量子不和谐、CHSH不等式与隐变量--对隐变量模型的批判性再评价
Quantum Discord, CHSH Inequality and Hidden Variables -- Critical reassessment of hidden-variables models
摘要：
隐藏变量模型被重新评估。首先用$d=2$检验了Hilbert空间中Bell隐变量模型是否经典地描述了量子不和谐。量子不和谐消失的判据与约化的概念有关，令人惊讶的是，迄今为止一直被认为是一致的$d=2$中的隐变量模型实际上是不一致的，并被条件测量和约化的分析所排除。用确定性隐变量模型来描述量子不和谐的全部内容是不可能的。我们还重新研究了CHSH不等式。本文证明了著名的CHSH不等式$|B|\leq 2$对Cirel'son引入的CHSH算子$B$的预言是不唯一的.这种非唯一性是由于Bell和CHSH使用的$d=4$中的非上下文隐藏变量模型中的线性条件失败而产生的，这与Gleason定理一致，该定理排除了$d=4$非上下文隐藏变量模型。如果施加线性条件，则其模型被转换为描述量子力学可分离状态的两个$d=2$模型的因子乘积。因此，CHSH不等式不能检验$d=4$中的隐藏变量模型。这一观察结果与埃克特将CHSH不等式应用于量子密码学是一致的，后者基于混合可分态，而不涉及无色散表示。至于隐变量模型，在任何维度上都不存在可行的局部非上下文模型。
英文摘要：
Hidden-variables models are critically reassessed. It is first examined if the quantum discord is classically described by the hidden-variable model of Bell in the Hilbert space with $d=2$. The criterion of vanishing quantum discord is related to the notion of reduction and, surprisingly, the hidden-variable model in $d=2$, which has been believed to be consistent so far, is in fact inconsistent and excluded by the analysis of conditional measurement and reduction. The description of the full contents of quantum discord by the deterministic hidden-variables models is not possible. We also re-examine CHSH inequality. It is shown that the well-known prediction of CHSH inequality $|B|\leq 2$ for the CHSH operator $B$ introduced by Cirel'son is not unique. This non-uniqueness arises from the failure of linearity condition in the non-contextual hidden-variables model in $d=4$ used by Bell and CHSH, in agreement with Gleason's theorem which excludes $d=4$ non-contextual hidden-variables models. If one imposes the linearity condition, their model is converted to a factored product of two $d=2$ models which describes quantum mechanical separable states. The CHSH inequality thus does not test the hidden-variables model in $d=4$. This observation is consistent with an application of the CHSH inequality to quantum cryptography by Ekert, which is based on mixed separable states without referring to dispersion-free representations. As for hidden-variables models, there exist no viable local non-contextual models in any dimensions.
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