Local Differential Privacy Is Equivalent to Contraction of $E_γ$-Divergence

Asoodeh, Shahab; Aliakbarpour, Maryam; Calmon, Flávio P.

doi:10.48550/arxiv.2102.01258

Cited by 2 publications

(6 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We can also bound the hockey-stick divergence for any γ ≥ 1 directly by the trace-distance, leading to an alternative way of bounding the contraction coefficients. This generalizes the analog classical result in [3].…”

Section: The Quantum Hockey-stick Divergencesupporting

confidence: 85%

“…In fact from the properties of E γ one can see that this condition is restrictive enough to imply a bound on the trace distance contraction coefficient. This generalizes a classical result in [3]. Now the corollary follows because from Lemma 2.4 we get…”

Section: Local Quantum Differential Privacysupporting

confidence: 80%

“…In principle, Corollary 5.1 also holds for ( , δ)-LDP with respect to any set of states that includes all orthogonal pure states. For the minimal such set, ( , δ)-LDP would not just imply but indeed be equivalent to η e (A) ≤ δ as observed in the classical setting [3].…”

Section: Local Quantum Differential Privacymentioning

confidence: 85%

“…This in turn lets us make several observations that are solely based on the properties of the divergence, giving a fruitful new approach to discussing quantum differential privacy. The divergence of choice is the quantum hockey-stick divergence introduced in [30] and the general framework follows classical work presented among others in [4,3] using tools such as contraction coefficients to bound differential privacy in iterative algorithms.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Quantum Differential Privacy: An Information Theory Perspective

Hirche¹,

Rouzé²,

França³

2022

Preprint

View full text Add to dashboard Cite

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, Rényi differential privacy and the hypothesis testing interpretation to the quantum setting, providing several new properties and insights.

show abstract

Section: The Quantum Hockey-stick Divergencesupporting

confidence: 85%

Section: Local Quantum Differential Privacysupporting

confidence: 80%

Section: Local Quantum Differential Privacymentioning

confidence: 85%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Quantum Differential Privacy: An Information Theory Perspective

Hirche¹,

Rouzé²,

França³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…We give a more formal definition below, but we observe here that the notion of f -divergence generalizes common divergences including total variation, KL-divergence, Renyi divergences, and E γ divergence [Polyanskiy and Wu, 2022+, Van Erven and Harremos, 2014, Asoodeh et al, 2021. We will make the assumption that for some convex f , the source and target measures satisfy D f (ν||µ) < ∞ and ask what the sample complexity of ε-approximate rejection sampling is under this constraint.…”

Section: Introductionmentioning

confidence: 99%

The Sample Complexity of Approximate Rejection Sampling with Applications to Smoothed Online Learning

Block¹,

Polyanskiy²

2023

Preprint

View full text Add to dashboard Cite

Suppose we are given access to n independent samples from distribution µ and we wish to output one of them with the goal of making the output distributed as close as possible to a target distribution ν. In this work we show that the optimal total variation distance as a function of n is given by Θ( D f ′ (n) ) over the class of all pairs ν, µ with a bounded f -divergence D f (ν µ) ≤ D. Previously, this question was studied only for the case when the Radon-Nikodym derivative of ν with respect to µ is uniformly bounded. We then consider an application in the seemingly very different field of smoothed online learning, where we show that recent results on the minimax regret and the regret of oracle-efficient algorithms still hold even under relaxed constraints on the adversary (to have bounded f -divergence, as opposed to bounded Radon-Nikodym derivative). Finally, we also study efficacy of importance sampling for mean estimates uniform over a function class and compare importance sampling with rejection sampling.

show abstract

Local Differential Privacy Is Equivalent to Contraction of $E_γ$-Divergence

Cited by 2 publications

References 0 publications

Quantum Differential Privacy: An Information Theory Perspective

Quantum Differential Privacy: An Information Theory Perspective

The Sample Complexity of Approximate Rejection Sampling with Applications to Smoothed Online Learning

Contact Info

Product

Resources

About