报告题目：A Novel and Error Exponent for Quantum Soft Covering

报告时间：2024-06-18   14:00-15:00

报  告 人：Prof. Hao-Chung Cheng (台湾大学)

报告地点：理学院东北楼四楼报告厅(404)

报告摘要:How well can we approximate a quantum channel output state using a codebook with a certain size? In this work, we study the so-called quantum soft covering problem, which is using a random codebook to approximate the target output state of a quantum channel. We establish a one-shot exponential bound on the expected trace-norm distance between the codebook-induced state and the true state. When using an independently and identically distributed random codebook with a rate above the quantum mutual information, we prove that the trace distances decay exponentially with error exponents determined by the Legendre transform of the quantum sandwiched Rényi information. As a result, it implies a tight bound on the information leakage to Eavesdroppers in private communication over wiretap quantum channels. Our proof technique is to establish a novel matrix concentration inequality by using interpolation of noncommutative L_p space. This may have applications elsewhere.

This talk is based on [IEEE TIT 70(5), 2024].