# Quantum Differential Privacy: An Information Theory Perspective

arXiv: https://arxiv.org/abs/2202.10717 · HTML: https://mlsanity.com/paper/2202.10717/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 67 references that are in the map.
- First posted on arXiv 22 Feb 2022.

## Builds on (most cited first, 10 of 10)

- [Renyi Differential Privacy](https://mlsanity.com/paper/1702.07476/) (2017)
- [The Composition Theorem for Differential Privacy](https://mlsanity.com/paper/1311.0776/) (2013)
- [Hypothesis Testing Interpretations and Renyi Differential Privacy](https://mlsanity.com/paper/1905.09982/) (2019)
- [Quantum noise protects quantum classifiers against adversaries](https://mlsanity.com/paper/2003.09416/) (2020)
- [Quantum federated learning through blind quantum computing](https://mlsanity.com/paper/2103.08403/) (2021)
- [Quantum machine learning with differential privacy](https://mlsanity.com/paper/2103.06232/) (2021)
- [Local Privacy, Data Processing Inequalities, and Statistical Minimax Rates](https://mlsanity.com/paper/1302.3203/) (2013)
- [Quantum Differentially Private Sparse Regression Learning](https://mlsanity.com/paper/2007.11921/) (2020)
- [Local Differential Privacy Is Equivalent to Contraction of Eγ-Divergence](https://mlsanity.com/paper/2102.01258/) (2021)
- [Private learning implies quantum stability](https://mlsanity.com/paper/2102.07171/) (2021)

## Built on by (most cited first, 30 of 32)

- [Enhancing Quantum Adversarial Robustness by Randomized Encodings](https://mlsanity.com/paper/2212.02531/) (2022)
- [Quantum Local Differential Privacy and Quantum Statistical Query Model](https://mlsanity.com/paper/2203.03591/) (2022)
- [Quantum Federated Learning: A Comprehensive Survey](https://mlsanity.com/paper/2508.15998/) (2025)
- [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)
- [Expressibility-induced Concentration of Quantum Neural Tangent Kernels](https://mlsanity.com/paper/2311.04965/) (2023)
- [Contraction of Private Quantum Channels and Private Quantum Hypothesis Testing](https://mlsanity.com/paper/2406.18651/) (2024)
- [Differential Privacy Amplification in Quantum and Quantum-inspired Algorithms](https://mlsanity.com/paper/2203.03604/) (2022)
- [An invitation to the sample complexity of quantum hypothesis testing](https://mlsanity.com/paper/2403.17868/) (2024)
- [Constructing Optimal Noise Channels for Enhanced Robustness in Quantum Machine Learning](https://mlsanity.com/paper/2404.16417/) (2024)
- [When Federated Learning Meets Quantum Computing: Survey and Research Opportunities](https://mlsanity.com/paper/2504.08814/) (2025)
- [Detecting Violations of Differential Privacy for Quantum Algorithms](https://mlsanity.com/paper/2309.04819/) (2023)
- [Quantum Information Ordering and Differential Privacy](https://mlsanity.com/paper/2511.01467/) (2025)
- [Measured Hockey-Stick Divergence and its Applications to Quantum Pufferfish Privacy](https://mlsanity.com/paper/2501.12359/) (2025)
- [A Numerical Gradient Inversion Attack in Variational Quantum Neural-Networks](https://mlsanity.com/paper/2504.12806/) (2025)
- [Adversarial Robustness in Distributed Quantum Machine Learning](https://mlsanity.com/paper/2508.11848/) (2025)
- [Differentially Private Federated Quantum Learning via Quantum Noise](https://mlsanity.com/paper/2508.20310/) (2025)
- [Towards Adapting Federated & Quantum Machine Learning for Network Intrusion Detection: A Survey](https://mlsanity.com/paper/2509.21389/) (2025)
- [Query Complexity of Classical and Quantum Channel Discrimination](https://mlsanity.com/paper/2504.12989/) (2025)
- [Generalization Bounds for Quantum Learning via R'enyi Divergences](https://mlsanity.com/paper/2505.11025/) (2025)
- [Entangled Threats: A Unified Kill Chain Model for Quantum Machine Learning Security](https://mlsanity.com/paper/2507.08623/) (2025)
- [Non-Linear Strong Data-Processing for Quantum Hockey-Stick Divergences](https://mlsanity.com/paper/2512.16778/) (2025)
- [QUPID: A Partitioned Quantum Neural Network for Anomaly Detection in Smart Grid](https://mlsanity.com/paper/2601.11500/) (2026)
- [Q-ShiftDP: A Differentially Private Parameter-Shift Rule for Quantum Machine Learning](https://mlsanity.com/paper/2602.02962/) (2026)
- [Quantum-machine-assisted Drug Discovery](https://mlsanity.com/paper/2408.13479/) (2024)
- [Differential Privacy of Quantum and Quantum-Inspired Classical Recommendation Algorithms](https://mlsanity.com/paper/2502.04758/) (2025)
- [Sample-optimal learning of quantum states using gentle measurements](https://mlsanity.com/paper/2505.24587/) (2025)
- [Black-Box Auditing of Quantum Model: Lifted Differential Privacy with Quantum Canaries](https://mlsanity.com/paper/2512.14388/) (2025)
- [Sample Complexity of Composite Quantum Hypothesis Testing](https://mlsanity.com/paper/2601.08588/) (2026)
- [Privacy Implies Stability: Information-Theoretic Generalization Bounds for Quantum Learning](https://mlsanity.com/paper/2602.01177/) (2026)

## Abstract (arXiv)

Differential privacy has been an exceptionally successful concept when it comes to providing provable security guarantees for classical computations. More recently, the concept was generalized to quantum computations. While classical computations are essentially noiseless and differential privacy is often achieved by artificially adding noise, near-term quantum computers are inherently noisy and it was observed that this leads to natural differential privacy as a feature. In this work we discuss quantum differential privacy in an information theoretic framework by casting it as a quantum divergence. A main advantage of this approach is that differential privacy becomes a property solely based on the output states of the computation, without the need to check it for every measurement. This leads to simpler proofs and generalized statements of its properties as well as several new bounds for both, general and specific, noise models. In particular, these include common representations of quantum circuits and quantum machine learning concepts. Here, we focus on the difference in the amount of noise required to achieve certain levels of differential privacy versus the amount that would make any computation useless. Finally, we also generalize the classical concepts of local differential privacy, Renyi differential privacy and the hypothesis testing interpretation to the quantum setting, providing several new properties and insights.