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.

报告人简介：李科，哈尔滨工业大学数学研究院教授，博士生导师。他分别于2004年和2009年在中国科学技术大学获得学士和博士学位，其后在新加坡国立大学、IBM 沃森研究中心和麻省理工学院、加州理工学院从事研究工作，2017年回国加入哈尔滨工业大学，入选国家青年人才计划。李科的研究兴趣为量子信息理论，相关工作发表在Ann. Statist, Comm. Math. Phys, IEEE Trans. Inf. Theory, Nat. Phys, Phys. Rev. Lett等杂志上。