论文标题
使用张量网络和稀疏恢复的贝尔非本地性
Bell non-locality using tensor networks and sparse recovery
论文作者
论文摘要
贝尔的定理指出，量子预测与局部隐藏变量描述不符，是量子理论的基石，也是许多量子信息处理协议的中心。多年来，已经提出了关于非本地性的不同观点，以及检测非本地性和量化的不同方法。不幸的是，尽管它具有相关性，但随着铃铛场景的复杂性的增加，决定给定的观察到的相关性是否是非本地的，在计算上是棘手的。在这里，我们建议将铃铛方案分析为张量网络，这是一个允许测试和量化非局部性的视角，以依靠压缩传感的非常有效的算法，与标准线性编程方法相比，该算法源于压缩传感。此外，它允许证明可以通过由准概率控制的隐藏变量模型来描述非信号相关性。
Bell's theorem, stating that quantum predictions are incompatible with a local hidden variable description, is a cornerstone of quantum theory and at the center of many quantum information processing protocols. Over the years, different perspectives on non-locality have been put forward as well as different ways to to detect non-locality and quantify it. Unfortunately and in spite of its relevance, as the complexity of the Bell scenario increases, deciding whether a given observed correlation is non-local becomes computationally intractable. Here, we propose to analyse a Bell scenario as a tensor network, a perspective permitting to test and quantify non-locality resorting to very efficient algorithms originating from compressed sensing and that offer a significant speedup in comparison with standard linear programming methods. Furthermore, it allows to prove that non-signalling correlations can be described by hidden variable models governed by a quasi-probability.
