Privacy amplification and decoupling without smoothing

2021/05/11 by Frédéric Dupuis, Dupuis, Frédéric · 9 citations
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Algorithm #Artificial intelligence #Computer science #Decoupling (probability) #Engineering #Entropy (arrow of time) #Exponent #FOS: Physical sciences #Mathematics #Physics #Privacy-Preserving Technologies in Data #Quantum #Quantum Physics (quant-ph) #Quantum mechanics #Sample complexity #Smoothing #Statistical physics #Statistics #Stochastic Gradient Optimization Techniques #Wireless Communication Security Techniques #quant-ph

paper · pdf · doi:10.48550/arxiv.2105.05342

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2021/05/11 · arxiv created 2022/01/09 · arxiv updated 2022/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

We prove an achievability result for privacy amplification and decoupling in terms of the sandwiched Rényi entropy of order α∈ (1,2]; this extends previous results which worked for α=2. The fact that this proof works for α close to 1 means that we can bypass the smooth min-entropy in the many applications where the bound comes from the fully quantum AEP or entropy accumulation, and carry out the whole proof using the Rényi entropy, thereby easily obtaining an error exponent for the final task. This effectively replaces smoothing, which is a difficult high-dimensional optimization problem, by an optimization problem over a single real parameter α.

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