A general framework for differentially private quantum measurements

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 emphasize 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 neighboring 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 depolarizing and generalized 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 neighboring relation is compatible with quantum encodings of classical data, enabling privacy guarantees for the underlying classical inputs.