We show that the communication cost of quantum broadcast channel simulation under free entanglement assistance between the sender and the receivers is asymptotically characterized by an efficiently computable single-letter formula in terms of the channel's multipartite mutual information. Our core contribution is a new one-shot achievability result for multipartite quantum state splitting via multipartite convex splitting. As part of this, we face a general instance of the quantum joint typicality problem with arbitrarily overlapping marginals. The crucial technical ingredient to sidestep this difficulty is a conceptually novel multipartite mean-zero decomposition lemma, together with employing recently introduced complex interpolation techniques for sandwiched R\'enyi divergences. Moreover, we establish an exponential convergence of the simulation error when the communication costs are within the interior of the capacity region. As the costs approach the boundary of the capacity region moderately quickly, we show that the error still vanishes asymptotically.

翻译：我们证明，在发送方与接收方之间具有自由纠缠辅助的条件下，量子广播信道模拟的通信成本可由信道多部分互信息的一个有效可计算的单字母公式渐近刻画。我们的核心贡献是通过多部分凸分裂实现多部分量子态分裂的新单次可达性结果。作为该工作的一部分，我们面临一个具有任意重叠边际的量子联合典型性问题的通用实例。绕过这一困难的关键技术要素是概念新颖的多部分均值零分解引理，以及采用最近引入的夹层Rényi散度的复插值技术。此外，我们建立了当通信成本处于容量区域内部时模拟误差的指数收敛性。当成本以适度速度趋近容量区域边界时，我们证明误差仍会渐近消失。