I will talk about the reliability function of general classical-quantum channels, which describes the optimal exponent of the decay of decoding error when the communication rate is below the capacity. As the main result, we prove a lower bound, in terms of the quantum Rényi information in Petz's form, for the reliability function. This resolves Holevo's conjecture proposed in 2000, a long-standing open problem in quantum information theory. It turns out that the obtained lower bound matches the upper bound derived by Dalai in 2013, when the communication rate is above a critical value. Thus, we have determined the reliability function in this high-rate case. Our approach relies on Renes' breakthrough made in 2022, which relates classical-quantum channel coding to that of privacy amplification, as well as our new characterization of the channel Rényi information. Based on joint work with Dong Yang.

Speaker's Bio: Li Ke, Professor and Doctoral Supervisor at the Mathematics Research Institute of Harbin Institute of Technology. He obtained his bachelor's and doctoral degrees from the University of Science and Technology of China in 2004 and 2009, respectively. He then conducted research at the National University of Singapore, IBM Watson Research Center, Massachusetts Institute of Technology, and California Institute of Technology. In 2017, he returned to China to join Harbin Institute of Technology and was selected for the National Youth Talent Program. Li Ke's research interest is quantum information theory, and related work has been published in Ann. Statist, Comm. Math. Phys, IEEE Trans. Inf. Theory, Nat. Phys, Phys. Rev. Lett Waiting for the magazine.