发表机构
Institute for Theoretical Physics, University of Cologne; Inria, CPHT, LIX, CNRS, École Polytechnique, Institut Polytechnique de Paris（科隆大学理论物理研究所; 法国国家信息与自动化研究所，高等师范学院巴黎校区，法国国家科学研究中心，巴黎综合理工学院，巴黎理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文构造有限数量的两体关联，证明唯一能实现它们并在迭代隐形传态下保持稳定的概率论理论是量子理论，从而实现了有限维量子理论的自检验。
AI 中文摘要
量子力学基础研究的一个关键目标是识别刻画物理理论的操作性约束。贝尔不等式对经典概率论起到了这样的作用，而蔡雷尔森界则为量子力学提供了第一步。在此，我们探讨一个对偶问题：能否证明量子理论所预测的所有关联实际上都是可实现的？在本工作中，我们构造了有限数量的两体关联，使得唯一能够（1）实现这些关联，并且（2）以在迭代隐形传态下保持稳定的方式实现它们的概率论理论，就是量子理论。对于$(\mathbb{C}^d)^{\otimes n}$，条件（1）可以通过$\operatorname{poly}(d,n)$个测量设置来验证。条件（2）可以理解为一系列测试的层级结构，每个测试对应一个隐形传态步骤数$N$。因此，在某种意义上，有限维量子理论可以被自检验。特别是，可以证明存在比任何直接观测到的贝尔不等式违背更大的违背。
英文摘要
A key goal in the foundations of quantum mechanics is to identify operational constraints characterizing physical theories. Bell inequalities do so for classical probability theory, while Tsirelson's bound provides a first step for quantum mechanics. Here, we address the dual question: Can one certify that all correlations predicted by quantum theory are actually realizable? In this work, we construct a finite number of two-body correlations such that the only probabilistic theory that (1) realizes them, and (2) does so in a way that is stable under iterated teleportation, is quantum theory. For $n$ quantum systems of dimension $d$ each, Condition (1) can be verified using $\operatorname{poly}(d,n)$ measurement settings. Condition (2) may be understood as a hierarchy of tests, one for each number $N$ of teleportation steps. There is thus a sense in which finite-dimensional quantum theory can be self-tested. In particular, one can certify the existence of Bell inequality violations larger than any that have been directly observed.
Comments17 pages, 7 figures; v2: Added funding information, cleaned up the introduction and conclusion sections, fixed some typos
