# Differential Privacy Amplification in Quantum and Quantum-inspired Algorithms

arXiv: https://arxiv.org/abs/2203.03604 · HTML: https://mlsanity.com/paper/2203.03604/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 53 references that are in the map.
- First posted on arXiv 7 Mar 2022.

## Builds on (most cited first, 25 of 25)

- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Certified Robustness to Adversarial Examples with Differential Privacy](https://mlsanity.com/paper/1802.03471/) (2018)
- [Semi-supervised Knowledge Transfer for Deep Learning from Private Training Data](https://mlsanity.com/paper/1610.05755/) (2016)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [The Composition Theorem for Differential Privacy](https://mlsanity.com/paper/1311.0776/) (2013)
- [Privacy Amplification by Subsampling: Tight Analyses via Couplings and Divergences](https://mlsanity.com/paper/1807.01647/) (2018)
- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (2021)
- [Distributed Differential Privacy via Shuffling](https://mlsanity.com/paper/1808.01394/) (2018)
- [Privacy Amplification by Iteration](https://mlsanity.com/paper/1808.06651/) (2018)
- [Robust data encodings for quantum classifiers](https://mlsanity.com/paper/2003.01695/) (2020)
- [Encoding-dependent generalization bounds for parametrized quantum circuits](https://mlsanity.com/paper/2106.03880/) (2021)
- [Quantum Recommendation Systems](https://mlsanity.com/paper/1603.08675/) (2016)
- [A quantum-inspired classical algorithm for recommendation systems](https://mlsanity.com/paper/1807.04271/) (2018)
- [Quantum noise protects quantum classifiers against adversaries](https://mlsanity.com/paper/2003.09416/) (2020)
- [An Equivalence Between Private Classification and Online Prediction](https://mlsanity.com/paper/2003.00563/) (2020)
- [q-means: A quantum algorithm for unsupervised machine learning](https://mlsanity.com/paper/1812.03584/) (2018)
- [Sampling-based sublinear low-rank matrix arithmetic framework for dequantizing quantum machine learning](https://mlsanity.com/paper/1910.06151/) (2019)
- [Quantum principal component analysis only achieves an exponential speedup because of its state preparation assumptions](https://mlsanity.com/paper/1811.00414/) (2018)
- [Quantum Differential Privacy: An Information Theory Perspective](https://mlsanity.com/paper/2202.10717/) (2022)
- [Privacy Amplification by Mixing and Diffusion Mechanisms](https://mlsanity.com/paper/1905.12264/) (2019)
- [Quantum statistical query learning](https://mlsanity.com/paper/2002.08240/) (2020)
- [Quantum-inspired low-rank stochastic regression with logarithmic dependence on the dimension](https://mlsanity.com/paper/1811.04909/) (2018)
- [Learning with Differential Privacy: Stability, Learnability and the Sufficiency and Necessity of ERM Principle](https://mlsanity.com/paper/1502.06309/) (2015)
- [Quantum-inspired sublinear classical algorithms for solving low-rank linear systems](https://mlsanity.com/paper/1811.04852/) (2018)
- [Private learning implies quantum stability](https://mlsanity.com/paper/2102.07171/) (2021)

## Built on by (most cited first, 6 of 6)

- [Federated Quantum Machine Learning with Differential Privacy](https://mlsanity.com/paper/2310.06973/) (2023)
- [Quantum Pufferfish Privacy: A Flexible Privacy Framework for Quantum Systems](https://mlsanity.com/paper/2306.13054/) (2023)
- [Detecting Violations of Differential Privacy for Quantum Algorithms](https://mlsanity.com/paper/2309.04819/) (2023)
- [Adversarial Robustness in Distributed Quantum Machine Learning](https://mlsanity.com/paper/2508.11848/) (2025)
- [Non-Linear Strong Data-Processing for Quantum Hockey-Stick Divergences](https://mlsanity.com/paper/2512.16778/) (2025)
- [Unclonability and Quantum Cryptanalysis: From Foundations to Applications](https://mlsanity.com/paper/2210.17545/) (2022)

## Abstract (arXiv)

Differential privacy provides a theoretical framework for processing a dataset about n users, in a way that the output reveals a minimal information about any single user. Such notion of privacy is usually ensured by noise-adding mechanisms and amplified by several processes, including subsampling, shuffling, iteration, mixing and diffusion. In this work, we provide privacy amplification bounds for quantum and quantum-inspired algorithms. In particular, we show for the first time, that algorithms running on quantum encoding of a classical dataset or the outcomes of quantum-inspired classical sampling, amplify differential privacy. Moreover, we prove that a quantum version of differential privacy is amplified by the composition of quantum channels, provided that they satisfy some mixing conditions.