部分独立性足以排除实量子理论的实验性解释
Partial independence suffices to rule out Real Quantum Theory experimentally
AI总结：
该研究证明部分独立性足以排除实量子理论的实验性解释，并展示了如何通过实量子理论模拟复量子设置。
摘要：
复数量在量子理论中的作用自理论开始以来就让物理学家感到困惑。因此，自然会问是否在描述我们的实验时，所依赖的复希尔伯特空间的数学结构是必不可少的。最近的研究表明，在具有独立源的网络场景中，这种结构是不可避免的。更具体地说，实量子理论无法解释复量子理论的预测[Renou等，Nature 600，2021]。在这里，我们重新审视这项工作的独立性假设。我们证明，假设部分独立性足以显示实量子理论的不足。我们推导出源独立性与实量子理论可实现的贝尔值之间的权衡，这也界定了解释先前实验所需的源相关性下限。我们进一步证明，在[Renou等，Nature 600，2021]的场景中，1比特的纠缠是必要且充分的，通过实量子理论恢复复量子相关性。最后，基于[McKague等，PRL 102，2009]，我们提供了一种构造，通过允许源共享一个m个实旋子纠缠态，在实验的第一轮中用实量子理论模拟任何复量子设置。
英文摘要：
The role of complex quantities in quantum theory has been puzzling physicists since the beginnings. It is thus natural to ask whether, in order to describe our experiments, the mathematical structure of complex Hilbert spaces it is built on is really necessary. Recently, it was shown that this structure is inevitable in network scenarios with independent sources. More precisely, Real Quantum Theory cannot explain the predictions of (Complex) Quantum Theory [Renou et al., Nature 600, 2021]. Here, we revisit the independence assumption underlying this work. We show that assuming partial independence is sufficient for showing the inadequacy of Real Quantum Theory. We derive a tradeoff between source independence and the Bell value achievable in Real Quantum Theory, which also lower bounds the source correlations required to explain previous experiments by means of real quantum systems. We further show that 1 bit of entanglement is necessary and sufficient for recovering the complex quantum correlations by means of Real Quantum Theory in the scenario from [Renou et al., Nature 600, 2021]. Finally, building on [McKague et al., PRL 102, 2009], we provide a construction to simulate any complex quantum setup with m independent sources by means of Real Quantum Theory, by allowing the sources to share a m real-qubit entangled state in the first round of the experiment.
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