  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.
