2022/09/01 by Milán Mosonyi, Mosonyi, Milán, Hiai, Fumio · 3 citations
Computer Science · Engineering · #Adversarial Robustness in Machine Learning #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Information Theory (cs.IT) #Mathematical Physics (math-ph) #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Wireless Communication Security Techniques
paper · pdf · doi:10.48550/arxiv.2209.00646
openalex publication_date 2022/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In the problem of binary quantum channel discrimination with product inputs, the supremum of all type II error exponents for which the optimal type I errors go to zero is equal to the Umegaki channel relative entropy, while the infimum of all type II error exponents for which the optimal type I errors go to one is equal to the infimum of the sandwiched channel Rényi α-divergences over all α>1. We prove the equality of these two threshold values (and therefore the strong converse property for this problem) using a minimax argument based on a newly established continuity property of the sandwiched Rényi divergences. Motivated by this, we give a detailed analysis of the continuity properties of various other quantum (channel) Rényi divergences, which may be of independent interest.