Continuous and discrete local hidden variable theories are equivalent
Continuous and discrete local hidden variable theories are equivalent
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DOI：
10.1016/j.ins.2023.119440
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发表时间：
2023-08-14
影响因子：
8.1
通讯作者：
Cao，Huaixin
中科院分区：
文献类型：
--
作者：
Chen，Yanni;Xiao，Shu;Cao，Huaixin
在量子理论中，量子态的贝尔局域性(通常是关联或盒)由积分和给出的局域隐变量模型(LHEM)来表征。我们将这些模型分别称为连续的和离散的两种模型(C-LHEM和D-LHEM)。从理论上讲，这似乎导致了两种类型的局部隐变量理论，分别由C-LHvms和D-LHvms给出。在这篇文章中，我们通过数学证明了相关张量(等价于盒子)有C-LHVM当且仅当它有D-LHVM，从而证明了这两种LHV的等价性。作为应用，我们检验了由积分定义的一些相关张量的Bell局部性。
In quantum theory, Bell locality of quantum states (generally, of correlations, or boxes) is characterized by local hidden variable models (LHVMs) given by integrals and sums. We call these models continuous and discrete LHVMs (C-LHVMs and D-LHVMs), respectively. Theoretically, this seems leading to two types of local hidden variable theories (LHVTs) given by C-LHVMs and D-LHVMs, respectively. In this paper, we show the equivalence of these two types of LHVTs by mathematically proving that a correlation tensor (equivalently, a box) has a C-LHVM if and only if it has a D-LHVM. As application, we check the Bell locality of some correlation tensors that are defined by integrals.