发表机构
National Cheng Kung University; Hon Hai (Foxconn) Research Institute; National Center for Theoretical Sciences; Patna Science College, Patna University（国立成功大学; 鸿海研究院; 国家理论科学中心; 巴特那大学巴特那理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究从非局域博弈推导出输入平均通信成本下界，证明并行魔方关联和CHSH关联的精确模拟成本分别下界为n log2(3/2)比特和约0.04627n比特，并给出层级上下界以精确确定平均通信成本。
AI 中文摘要
贝尔非局域关联无法在没有通信的局部隐变量模型下重现，因此经典通信成本成为非局域性的自然定量度量。尽管在固定的有限贝尔场景中，有限通信总是足以模拟任何关联，但确定（精确）模拟任何给定非局域关联所需的最小通信量仍然具有挑战性，尤其是在平均成本设置中。在此，我们从非局域博弈中推导出输入平均通信成本的下界，允许变长、完全交互的双向协议。当应用于并行博弈时，这些下界产生了明确的有限量子关联，其精确模拟成本超过任何预设的有限输入平均通信预算。对于n个并行的魔方获胜关联，我们证明了n log2(3/2)比特的下界，并给出了一种单向通信协议，该协议渐近地达到此速率。对于在n份Clauser-Horne-Shimony-Holt非局域博弈中最大获胜的量子关联，我们获得了精确模拟的输入平均下界约为0.04627n比特。最后，我们使用确定性关联在选定的通信成本下构建了一个下界和互补上界的层级结构。两者在最终层级都恢复了精确的输入平均成本，如果下界在较低层级一致，它们的共同值就给出了精确的输入平均成本，而无需考虑所有通信策略。
英文摘要
Bell nonlocal correlations cannot be reproduced by local hidden-variable models without communication, making classical communication cost a natural quantitative measure of nonlocality. Although finite communication always suffices to simulate any correlation in a fixed finite Bell scenario, determining the minimum amount needed to (exactly) simulate any given nonlocal correlation remains challenging, especially in the average-cost setting. Here, we derive lower bounds on input-average communication cost from nonlocal games, allowing variable-length, fully interactive two-way protocols. When applied to parallel games, these bounds yield explicit finite quantum correlations for which the exact simulation cost exceeds any prescribed finite input-average communication budget. For $n$ parallel Magic-Square-winning correlations, we prove a lower bound of $n\log_2(3/2)$ bits and give a one-way communication protocol that attains this rate asymptotically. For the quantum correlation maximally winning the $n$-copy of the Clauser--Horne--Shimony--Holt nonlocal game, we obtain an input-average lower bound of approximately $0.04627n$ bits for exact simulation. Finally, we formulate a hierarchy of lower bounds and complementary upper bounds using deterministic correlations up to chosen communication costs. Both recover the exact input-average cost at their final levels, and if the bounds agree at lower levels, their common value yields the exact input-average cost without needing to consider all communication strategies.
Comments10+10 pages, 2 figures, 2 tables; Comments are welcome!
