  In this paper, we consider the standard quantum information decoupling, in
which Alice aims to decouple her system from the environment by local
operations and discarding some of her systems. To achieve an
$\varepsilon$-decoupling with trace distance as the error criterion, we
establish a near-optimal one-shot characterization for the largest dimension of
the remainder system in terms of the conditional
$(1-\varepsilon)$-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 matched moderate deviation rate. As an
application, we find an achievability bound in entanglement distillation
protocol, where the objective is for Alice and Bob to transform their quantum
state to maximally entangled state with largest possible dimension using only
local operations and one-way classical communications.
