The optimal success probability of a communication game sets fundamental limitations on an operational theory. The quantum advantage of a parity oblivious random access code (PORAC), a communication game, over classical resources reveals the preparation contextuality of quantum theory [R. W. Spekkens et al., Phys. Rev. Lett. 102, 010401 (2009)]. The optimal quantum advantage in the $N$-dit PORAC game for finite dimensions is an open problem. Here, we show that the degree of uncertainty allowed in an operational theory determines the amount of preparation contextuality. We connect the upper bound of the fine-grained uncertainty relation to the success probability of a PORAC game played with the quantum resource. Subsequently, we find the optimal success probability for a 2-dit PORAC game using mutually unbiased bases for the decoding strategy. Finally, we also derive an upper bound on the quantum advantage for the $N$-dit PORAC game.

中文翻译：

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细粒度不确定性在确定制备上下文限制中的作用

通信游戏的最佳成功概率对操作理论设置了基本限制。奇偶不经意随机访问码 (PORAC)（一种通信游戏）相对于经典资源的量子优势揭示了量子理论的准备背景 [RW Spekkens et al. ，物理。牧师莱特。 102 , 010401 (2009)]。最优量子优势$N$-dit PORAC 有限维博弈是一个开放问题。在这里，我们展示了操作理论中允许的不确定性程度决定了准备环境的数量。我们将细粒度不确定性关系的上限与使用量子资源玩的 PORAC 游戏的成功概率联系起来。随后，我们使用相互无偏的基为解码策略找到了 2-dit PORAC 游戏的最佳成功概率。最后，我们还推导出了量子优势的上限$N$-dit PORAC 游戏。