在具有因果独立源的纠缠交换量子网络中排除实数量子理论的方案
Proposals for ruling out the real quantum theories in an entanglement-swapping quantum network with causally independent sources
AI总结：
本研究针对复数在量子理论中的基础性作用争议，在因果独立源的更强假设下，利用修正的Navascués-Pironio-Acín方法和贝叶斯优化，提出了能更有效区分实数量子与复数量子理论的纠缠交换方案，为复杂量子网络中的相关研究开辟了新路径。
摘要：
自量子力学诞生以来，复数是否在量子理论中发挥基础性作用一直备受争议。近期，学界提出了一种基于贝尔非定域性检验技术来区分实数量子理论与复数量子理论的可行方案[Nature 600, 625-629 (2021)]。基于该方法，实数量子理论已在光子量子系统和超导量子系统中被实验证伪[Phys. Rev. Lett. 128, 040402 (2022), Phys. Rev. Lett. 128, 040403 (2022)]。\n包含多个无因果关联的独立源的量子网络为非定域性研究提供了新视角，因而受到广泛关注。这些源的独立性对可观测协方差施加了额外约束，并为经典关联和量子关联带来了新的边界。\n本研究在两个源具有因果独立性这一更强假设下，通过纠缠交换场景检验实数量子理论与复数量子理论的区分性，该假设在以往研究中并未被采用。我们利用修正的Navascués-Pironio-Acín方法和贝叶斯优化，找到了一种具有最优相关函数系数的方案，与现有方案相比，该方案能更大程度地区分实数量子理论与复数量子理论。这项工作为在具有因果独立参与方的复杂量子网络中进一步探索实数量子理论与复数量子理论的区分开辟了新途径。
英文摘要：
The question of whether complex numbers play a fundamental role in quantum theory has been debated since the inception of quantum mechanics. Recently, a feasible proposal to differentiate between real and complex quantum theories based on the technique of testing Bell nonlocalities has emerged [Nature 600, 625-629 (2021)]. Based on this method, the real quantum theory has been falsified experimentally in both photonic and superconducting quantum systems [Phys. Rev. Lett. 128, 040402 (2022), Phys. Rev. Lett. 128, 040403 (2022)]. The quantum networks with multiple independent sources which are not causally connected have gained significant interest as they offer new perspective on studying the nonlocalities. The independence of these sources imposes additional constraints on observable covariances and leads to new bounds for classical and quantum correlations. In this study, we examine the discrimination between the real and complex quantum theories with an entanglement swapping scenario under a stronger assumption that the two sources are causally independent, which wasn't made in previous works. Using a revised Navascués-Pironio-Acín method and Bayesian optimization, we find a proposal with optimal coefficients of the correlation function which could give a larger discrimination between the real and quantum theories comparing with the existing proposals. This work opens up avenues for further exploration of the discrimination between real and complex quantum theories within intricate quantum networks featuring causally independent parties.
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