# Quantum Local Differential Privacy and Quantum Statistical Query Model

arXiv: https://arxiv.org/abs/2203.03591 · HTML: https://mlsanity.com/paper/2203.03591/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 108 references that are in the map.
- First posted on arXiv 7 Mar 2022.

## Builds on (most cited first, 24 of 24)

- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Certified Robustness to Adversarial Examples with Differential Privacy](https://mlsanity.com/paper/1802.03471/) (2018)
- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [Noise-Induced Barren Plateaus in Variational Quantum Algorithms](https://mlsanity.com/paper/2007.14384/) (2020)
- [Quantum noise protects quantum classifiers against adversaries](https://mlsanity.com/paper/2003.09416/) (2020)
- [Privacy for Free: Posterior Sampling and Stochastic Gradient Monte Carlo](https://mlsanity.com/paper/1502.07645/) (2015)
- [Privacy-preserving Prediction](https://mlsanity.com/paper/1803.10266/) (2018)
- [Local Differential Privacy for Deep Learning](https://mlsanity.com/paper/1908.02997/) (2019)
- [Online Learning of Quantum States](https://mlsanity.com/paper/1802.09025/) (2018)
- [Sample-efficient learning of quantum many-body systems](https://mlsanity.com/paper/2004.07266/) (2020)
- [Optimal Quantum Sample Complexity of Learning Algorithms](https://mlsanity.com/paper/1607.00932/) (2016)
- [Quantum Differential Privacy: An Information Theory Perspective](https://mlsanity.com/paper/2202.10717/) (2022)
- [Local Privacy, Data Processing Inequalities, and Statistical Minimax Rates](https://mlsanity.com/paper/1302.3203/) (2013)
- [Enabling Multi-programming Mechanism for Quantum Computing in the NISQ Era](https://mlsanity.com/paper/2102.05321/) (2021)
- [Quantum statistical query learning](https://mlsanity.com/paper/2002.08240/) (2020)
- [Local Differential Privacy Is Equivalent to Contraction of Eγ-Divergence](https://mlsanity.com/paper/2102.01258/) (2021)
- [Sample Efficient Algorithms for Learning Quantum Channels in PAC Model and the Approximate State Discrimination Problem](https://mlsanity.com/paper/1810.10938/) (2018)
- [Private learning implies quantum stability](https://mlsanity.com/paper/2102.07171/) (2021)
- [Stabiliser states are efficiently PAC-learnable](https://mlsanity.com/paper/1705.00345/) (2017)
- [Two new results about quantum exact learning](https://mlsanity.com/paper/1810.00481/) (2018)
- [Towards quantum advantage via topological data analysis](https://mlsanity.com/paper/2005.02607/) (2020)
- [On the Hardness of PAC-learning Stabilizer States with Noise](https://mlsanity.com/paper/2102.05174/) (2021)
- [Secure Multi-party Quantum Computation with a Dishonest Majority](https://mlsanity.com/paper/1909.13770/) (2019)

## Built on by (most cited first, 12 of 12)

- [Quantum Pufferfish Privacy: A Flexible Privacy Framework for Quantum Systems](https://mlsanity.com/paper/2306.13054/) (2023)
- [A unifying framework for differentially private quantum algorithms](https://mlsanity.com/paper/2307.04733/) (2023)
- [Contraction of Private Quantum Channels and Private Quantum Hypothesis Testing](https://mlsanity.com/paper/2406.18651/) (2024)
- [On the Role of Entanglement and Statistics in Learning](https://mlsanity.com/paper/2306.03161/) (2023)
- [Learning unitaries with quantum statistical queries](https://mlsanity.com/paper/2310.02254/) (2023)
- [Learning Quantum Processes with Quantum Statistical Queries](https://mlsanity.com/paper/2310.02075/) (2023)
- [Quantum Information Ordering and Differential Privacy](https://mlsanity.com/paper/2511.01467/) (2025)
- [Adversarial Robustness in Distributed Quantum Machine Learning](https://mlsanity.com/paper/2508.11848/) (2025)
- [Generalization Bounds for Quantum Learning via R'enyi Divergences](https://mlsanity.com/paper/2505.11025/) (2025)
- [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)

Quantum statistical queries provide a theoretical framework for investigating the computational power of a learner with limited quantum resources. This model is particularly relevant in the current context, where available quantum devices are subject to severe noise and have limited quantum memory. On the other hand, the framework of quantum differential privacy demonstrates that noise can, in some cases, benefit the computation, enhancing robustness and statistical security. In this work, we establish an equivalence between quantum statistical queries and quantum differential privacy in the local model, extending a celebrated classical result to the quantum setting. Furthermore, we derive strong data processing inequalities for the quantum relative entropy under local differential privacy and apply this result to the task of asymmetric hypothesis testing with restricted measurements. Finally, we consider the task of quantum multi-party computation under local differential privacy. As a proof of principle, we demonstrate that the parity function is efficiently learnable in this model, whereas the corresponding classical task requires exponentially many samples.