In this paper, we find the minimal number of correlation tests required to certify independence of two classical random variables of arbitrary finite support. Moreover, we completely characterize the constraints implied by zero correlations upon an arbitrary heterogeneous quantum state, and we solve the conjecture proposed by Ohira in 2020. Finally, we find the first ever algorithm for computing (or checking) the Schmidt rank of any unknown pure quantum state using only zero-correlation tests, finding a sufficient amount of tests certifying separability or full entanglement.

中文翻译：

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零相关纠缠与Schmidt秩

在本文中，我们找到了证明任意有限支持的两个经典随机变量的独立性所需的最小相关测试次数。此外，我们完全刻画了任意异质量子态上零相关性所隐含的约束，并解决了Ohira在2020年提出的猜想。最后，我们找到了有史以来第一个用于计算（或检查）任何未知纯Schmidt秩的算法。仅使用零相关测试的量子态，找到足够数量的证明可分离性或完全纠缠的测试。