共 53 条
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.
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页码:2674 / 2700
页数:27
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