shown that these definitions are intertwined in some parameter regimes. This enables us to provide an interpretation for the privacy budget in quantum differential privacy based on its relationship with privacy against hypothesis testing adversaries.
We study quantum differential privacy (QDP) by defining a notion of the order of informativeness between two pairs of quantum states. In particular, we show that if the hypothesis testing divergence of the one pair dominates over that of the other pair, then this dominance holds for every f-divergence. This approach completely characterizes (ε,δ)-QDP mechanisms by identifying the most informative (ε,δ)-DP quantum state pairs. We apply this to study precise limits for privatized hypothesis testing and privatized quantum parameter estimation, including tight upper-bounds on the quantum Fisher information under QDP. Finally, we establish near-optimal contraction bounds for differentially private quantum channels with respect to the Hockey-Stick divergence.
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, Rényi differential privacy and the hypothesis testing interpretation to the quantum setting, providing several new properties and insights.
Differential privacy provides a rigorous framework for quantifying privacy leakage in data analysis, while its quantum extensions have become increasingly relevant with the development of quantum computing and quantum machine learning. In this work, we introduce and study quantum probabilistic local differential privacy, a relaxation of quantum local differential privacy in which the privacy constraint is allowed to fail on a spectral violation event with low probability. This quantity can be interpreted as the probability under the quantum superoperation of a quantum privacy-loss violation, and is closely related to the acceptance probability of the quantum Neyman-Pearson test at a small threshold. We investigate the basic structural properties of this privacy notion and clarify its relationship with existing forms of quantum differential privacy. We show the properties of quantum probabilistic local differential privacy under tensor-product composition and unitary post-processing, while it is in general neither convex nor closed under post-processing by arbitrary quantum channels. We further characterize when depolarizing noise satisfies quantum probabilistic local differential privacy under several representative scenarios. Finally, we connect quantum probabilistic privacy constraints with statistical inference by deriving a lower bound on probabilistically privatized contraction coefficients in terms of the hockey-stick divergence. As an application, we obtain sample complexity bounds of probabilistically privated asymmetric and symmetric quantum hypothesis testing. These results provide a systematic foundation for studying probabilistic privacy guarantees in quantum information processing and their operational consequences for private quantum statistical inference.
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.
Differential privacy provides a robust framework for protecting sensitive data, while maintaining its utility for computation. In essence, a differentially private algorithm takes as input the data of multiple parties, and returns an output disclosing minimal information about any individual party. Previous research has introduced several quantum extensions of differential privacy, with applications ranging from quantum machine learning on private classical data to quantum shadow tomography. However, the local model of quantum differential privacy – where each party is responsible for privatizing their own data at a local level – has received limited attention. This work delves into locally differentially private quantum measurements. Although any measurement can be made locally differentially private by adding noise to the outcome, we demonstrate that certain quantum measurements inherently satisfy some degree of local differential privacy for specific classes of input states. This finding has two significant implications: first, limiting the analysis to classical noise injection mechanisms may lead to suboptimal privacy-utility trade-offs for quantum data; second, the theory of differential privacy can be harnessed to further investigate the capabilities of quantum measurements. Motivated by these insights, we establish strong data processing inequalities for the quantum relative entropy under local differential privacy and apply these results to asymmetric hypothesis testing of quantum states with restricted measurements. Additionally, we prove an equivalence between quantum statistical queries and quantum differential privacy in the local model, thereby addressing an open question posed by Arunachalam et al. (2021). Finally, we consider the task of quantum multi-party computation under local differential privacy, demonstrating that parity functions can be efficiently learned in this model, whereas the corresponding classical task requires exponentially many samples.