AI 中文总结
该研究针对量子非局域性领域的长期开放性问题，构造了输入集大小为4和3、输出集均为6的双体内积游戏，作为最大纠缠态对于伪心灵感应游戏不完备的反例，证明了最大纠缠态并非此类游戏的完备资源。
AI 中文摘要
量子非局域性领域长期存在的开放性问题之一是，确定最大纠缠态对于 bipartite（ bipartite 译为“双体”）伪心灵感应游戏是否完备，即：每个存在完美纠缠策略的非局域游戏，是否都存在使用最大纠缠态的此类策略。我们构造了一个反例，形式为输入集大小分别为4和3、输出集均为6的双体非局域游戏，该游戏属于一类新的非局域游戏，我们称之为 inner product（内积）游戏，这类游戏可能具有独立的研究价值。
英文摘要
One of the longstanding open problems in quantum nonlocality is to determine if maximally entangled states are complete for bipartite pseudo-telepathic games: namely, if every nonlocal game which admits a perfect entangled strategy admits such a strategy which uses a maximally entangled state. We exhibit a counterexample to this in the form of a bipartite nonlocal game with input sets of size 4 and 3 and output sets both of size 6. This game is part of a new class of nonlocal games, which we call inner product games, which could be of independent interest.
