Centralized differential privacy has been successfully applied to quantum computing and information processing to protect privacy and avoid leaks in the connections between neighboring quantum states. Consequently, quantum local differential privacy (QLDP) has been newly proposed to preserve quantum data privacy akin to the classical scenario where all states are viewed as neighboring states. However, the exploration of the QLDP framework is still in its early stages, primarily conceptual, which poses challenges for its practical implementation in safeguarding quantum state privacy.
Centralized differential privacy has been successfully applied to quantum computing and information processing to protect privacy and avoid leaks in the connections between neighboring quantum states. Consequently, quantum local differential privacy (QLDP) has been newly proposed to preserve quantum data privacy akin to the classical scenario where all states are viewed as neighboring states. However, the exploration of the QLDP framework is still in its early stages, primarily conceptual, which poses challenges for its practical implementation in safeguarding quantum state privacy.
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.
Quantum differential privacy provides a rigorous framework for quantifying privacy guarantees in quantum information processing. While classical correlations are typically regarded as adversarial to privacy, the role of their quantum analogue, entanglement, is not well understood. In this work, we investigate how quantum entanglement fundamentally shapes quantum local differential privacy (QLDP). We consider a bipartite quantum system whose input state has a prescribed level of entanglement, characterized by a lower bound on the entanglement entropy. Each subsystem is then processed by a local quantum mechanism and measured using local operations only, ensuring that no additional entanglement is generated during the process. Our main result reveals a sharp phase-transition phenomenon in the relation between entanglement and QLDP: below a mechanism-dependent entropy threshold, the optimal privacy leakage level mirrors that of unentangled inputs; beyond this threshold, the exact privacy leakage is strictly smaller than its unentangled value and admits an explicitly computable upper bound that strictly decreases with the entropy. This bound can also certify that some non-private mechanisms become private under sufficiently strong entanglement constraints. The phase-transition phenomenon gives rise to a nonlinear dependence of the certified privacy-leakage upper bound on the entanglement entropy, even though the underlying quantum mechanisms and measurements are linear. We show that the transition is governed by the intrinsic non-convex geometry of the set of entanglement-constrained quantum states, which we parametrize as a smooth manifold and analyze via Riemannian optimization. Our findings demonstrate that entanglement serves as a genuine privacy-enhancing resource, offering a geometric and operational foundation for designing robust privacy-preserving quantum protocols.
Quantum computing has gained widespread interest due to its exponential computational capabilities. In practical scenarios, users often access real quantum computers indirectly through cloud-based platforms (e.g., IBM Quantum), which requires transmitting data to third-party servers. Quantum-specific attacks, such as crosstalk attacks, have demonstrated high success rates in inferring the output of legitimate users. These issues raise serious privacy concerns. To protect client-side privacy, quantum local differential privacy (QLDP) has been proposed, where legitimate users perturbed their true output by adding quantum noise to the circuits. However, we observe that the classical local differential privacy (LDP) properties have not been fully adapted to the quantum domain, and the information can still be inferred from the perturbed output if attackers access the noise type added by legitimate users. To fill this gap, we propose a novel QLDP-based approach to protect the true output of legitimate users. We find that QLDP can be achieved using only simple quantum noise, but not all types of quantum noise can effectively perturb the output under different quantum measurements. In addition, to prevent advanced attackers who have partial user information, we introduce a probabilistic noise addition mechanism. To allow legitimate users to accurately estimate the true output of a quantum circuit, we also propose a new quantum frequency estimation. Our approach is validated using real quantum computers and quantum simulators, achieving 94% accuracy and 90% utility to estimate the true output from the perturbed output.
Differential privacy provides a mathematical framework for guaranteeing privacy for sensitive data. In quantum information processing, the interaction of privacy constraints with quantum resources such as entanglement remains a question of interest. Given that the utility of many protocols, and often the presence of a quantum advantage, relies on quantum resources such as entanglement, it is crucial to understand when a privacy requirement for a quantum channel is compatible with the channel's ability to preserve entanglement. We study this question for quantum local differential privacy (QLDP). Our main result shows that every ε-QLDP channel with a d-dimensional input is entanglement-breaking whenever ε≤logd−1d. We also prove an approximate version for (ε,δ)-QLDP, where channels in the same high-privacy regime are close in diamond norm to an entanglement-breaking channel. We further prove a composition result for a collection of private quantum channels having entangled inputs and global measurements in the high-privacy regime. Finally, we apply our results to private quantum learning theory. We prove that any learning protocol using arbitrary quantum memory on copies of the output of an entanglement-breaking channel can be simulated by a protocol that measures the corresponding unprocessed input copies one at a time while storing only classical information. Combining this result with our high-privacy entanglement-breaking theorem, we show that under sufficiently private local noise, a learning protocol with quantum memory for purity testing and bipartite product testing is subject to the sample complexity lower bounds for protocols with single-copy measurements on the noiseless tasks. We also obtain stronger sample complexity lower bounds when a single highly private channel acts on the entire multipartite input.
While quantum computing has strong potential in data-driven fields, the privacy issue of sensitive or valuable information involved in the quantum algorithm should be considered. Differential privacy (DP), which is a fundamental privacy tool widely used in the classical scenario, has been extended to the quantum domain, i.e., quantum differential privacy (QDP). QDP may become one of the most promising approaches toward privacy-preserving quantum computing since it is not only compatible with classical DP mechanisms but also achieves privacy protection by exploiting unavoidable quantum noise in noisy intermediate-scale quantum (NISQ) devices. This paper provides an overview of the various implementations of QDP and their performance in terms of privacy parameters under the DP setting. Specifically, we propose a taxonomy of QDP techniques, categorizing the literature on whether internal or external randomization is used as a source to achieve QDP and how these implementations are applied to each phase of the quantum algorithm. We also discuss challenges and future directions for QDP. By summarizing recent advancements, we hope to provide a comprehensive, up-to-date review for researchers venturing into this field.
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.