发表机构
S. N. Bose National Centre for Basic Sciences（S.N. 玻色基础科学国家中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出奇偶性忽略隐藏匹配任务，证明量子协议以单量子比特消息实现完美成功，而制备非情境模型无法达到，从而以全有或全无方式体现制备情境性，并给出非情境成功概率的精确与渐近界限。
AI 中文摘要
制备情境性通常通过在信息处理任务中对制备非情境模型的数量优势来操作性体现，然而量子理论往往无法达到完美成功。这里我们引入一个奇偶性忽略的隐藏匹配任务，该任务反而产生制备情境性的全有或全无体现。Alice编码一个n位字符串，使得她的消息除了两位奇偶性外，不泄露任何输入奇偶性的信息。Bob在给定输入位置上的一个完美匹配后，必须输出该匹配的一条边及其两位的奇偶性。使用单个⌈log₂ n⌉量子比特消息的量子协议满足奇偶性忽略约束并以确定性成功。我们证明对于任何偶数n≥6，没有制备非情境模型能达到完美成功。该结果适用于任意本体态空间，且不假设结果决定论或测量非情境性。对于n=6和n=8，最优非情境成功概率分别为4/5和3/4，而渐近地，最优非情境成功概率为1/2+Θ(1/√n)。我们的渐近上界源于通过布尔超立方体上的超压缩性导出的傅里叶分析求和规则。由此产生的分离是定性的而非仅仅是定量的：量子理论达到完美成功，而制备非情境模型则不能。我们还表明，在n=8时，即使Bob仅限于105个可能完美匹配中的4个合适匹配，非情境界限仍保持为3/4，从而使该效应进入实验可及范围。
英文摘要
Preparation contextuality is often manifested operationally through a quantitative advantage over preparation-noncontextual models in information-processing tasks, yet quantum theory typically falls short of perfect success. Here we introduce a parity-oblivious Hidden Matching task that instead yields an all-vs-nothing manifestation of preparation contextuality. Alice encodes an $n$-bit string so that her message reveals no information about any input parity other than the two-bit parities. Bob, given a perfect matching on the input positions, must output an edge of the matching together with the parity of its two bits. A quantum protocol using a single $\lceil\log_2 n\rceil$-qubit message satisfies the parity-obliviousness constraint and succeeds with certainty. We prove that no preparation-noncontextual model achieves perfect success for any even $n\ge6$. The result holds for arbitrary ontic state spaces and assumes neither outcome determinism nor measurement noncontextuality. For $n=6$ and $n=8$, the optimal noncontextual success probabilities are $4/5$ and $3/4$, respectively, while asymptotically the optimal noncontextual success probability is $1/2+Θ(1/\sqrt n)$. Our asymptotic upper bound follows from a Fourier-analytic sum rule derived via hypercontractivity on the Boolean hypercube. The resulting separation is qualitative rather than merely quantitative: quantum theory achieves perfect success, whereas preparation-noncontextual models cannot. We aslo show that at $n=8$ the noncontextual bound remains $3/4$ even when Bob is restricted to just suitable $4$ of the $105$ possible perfect matchings, bringing the effect within experimental reach.
Comments21 pages (two-column) + 4 figures; Comments are welcome
