Quantum Blackwell's Ordering and Differential Privacy

We develop a framework for quantum differential privacy (QDP) based on quantum hypothesis testing and Blackwell's ordering. This approach characterizes $(\eps,\delta)$-QDP via hypothesis testing divergences and identifies the most informative quantum state pairs under privacy constraints. We apply this to analyze the stability of quantum learning algorithms, generalizing classical results to the case $\delta>0$. Additionally, we study privatized quantum parameter estimation, deriving tight bounds on the quantum Fisher information under QDP. Finally, we establish near-optimal contraction bounds for differentially private quantum channels with respect to the hockey-stick divergence.