Quantum Differential Privacy: An Information Theory Perspective
This work provides foundational insights for quantum computing security, addressing privacy guarantees in inherently noisy quantum systems, though it is incremental by extending classical differential privacy concepts to the quantum domain.
The paper tackles the problem of analyzing quantum differential privacy by framing it as a quantum divergence, which simplifies proofs and yields new bounds for noise models, including in quantum circuits and machine learning, with a focus on comparing noise levels for privacy versus computational utility.
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, Renyi differential privacy and the hypothesis testing interpretation to the quantum setting, providing several new properties and insights.