We show that a simple telescoping sum trick, together with the triangle inequality and a tensorisation property of expected-contractive coefficients of random channels, allow us to achieve general simultaneous decoupling for multiple users via local actions. Employing both old [Dupuis et al. Commun. Math. Phys. 328:251-284 (2014)] and new methods [Dupuis, arXiv:2105.05342], we obtain bounds on the expected deviation from ideal decoupling either in the one-shot setting in terms of smooth min-entropies, or the finite block length setting in terms of R\'enyi entropies. These bounds are essentially optimal without the need to address the simultaneous smoothing conjecture, which remains unresolved. This leads to one-shot, finite block length, and asymptotic achievability results for several tasks in quantum Shannon theory, including local randomness extraction of multiple parties, multi-party assisted entanglement concentration, multi-party quantum state merging, and quantum coding for the quantum multiple access channel. Because of the one-shot nature of our protocols, we obtain achievability results without the need for time-sharing, which at the same time leads to easy proofs of the asymptotic coding theorems. We show that our one-shot decoupling bounds furthermore yield achievable rates (so far only conjectured) for all four tasks in compound settings, that is for only partially known i.i.d. source or channel, which are furthermore optimal for entanglement of assistance and state merging.

翻译：我们证明，通过简单的伸缩求和技巧，结合三角不等式以及随机信道期望收缩系数的张量化特性，可以实现多用户通过局部操作达成一般性同步解耦。运用既有方法[Dupuis et al. Commun. Math. Phys. 328:251-284 (2014)]与新技术[Dupuis, arXiv:2105.05342]，我们在单次设定中以平滑最小熵为度量，或在有限块长设定中以Rényi熵为度量，获得了理想解耦期望偏差的界。这些界在本质上是最优的，且无需处理尚未解决的同步平滑猜想。由此我们为量子香农理论中的多项任务得到了单次、有限块长及渐近可达性结果，包括多方局部随机性提取、多方辅助纠缠浓缩、多方量子态合并以及量子多址信道的量子编码。由于协议的单次特性，我们无需时分复用即获得可达性结果，同时这也简化了渐近编码定理的证明。我们进一步证明，我们的单次解耦界能为复合设定（即仅部分已知的独立同分布信源或信道）中的所有四项任务提供可达速率（此前仅为猜想），且该速率对于辅助纠缠与态合并任务是最优的。