# Quantum Information Ordering and Differential Privacy

arXiv: https://arxiv.org/abs/2511.01467 · HTML: https://mlsanity.com/paper/2511.01467/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 33 references that are in the map.
- First posted on arXiv 3 Nov 2025.

## Builds on (most cited first, 5 of 5)

- [Quantum noise protects quantum classifiers against adversaries](https://mlsanity.com/paper/2003.09416/) (2020)
- [Quantum Differential Privacy: An Information Theory Perspective](https://mlsanity.com/paper/2202.10717/) (2022)
- [Quantum Local Differential Privacy and Quantum Statistical Query Model](https://mlsanity.com/paper/2203.03591/) (2022)
- [Quantum Pufferfish Privacy: A Flexible Privacy Framework for Quantum Systems](https://mlsanity.com/paper/2306.13054/) (2023)
- [Contraction of Private Quantum Channels and Private Quantum Hypothesis Testing](https://mlsanity.com/paper/2406.18651/) (2024)

## Built on by (most cited first, 3 of 3)

- [Non-Linear Strong Data-Processing for Quantum Hockey-Stick Divergences](https://mlsanity.com/paper/2512.16778/) (2025)
- [Privacy Implies Stability: Information-Theoretic Generalization Bounds for Quantum Learning](https://mlsanity.com/paper/2602.01177/) (2026)
- [Privacy-Utility Tradeoffs in Quantum Information Processing](https://mlsanity.com/paper/2602.10510/) (2026)

## Abstract (arXiv)

We study quantum differential privacy (QDP) by defining a notion of the order of informativeness between two pairs of quantum states. In particular, we show that if the hypothesis testing divergence of the one pair dominates over that of the other pair, then this dominance holds for every f-divergence. This approach completely characterizes (varepsilon,δ)-QDP mechanisms by identifying the most informative (varepsilon,δ)-DP quantum state pairs. We apply this to study precise limits for privatized hypothesis testing and privatized quantum parameter estimation, including tight upper-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.