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 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 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.
Differential privacy is a widely used notion of security that enables the processing of sensitive information. In short, differentially private algorithms map "neighbouring" inputs to close output distributions. Prior work proposed several quantum extensions of differential privacy, each of them built on substantially different notions of neighbouring quantum states. In this paper, we propose a novel and general definition of neighbouring quantum states. We demonstrate that this definition captures the underlying structure of quantum encodings and can be used to provide exponentially tighter privacy guarantees for quantum measurements. Our approach combines the addition of classical and quantum noise and is motivated by the noisy nature of near-term quantum devices. Moreover, we also investigate an alternative setting where we are provided with multiple copies of the input state. In this case, differential privacy can be ensured with little loss in accuracy combining concentration of measure and noise-adding mechanisms. En route, we prove the advanced joint convexity of the quantum hockey-stick divergence and we demonstrate how this result can be applied to quantum differential privacy. Finally, we complement our theoretical findings with an empirical estimation of the certified adversarial robustness ensured by differentially private measurements.
Quantum computing, as an emerging research field, is attracting people’s attention. It has been proven to be superior in many ways to classical computing. Differential privacy provides an easy way to achieve demonstrable privacy, and the most common method is to add noise to datasets. At this stage of quantum computers, noise is a factor that cannot be ignored. Indeed, the existence of noise will negatively affect the performance of quantum computers, but we can apply it to privacy protection. In this work, we will consider two situations: inherent noise and artificially added noise. The noise is added to the variational quantum algorithm to implement quantum machine learning with differential privacy. The importance of each type will be examined and less artificial noise is needed for a common privacy budget over classical machine learning. Composition theory will be invoked to prove the advantage of the entire quantum machine learning process.
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.
Quantum technologies are beginning to reshape how large volumes of data are processed, yet they also introduce a new class of privacy challenges with no classical counterparts. These concerns stem from the availability of quantum side information, the encoding of data in non-classical states, and the fragility of conventional cryptographic systems in post-quantum environments. This work reviews the main privacy-preserving strategies proposed in peer-reviewed literature from 2020 to 2025, covering both quantum and post-quantum settings. The survey examines several key directions: (i) the integration of differential privacy into quantum machine learning pipelines, (ii) privacy guarantees derived from gentle-measurement principles, (iii) secure aggregation for quantum federated learning, and (iv) privacy amplification methods designed to remain robust under noisy quantum-channel conditions. Representative examples include the mechanisms introduced by Watkins et al. for embedding differential privacy into variational circuits, the theoretical limits established by Aaronson and Rothblum for privacy under gentle measurements, the distributed-learning protections developed by Liu and Zhang, and the noise-aware key-extraction analysis presented by Singh and colleagues. System-level considerations for future quantum infrastructures are discussed in the work of, while previous literature proposes hybrid quantum classical designs to strengthen privacy in post-quantum frameworks. Taken together, these studies reveal open challenges related to scalability, composability, and adversarial modelling, and they motivate a roadmap toward developing practical and verifiable privacy guarantees for emerging quantum platforms.
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.