Some Continuity Properties of Quantum Renyi Divergences

被引:3
作者
Mosonyi, Milan [1 ,2 ]
Hiai, Fumio [3 ]
机构
[1] MTA BME Lendulet Momentum Quantum Informat Theory, H-1111 Budapest, Hungary
[2] Budapest Univ Technol & Econ, Inst Math, Dept Anal & Operat Res, H-1111 Budapest, Hungary
[3] HUN REN Alfred Reny Inst Math, H-1053 Budapest, Hungary
关键词
Entropy; Particle measurements; Hilbert space; Atmospheric measurements; Task analysis; Quantum channels; Error probability; Quantum Renyi divergences; measured Renyi divergences; maximal Renyi divergences; relative entropy; quantum channel divergences; channel discrimination; strong converse; STRONG CONVERSE; RELATIVE ENTROPIES; CAPACITY; INEQUALITY; CHANNELS; TRACE;
D O I
10.1109/TIT.2023.3324758
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
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 Renyi alpha -divergences over all alpha >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 Renyi divergences. Motivated by this, we give a detailed analysis of the continuity properties of various other quantum (channel) Renyi divergences, which may be of independent interest.
引用
收藏
页码:2674 / 2700
页数:27
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