Optimal Second-Order Rates for Quantum Information Decoupling
Yu-Chen Shen, Li Gao, Hao-Chung Cheng
TL;DR
This work resolves the problem of tightly characterizing the maximal remainder dimension in quantum information decoupling under trace distance by deriving near-optimal one-shot bounds expressed through the conditional hypothesis-testing entropy $H_{\mathrm{h}}^{\varepsilon}$. The results yield the exact second-order asymptotics in the i.i.d. setting, with a leading term $\frac{1}{2}(\log|A|+H(A|E))$ and a variance-driven correction $\frac{1}{2}\sqrt{nV(A|E)}\,\Phi^{-1}(\varepsilon)$, plus a moderate-deviation regime. The bounds are complemented by a converse and an application to entanglement distillation under $1$-LOCC, providing a practical achievability bound for distillable entanglement. Overall, the paper delivers a tight one-shot decoupling characterization that closes gaps in prior second-order analyses and offers valuable implications for quantum communication protocols.
Abstract
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.