# Privacy-Utility Tradeoffs in Quantum Information Processing

arXiv: https://arxiv.org/abs/2602.10510 · HTML: https://mlsanity.com/paper/2602.10510/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 46 references that are in the map.
- First posted on arXiv 11 Feb 2026.

## Builds on (most cited first, 28 of 28)

- [Renyi Differential Privacy](https://mlsanity.com/paper/1702.07476/) (2017)
- [RAPPOR: Randomized Aggregatable Privacy-Preserving Ordinal Response](https://mlsanity.com/paper/1407.6981/) (2014)
- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [Minimax Optimal Procedures for Locally Private Estimation](https://mlsanity.com/paper/1604.02390/) (2016)
- [Privately Learning High-Dimensional Distributions](https://mlsanity.com/paper/1805.00216/) (2018)
- [Private Mean Estimation of Heavy-Tailed Distributions](https://mlsanity.com/paper/2002.09464/) (2020)
- [Differential Privacy as a Mutual Information Constraint](https://mlsanity.com/paper/1608.03677/) (2016)
- [Quantum Differential Privacy: An Information Theory Perspective](https://mlsanity.com/paper/2202.10717/) (2022)
- [The Structure of Optimal Private Tests for Simple Hypotheses](https://mlsanity.com/paper/1811.11148/) (2018)
- [Differentially Private Testing of Identity and Closeness of Discrete Distributions](https://mlsanity.com/paper/1707.05128/) (2017)
- [Local Differential Privacy Is Equivalent to Contraction of Eγ-Divergence](https://mlsanity.com/paper/2102.01258/) (2021)
- [Classical Shadows With Noise](https://mlsanity.com/paper/2011.11580/) (2020)
- [Privacy-Utility Trade-off of Linear Regression under Random Projections and Additive Noise](https://mlsanity.com/paper/1902.04688/) (2019)
- [Not one but many Tradeoffs: Privacy Vs. Utility in Differentially Private Machine Learning](https://mlsanity.com/paper/2008.08807/) (2020)
- [Utility-Optimized Local Differential Privacy Mechanisms for Distribution Estimation](https://mlsanity.com/paper/1807.11317/) (2018)
- [Quantum Local Differential Privacy and Quantum Statistical Query Model](https://mlsanity.com/paper/2203.03591/) (2022)
- [Simple Binary Hypothesis Testing under Local Differential Privacy and Communication Constraints](https://mlsanity.com/paper/2301.03566/) (2023)
- [Quantum Pufferfish Privacy: A Flexible Privacy Framework for Quantum Systems](https://mlsanity.com/paper/2306.13054/) (2023)
- [Contraction of Locally Differentially Private Mechanisms](https://mlsanity.com/paper/2210.13386/) (2022)
- [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)
- [An invitation to the sample complexity of quantum hypothesis testing](https://mlsanity.com/paper/2403.17868/) (2024)
- [Privacy-Utility Tradeoffs under Constrained Data Release Mechanisms](https://mlsanity.com/paper/1710.09295/) (2017)
- [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)
- [Query Complexity of Classical and Quantum Channel Discrimination](https://mlsanity.com/paper/2504.12989/) (2025)
- [Non-Linear Strong Data-Processing for Quantum Hockey-Stick Divergences](https://mlsanity.com/paper/2512.16778/) (2025)
- [When Does Quantum Differential Privacy Compose?](https://mlsanity.com/paper/2601.00337/) (2026)

## Abstract (arXiv)

When sensitive information is encoded in data, it is important to ensure the privacy of information when attempting to learn useful information from the data. There is a natural tradeoff whereby increasing privacy requirements may decrease the utility of a learning protocol. In the quantum setting of differential privacy, such tradeoffs between privacy and utility have so far remained largely unexplored. In this work, we study optimal privacy-utility tradeoffs for both generic and application-specific utility metrics when privacy is quantified by (varepsilon,δ)-quantum local differential privacy. In the generic setting, we focus on optimizing fidelity and trace distance between the original state and the privatized state. We show that the depolarizing mechanism achieves the optimal utility for given privacy requirements. We then study the specific application of learning the expectation of an observable with respect to an input state when only given access to privatized states. We derive a lower bound on the number of samples of privatized data required to achieve a fixed accuracy guarantee with high probability. To prove this result, we employ existing lower bounds on private quantum hypothesis testing, thus showcasing the first operational use of them. We also devise private mechanisms that achieve optimal sample complexity with respect to the privacy parameters and accuracy parameters, demonstrating that utility can be significantly improved for specific tasks in contrast to the generic setting. In addition, we show that the number of samples required to privately learn observable expectation values scales as Theta((varepsilon β)-2), where varepsilon ∈ (0,1) is the privacy parameter and β is the accuracy tolerance. We conclude by initiating the study of private classical shadows, which promise useful applications for private learning tasks.