We determine the exact error and strong converse exponent for entanglement-assisted classical-quantum channel simulation in worst case input purified distance. The error exponent is expressed as a single-letter formula optimized over sandwiched R\'enyi divergences of order $\alpha \in [1, \infty)$, notably without the need for a critical rate--a sharp contrast to the error exponent for classical-quantum channel coding. The strong converse exponent is expressed as a single-letter formula optimized over sandwiched R\'enyi divergences of order $\alpha\in [\frac{1}{2},1]$. As in the classical work [Oufkir et al., arXiv:2410.07051], we start with the goal of asymptotically expanding the meta-converse for channel simulation in the relevant regimes. However, to deal with non-commutativity issues arising from classical-quantum channels and entanglement-assistance, we critically use various properties of the quantum fidelity, additional auxiliary channel techniques, approximations via Chebyshev inequalities, and entropic continuity bounds.

翻译：我们确定了在最坏情况输入纯化距离下，纠缠辅助的经典-量子信道模拟的精确误差指数与强逆指数。误差指数表示为一个单字母公式，其优化范围在阶数 $\alpha \in [1, \infty)$ 的夹层R\'enyi散度上，值得注意的是，该公式无需临界速率——这与经典-量子信道编码的误差指数形成鲜明对比。强逆指数同样表示为一个单字母公式，其优化范围在阶数 $\alpha\in [\frac{1}{2},1]$ 的夹层R\'enyi散度上。与经典工作[Oufkir et al., arXiv:2410.07051]类似，我们首先旨在相关区域内渐近展开信道模拟的元逆。然而，为了处理由经典-量子信道和纠缠辅助引起的非对易性问题，我们关键性地利用了量子保真度的各种性质、额外的辅助信道技术、通过切比雪夫不等式进行的近似以及熵连续性界。