  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.
