AI 中文总结
该研究针对有界通信维度的完美博弈，将二元输出博弈归约为冲突图，证明量子比特策略可经典比特实现，还给出13射线qutrit图的压缩博弈应用，关联了通信、图论等多个领域。
AI 中文摘要
完美制备-测量博弈展现出全有或全无的量子优势：维度为$d$的量子系统可满足所有规定的获胜约束，而经典的$d$级消息无法做到。我们针对这类禁止输出支持约束建立了两个结构性结果：第一，每个二元输出支持博弈可精确归约为冲突图：用$d$级消息实现完美经典等价于$d$着色，用$d$维量子实现完美等价于$d$维正交表示，实现固定冲突图所需的最小Bob输入数是其边双覆盖数；第二，对于任意有限输出字母表，每个完美量子比特策略都存在完美经典比特实现。作为核心应用，13射线qutrit图产生压缩博弈$(X,Y,B)=(13,8,2)$，其中$C_3=39<Q_3=S=40$，且8个Bob输入是该图所有二元输出实现中的最小值。图扩展在每个维度中展示了该机制，而Torpedo博弈和反可区分博弈则说明了真正的非二元情形。这些结果将精确通信、图着色、语境性、态排除和零误差信息论联系起来。
英文摘要
Perfect prepare-and-measure games exhibit an all-or-nothing quantum advantage: a quantum system of dimension $d$ satisfies every prescribed winning constraint, whereas a classical $d$-level message cannot. We establish three structural results for such forbidden-output support constraints. First, every binary-output support game reduces exactly to a conflict graph: perfect classical realization with a $d$-level message is equivalent to $d$-colorability, perfect $d$-dimensional quantum realization is equivalent to a $d$-dimensional orthogonal representation, and the minimum number of Bob inputs realizing a fixed conflict graph is its edge biclique-cover number. Second, for an arbitrary finite output alphabet, every perfect qubit strategy admits a perfect classical-bit realization. Third, with at most two Bob inputs every perfect qutrit strategy admits a perfect classical-trit realization. An explicit seven-preparation qutrit game with three Bob inputs satisfies $C_3=20<Q_3=S=21$, so three Bob inputs are necessary and sufficient in dimension three. Conversely, a two-input, six-output game in dimension five satisfies $C_5=39<Q_5=S=40$. Thus the smallest dimension admitting a two-input perfect same-dimensional separation is either four or five; the four-dimensional case remains open. As a flagship binary application, the $13$-ray qutrit graph yields a compressed game $(X,Y,B)=(13,8,2)$ with $C_3=39<Q_3=S=40$, and eight Bob inputs are minimal among all binary-output realizations of that graph. Graph extensions demonstrate the mechanism in every dimension, while Torpedo and antidistinguishability games illustrate the genuinely nonbinary regime. These results connect exact communication, graph coloring, contextuality, state exclusion, and zero-error information theory.
