Differential privacy (DP) is an influential privacy measure and has been studied to protect private data. DP has been often studied in classical probability theory, but few researchers studied quantum versions of DP. In this paper, we consider classical-quantum DP mechanisms which (i) convert binary private data to quantum states and (ii) satisfy a quantum version of the DP constraint. The class of classical-quantum DP mechanisms contains classical DP mechanisms. As a main result, we show that some classical DP mechanism optimizes any information quantity satisfying the information processing inequality. Therefore, the performance of classical DP mechanisms attains that of classical-quantum DP mechanisms.
Differential privacy (DP) is an influential privacy measure and has been studied to protect private data. DP has been often studied in classical probability theory, but few researchers studied quantum versions of DP. In this paper, we consider classical-quantum DP mechanisms which (i) convert binary private data to quantum states and (ii) satisfy a quantum version of the DP constraint. The class of classical-quantum DP mechanisms contains classical DP mechanisms. As a main result, we show that some classical DP mechanism optimizes any information quantity satisfying the information processing inequality. Therefore, the performance of classical DP mechanisms attains that of classical-quantum DP mechanisms.
Abstract Differential privacy (DP) is an influential method of protecting private data, and is a condition for a conditional probability distribution. Since we can regard DP as a condition for a tuple of probability vectors, it is natural to consider a similar condition for a tuple of density matrices as a quantum version of DP. This condition is called classical-quantum DP (CQ-DP) because it is considered in converting classical data to quantum states. In the study of DP (including CQ-DP), a positive parameter ɛ represents the privacy level to be guaranteed. In this paper, we show that CQ-DP has a quantum advantage in certain optimization problems. Moreover, we compare classical DP and CQ-DP mathematically to clarify a relation between privacy level and quantum advantage.
Differential privacy (DP) is a widely used framework for protecting sensitive information in data analysis and machine learning. With growing interest in quantum computing, substantial effort has gone into extending DP to quantum algorithms. However, many existing formulations emphasise global state distinguishability or privacy for channels that output quantum states, which is often misaligned with settings where the final output consists of classical measurement data, as in both fault-tolerant and near-term devices. In this work, we develop an observable-based approach to quantum DP tailored to expectation-value estimation from quantum measurements. We introduce a neighbouring relation defined directly in terms of observable expectation values and give general private mechanisms for broad measurement protocols, including classical shadows and eigenbasis measurements. We also show that realistic device noise (e.g., local depolarising and generalised amplitude damping) can amplify privacy guarantees for k -local observables. Complementing these positive results for private measurements, we establish limitations for differentially private mechanisms that release quantum states. Finally, we show that our neighbouring relation is compatible with quantum encodings of classical data, enabling privacy guarantees for the underlying classical inputs.
We optimize the trade-off between privacy and utility in the high-privacy regime. We adopt local differential privacy (LDP) and its quantum extension, quantum local differential privacy (QLDP), for privacy protection, and investigate utility functions including the Holevo information (which reduces to the mutual information in the classical case) and the error exponents in symmetric and asymmetric hypothesis testing. Under the LDP and QLDP constraints, these utility functions have classical and quantum optimal values, which we denote simply by C and Q, respectively, in this abstract. In this paper, we provide optimal LDP and QLDP mechanisms achieving the classical and quantum optimal values in the high-privacy regime, and prove that the asymptotic ratio Q/C in this regime takes the same value regardless of the utility function. Our results reveal quantum advantages (specifically, Q/C≥3/2) for the above utility functions when the private data take at least three possible values. In addition, conditional on a mathematical conjecture concerning equi-isoclinic tight fusion frames (EITFFs), our QLDP mechanisms also exhibit quantum advantages in a moderate-privacy regime.
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.
When sensitive information is encoded in data, it is important to ensure the privacy of information when attempting to learn useful information from the data. There is a natural tradeoff whereby increasing privacy requirements may decrease the utility of a learning protocol. In the quantum setting of differential privacy, such tradeoffs between privacy and utility have so far remained largely unexplored. In this work, we study optimal privacy-utility tradeoffs for both generic and application-specific utility metrics when privacy is quantified by (ε,δ)-quantum local differential privacy. In the generic setting, we focus on optimizing fidelity and trace distance between the original state and the privatized state. We show that the depolarizing mechanism achieves the optimal utility for given privacy requirements. We then study the specific application of learning the expectation of an observable with respect to an input state when only given access to privatized states. We derive a lower bound on the number of samples of privatized data required to achieve a fixed accuracy guarantee with high probability. To prove this result, we employ existing lower bounds on private quantum hypothesis testing, thus showcasing the first operational use of them. We also devise private mechanisms that achieve optimal sample complexity with respect to the privacy parameters and accuracy parameters, demonstrating that utility can be significantly improved for specific tasks in contrast to the generic setting. In addition, we show that the number of samples required to privately learn observable expectation values scales as Θ((εβ)−2), where ε∈(0,1) is the privacy parameter and β is the accuracy tolerance. We conclude by initiating the study of private classical shadows, which promise useful applications for private learning tasks.
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.