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，在发送端与接收端之间自由纠缠辅助下，量子广播信道模拟的通信成本可由信道多体互信息的一个高效可计算的单字母公式渐近刻画。本文的核心贡献在于通过多体凸分裂实现多体量子态分裂的新一shot可达性结果。为此，我们面临具有任意重叠边缘的量子联合典型性问题的通用情形。绕过这一困难的关键技术要素是概念新颖的多体均值零分解引理，以及采用近期引入的夹层Rényi散度复插值技术。此外，我们证明当通信成本处于容量区域内部时，模拟误差呈指数收敛；当成本以适当速度趋近容量区域边界时，误差仍渐近消失。