Quantum Pufferfish Privacy: A Flexible Privacy Framework for Quantum Systems

TL;DR

This paper introduces quantum pufferfish privacy (QPP), a flexible framework for protecting private information in quantum systems, generalizing quantum differential privacy and enabling privacy auditing with quantum algorithms.

Contribution

It formulates QPP using the Datta-Leditzky divergence, provides its operational interpretation, and develops properties like convexity and composability, advancing quantum privacy theory.

Findings

QPP can be expressed via the Datta-Leditzky divergence.

The divergence admits a semi-definite program formulation.

QPP mechanisms exhibit convexity, composability, and post-processing properties.

Abstract

We propose a versatile privacy framework for quantum systems, termed quantum pufferfish privacy (QPP). Inspired by classical pufferfish privacy, our formulation generalizes and addresses limitations of quantum differential privacy by offering flexibility in specifying private information, feasible measurements, and domain knowledge. We show that QPP can be equivalently formulated in terms of the Datta-Leditzky information spectrum divergence, thus providing the first operational interpretation thereof. We reformulate this divergence as a semi-definite program and derive several properties of it, which are then used to prove convexity, composability, and post-processing of QPP mechanisms. Parameters that guarantee QPP of the depolarization mechanism are also derived. We analyze the privacy-utility tradeoff of general QPP mechanisms and, again, study the depolarization mechanism as an explicit instance. The QPP framework is then applied to privacy auditing for identifying privacy violations via a hypothesis testing pipeline that leverages quantum algorithms. Connections to quantum fairness and other quantum divergences are also explored and several variants of QPP are examined.