HAO-CHUNG CHENGMin-Hsiu Hsieh2022-12-202022-12-202016-02-100018-9448https://www.scopus.com/inward/record.uri?eid=2-s2.0-84988614922&doi=10.1109%2fTIT.2016.2598835&partnerID=40&md5=69b843140e271014dddb9ef6641f6db3The auxiliary function of a classical channel appears in two fundamental quantities that upper and lower bound the error probability, respectively. A crucial property of the auxiliary function is its concavity, which leads to several important results in finite block length analysis. In this paper, we prove that the auxiliary function of a classical-quantum channel also enjoys the same concave property, extending an earlier partial result to its full generality. The key component in our proof is a beautiful result of geometric means of operators.Auxiliary function; classical-quantum channel; matrix geometric mean; reliability function; sphere-packing bound; LOWER BOUNDS; INEQUALITIES; PROBABILITY; ERROR; TRACE; Quantum Physics; Quantum Physics; Computer Science - Information Theory; Mathematics - Information Theoryjournal article10.1109/TIT.2016.25988352-s2.0-84988614922WOS:000384304600038http://arxiv.org/abs/1602.03297v1