Optimal Second-Order Rates for Quantum Information Decoupling

In this paper, we consider the standard quantum information decoupling, in which Alice aims to decouple her system from the environment by discarding some of her systems. To achieve an ε-decoupling with trace distance as the error criterion, we establish a one-shot characterization for the largest size of the remainder system in terms of the conditional (1 − ε)-hypothesis-testing entropy. When the underlying system is independent and identically prepared, our result leads to the matched second-order rate as well as the moderate deviation rate.