Quantum Soft-Covering Lemma and its Applications to Rate-Distortion Coding, Channel Resolvability, and Identification via Quantum Channels

The quantum soft-covering problem aims to find the minimum rank of an input state needed to approximate a given quantum channel output. The authors prove a one-shot quantum soft-covering lemma and demonstrate its applications in rate-distortion coding, channel resolvability, and identification capacities of quantum channels.