A unifying framework for differentially private quantum algorithms
This work addresses the challenge of securing sensitive information in quantum computing, providing a foundational framework that could impact privacy in near-term quantum devices, though it is incremental in refining existing quantum differential privacy concepts.
The paper tackles the problem of inconsistent definitions of neighboring quantum states in quantum differential privacy by proposing a novel, general definition that captures the structure of quantum encodings, resulting in exponentially tighter privacy guarantees for quantum measurements. It also shows that using multiple copies of input states can ensure differential privacy with minimal accuracy loss through concentration of measure and noise-adding mechanisms.
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.